Linear regression is a subtype of general regression analysis and is widely used for the identification of those independent variables, which relate strongly to the dependent variable (e.g., group membership). After the successful completion of the regression, it can furthermore be applied to predict the group membership of a newly added value.

The achieved PC-scores *X*˜ of each subject are entered as independent variables into the linear regression model *y* = *Xb*˜ + . The vector *y* of the subjects' group memberships, in this case AD and CTR, contains the dependent variables.

It is common to use only a subset of all PCs (determined by significance tests or the amount of variance they represent), but it should be noted that even a PC which captures little variance might still be related to a dependent variable (Jolliffe (1982)).

The regression results in a linear combination of those PCs which achieve the best differentiation of the two classes (e.g., Habeck et al. (2008); Scarmeas et al. (2004)).

If the dependent variables include more information than group membership (e.g., age or existence of genetic risk factors), partial least squares (PLS) regression can be applied (see also Section 4.3.4). This method generalizes PCA and multiple linear regression.

#### **4.3.2 Leave-one-out resampling**

In leave-one-out resampling, one subject is drawn from the underlying data sample per iteration and subsequent analysis is applied. This measures the individual contribution of each subject and can therefore be applied to sort out abnormal interference of particular subjects where necessary.

In Fripp et al. (2008a), *n* − 1 out of *n* images are decomposed by PCA in each iteration. Then, PC-scores of the subjects contained in the sample are plotted pairwise against each other. Those PCs which generally provide the best cluster and separation of the groups within iterations are considered for further analysis.

#### **4.3.3 Outline of canonical variate analysis**

10 Will-be-set-by-IN-TECH

AIC-value is chosen for subsequent analysis. However, it should be noted that the AIC does not recognize if none of the models is suited to represent the population, i.e., the PCs entered

With regards to the early detection of AD, the discriminative power of PCA can be very valuable. Discrimination should be trained on subjects with mild to moderate AD and asymptomatic CTR, and afterwards be tested on MCI cases, thereby assessing the capability

Due to the orthogonality of all eigenvectors, each PC is uncorrelated with all preceding PCs and therefore captures an independent feature of the dataset. As the main variance resides in the first PCs, they depict prominent features of the data (provided that there are no outliers). Hence, the PCs can be employed for the differentiation of groups within the dataset. Those PCs which best discriminate the subjects can either be determined in a linear regression model as presented in Section 4.3.1 (Habeck et al. (2008); Scarmeas et al. (2004)) or as in Section 4.3.2 by a leave-one-out approach (Fripp et al. (2008a)). If necessary, discrimination can be refined further, e.g., by Canonical variate analysis (Section 4.3.3) or Fisher's discriminant analysis

Linear regression is a subtype of general regression analysis and is widely used for the identification of those independent variables, which relate strongly to the dependent variable (e.g., group membership). After the successful completion of the regression, it can

The achieved PC-scores *X*˜ of each subject are entered as independent variables into the linear regression model *y* = *Xb*˜ + . The vector *y* of the subjects' group memberships, in this case

It is common to use only a subset of all PCs (determined by significance tests or the amount of variance they represent), but it should be noted that even a PC which captures little variance

The regression results in a linear combination of those PCs which achieve the best

If the dependent variables include more information than group membership (e.g., age or existence of genetic risk factors), partial least squares (PLS) regression can be applied (see also

In leave-one-out resampling, one subject is drawn from the underlying data sample per iteration and subsequent analysis is applied. This measures the individual contribution of each subject and can therefore be applied to sort out abnormal interference of particular

In Fripp et al. (2008a), *n* − 1 out of *n* images are decomposed by PCA in each iteration. Then, PC-scores of the subjects contained in the sample are plotted pairwise against each other.

furthermore be applied to predict the group membership of a newly added value.

differentiation of the two classes (e.g., Habeck et al. (2008); Scarmeas et al. (2004)).

Section 4.3.4). This method generalizes PCA and multiple linear regression.

into the AIC need to be chosen carefully.

to detect early AD cases among the data collected for the study.

**4.3 Discrimination methods**

(Section 4.3.5).

**4.3.1 Linear regression**

AD and CTR, contains the dependent variables.

**4.3.2 Leave-one-out resampling**

subjects where necessary.

might still be related to a dependent variable (Jolliffe (1982)).

Canonical variate analysis (CVA) is another regression model considered to enhance the discriminative strength of PCA in neuroimaging. Similarly to linear regression, it identifies the best separation of groups depending on PC-scores. The first canonical variable (CV) is the best of all possible linear combinations of PC-scores for differentiation of the groups and – analogous to PCs – the following CVs are computed under the condition to be orthogonal to all precedent CVs.

PCA is applied for dimensionality reduction and removal of noise (i.e., discarded PCs). The within- and between-group sum-of-squares and crossproduct matrices *W* and *B* are computed for the PC-scores of all subjects. Then the CVs, i.e., the eigenvectors of *W*−1*B*, are linear combinations of PC-scores and are sorted by their discriminative power (Borroni et al. (2006); Kerrouche et al. (2006)). CV-scores of all subjects are calculated analogous to PC-scores.

#### **4.3.4 Outline of partial least squares correlation and regression**

As in PCA, the main element of partial least squares (PLS) methods is the SVD, which is applied to the correlation matrix *YXT* (rather than the data matrix *X* containing the mean-centered data, as in PCA). The independent variables are the mean-centered and normalized voxel-values of all brain images stored in *X*, and the *n* vectors of dependent variables for all subjects (also mean-centered and normalized) form the *k* × *n* matrix *Y*. SVD of *YXT* produces *VSUT*, where *S* is a diagonal matrix containing singular values and *U* and *V* column-wise contain the left respectively right singular vectors. Analogous to PCA, it is sufficient to compute only the first few columns of *V*. Then, the high-dimensional data of *X* is reduced by *T* = *XTU* (a.k.a. brain scores), and *Y* is reduced to *YTV* (a.k.a. behavior scores).

It depends on the intention of the study, in which way these results are further analysed and applied. Krishnan et al. (2011) give an elaborate survey of the main PLS methods used in neuroimaging as well as of practical implementations. Generally, they present two basic approaches, i.e., PLS regression and PLS correlation. PLS regression is a generalization of multiple linear regression and PCA (Abdi (2010)), and is used to predict behavior on the basis of neuroimages, in this case PET or SPECT data. PLS correlation focuses on the analysis of the relation between two groups within the dataset and can be subdivided into more specific applications according to the design of the research.

#### **4.3.5 Outline of linear and Fisher's discriminant analysis**

Similar to CVA, linear discriminant analysis (LDA) seeks discriminative directions of the data rather than representative directions (as does PCA). It can be applied both to the original mean-centered voxel-values contained in the data matrix *X* or in a second step after performance of PCA to the PC-scores of all subjects. The latter approach is preferable when dealing with high-dimensional data, as either the inverse of an *m* × *m* scatter matrix has to be computed or a generalized eigenvalue decomposition of *m* × *m* matrices is required.

Fisher's discriminant analysis (FDA) is a special application of LDA, without the constraints of normal distributed groups and equal group covariance. It has lately been applied several

where *n* denotes the number of all subjects, *yi* the column vector of PC-scores of the *i*th subject and *ej* the eigenvalue corresponding to the *j*th PC. An abnormally large value of *ci*,*j* indicates that the removal of the *i*th subject might significantly change the results of PCA (Kerrouche

Principal Component Analysis Applied to SPECT and PET Data of Dementia Patients – A Review 179

In order to compare sets of PCs during resampling iterations, the use of principal angles between PC-subspaces of a fixed dimension is proposed by Markiewicz et al. (2009). If the largest principal angle between an original and resampled subspace is very small, the PCA can be considered to be sufficiently independent of the underlying training set. Otherwise, abnormal large principal angles can indicate that too many PCs (i.e., too much noise) are included in the analysis, or that the sample was not selected carefully enough with respect to

In bootstrap resampling, *n* subjects are drawn with replacement from the original training set (Efron & Tibshirani (1993)). For better replication of the original set, AD and CTR cases are

For every sample, PCA is performed and the subspace spanned by the first *i* PCs is compared to the *i*-dimensional PC-subspace of the original set. This is achieved by calculating the largest principal angle between the two subspaces (Golub & van Van Loan (1996); Knyazev et al. (2002)). For any number of PCs, the mean angle across all iterations is computed. Increased

The same method can be applied with leave-one-out resampling, i.e., one subject of each group

The computation of prinipal angles should be treated with caution, as round-off errors might cause inaccurate estimates for small angles. A solution to this problem is proposed by Knyazev et al. (2002), where a combined sine and cosine based approach is presented and

For analysis of SPECT and PET data, PCA is widely applied and commonly reported to deliver stable and efficient results when used correctly. However, some limitations of PCA outlined in Section 6.1 remain, which might interfere strongly with the outcome of the statistical analyses. In some cases it might even be advisable to apply alternative methods to obtain more reliable results. In Section 6.2, examples are given where the performance of PCA on neuroimaging

As PCA is based solely on the decomposition of the covariance matrix, the underlying data must be dealt with carefully. The preprocessing of the images has a crucial impact on the outcome of the analysis as pointed out by Fripp et al. (2008a), where PCA on 11C PiB PET data proved to be sensitive to inaccuracies originating from non-rigid registration and intensity normalization. On 99*m*Tc-ECD SPECT, the classification accuracy of AD and CTR subjects via PCA and subsequent FDA depends significantly on the data preprocessing method (Merhof

et al. (2006)).

outliers.

generalized.

**6. Discussion**

**5.3 Principal angles of PC-subspaces**

stratified in the bootstrap sample (Markiewicz et al. (2009)).

angles indicate the destabilization of the PCA.

is dropped in every iteration (Markiewicz et al. (2009)).

data was investigated and compared to other approaches.

**6.1 Limitations of the PCA in neuroimaging**

times to diffentiate between subjects with AD and normal controls, e.g., in Markiewicz et al. (2009; 2011a); Merhof et al. (2009; 2011).

The purpose of FDA is to maximize the ratio of the between- and the within-group scatter *SB* and *SW*, thereby projecting the data into a one-dimensional subspace. This is achieved by the projection vector *w*, i.e., the solution of the generalized eigenvalue problem *S*−1 *W SBw* = *λw* (Duda et al. (2001)). Subsequent classification can be computed with very limited effort by a threshold or nearest-neighbor approach.

#### **5. Derivation of robustness of the PCA**

So far, PCA and its applications in neuroimaging were introduced, but not yet validated and discussed. It is very important to assess the robustness of the PCA (and, where necessary, subsequent procedures) before interpretation of the results, as instability and overtraining may occur for various reasons. PCA is sensitive to conspicuous cases and it is therefore recommended to inspect the resulting PCs before further analysis. In order to ensure that no pathologically abnormal cases (outliers) remain in the training set, the T2-Hotelling test is executed, e.g., by Pagani et al. (2009); Zuendorf et al. (2003) (see Section 5.1). Kerrouche et al. (2006) also propose further measurement of the individual contribution of one observation to each PC (see Section 5.2), to assess if the removal of one observation changes the outcome of PCA significantly. Habeck et al. (2010) also observe that if the first PC contains more than 90% of the variance to the data, it is very probable that the dataset *X* includes one or more outliers (see Section 4.1).

By bootstrap resampling of the dataset and subsequent PCA the instability caused by removal of a subset of subjects is measured (Markiewicz et al. (2009; 2011a); Merhof et al. (2011)) via principal angles between PC-subspaces.

#### **5.1 Hotelling's T-square test**

Hotelling's T-square test is an adaption of the Student's T-test to the multivariate case (Hotelling (1931)). As the F-distribution is more prevalent, the T2-distribution is usually transformed to

$$T^2 \sim \frac{p(n-1)}{n-p} F\_{p,n-p\prime} \tag{6}$$

where *n* denotes the number of subjects and *p* the number of PCs retained in the model. Let *yi* denote the column vector of PC-scores of the *i*th subject, then its T2-value is obtained by *T*2 = *yT i yi*. Zuendorf et al. (2003) propose a threshold of *p* < 0.01, and further assess the validity of the T2-test by adding an abnormal case to a set of normal controls in 15 iterations. However, the T2-test can also be applied to a dataset containing two or more groups (Kerrouche et al. (2006); Pagani et al. (2009)).

#### **5.2 Contribution of subjects to PCs**

The amount of the contribution *ci*,*j* of the *i*th subject to the *j*th PC is measured by

$$c\_{i,j} = \frac{1}{n-1} \cdot \frac{y\_i(j)}{e\_j} \,. \tag{7}$$

where *n* denotes the number of all subjects, *yi* the column vector of PC-scores of the *i*th subject and *ej* the eigenvalue corresponding to the *j*th PC. An abnormally large value of *ci*,*j* indicates that the removal of the *i*th subject might significantly change the results of PCA (Kerrouche et al. (2006)).

#### **5.3 Principal angles of PC-subspaces**

12 Will-be-set-by-IN-TECH

times to diffentiate between subjects with AD and normal controls, e.g., in Markiewicz et al.

The purpose of FDA is to maximize the ratio of the between- and the within-group scatter *SB* and *SW*, thereby projecting the data into a one-dimensional subspace. This is achieved by the

(Duda et al. (2001)). Subsequent classification can be computed with very limited effort by a

So far, PCA and its applications in neuroimaging were introduced, but not yet validated and discussed. It is very important to assess the robustness of the PCA (and, where necessary, subsequent procedures) before interpretation of the results, as instability and overtraining may occur for various reasons. PCA is sensitive to conspicuous cases and it is therefore recommended to inspect the resulting PCs before further analysis. In order to ensure that no pathologically abnormal cases (outliers) remain in the training set, the T2-Hotelling test is executed, e.g., by Pagani et al. (2009); Zuendorf et al. (2003) (see Section 5.1). Kerrouche et al. (2006) also propose further measurement of the individual contribution of one observation to each PC (see Section 5.2), to assess if the removal of one observation changes the outcome of PCA significantly. Habeck et al. (2010) also observe that if the first PC contains more than 90% of the variance to the data, it is very probable that the dataset *X* includes one or more outliers

By bootstrap resampling of the dataset and subsequent PCA the instability caused by removal of a subset of subjects is measured (Markiewicz et al. (2009; 2011a); Merhof et al. (2011)) via

Hotelling's T-square test is an adaption of the Student's T-test to the multivariate case (Hotelling (1931)). As the F-distribution is more prevalent, the T2-distribution is usually

where *n* denotes the number of subjects and *p* the number of PCs retained in the model. Let *yi* denote the column vector of PC-scores of the *i*th subject, then its T2-value is obtained

the validity of the T2-test by adding an abnormal case to a set of normal controls in 15 iterations. However, the T2-test can also be applied to a dataset containing two or more groups

*n* − 1 ·

*i yi*. Zuendorf et al. (2003) propose a threshold of *p* < 0.01, and further assess

*yi*(*j*) *ej*

*Fp*,*n*−*p*, (6)

, (7)

*T*2 ∼ *p*(*n* − 1) *n* − *p*

The amount of the contribution *ci*,*j* of the *i*th subject to the *j*th PC is measured by

*ci*,*j* = 1

*W SBw* = *λw*

projection vector *w*, i.e., the solution of the generalized eigenvalue problem *S*−1

(2009; 2011a); Merhof et al. (2009; 2011).

threshold or nearest-neighbor approach.

principal angles between PC-subspaces.

(Kerrouche et al. (2006); Pagani et al. (2009)).

**5.2 Contribution of subjects to PCs**

**5.1 Hotelling's T-square test**

(see Section 4.1).

transformed to

by *T*2 = *yT*

**5. Derivation of robustness of the PCA**

In order to compare sets of PCs during resampling iterations, the use of principal angles between PC-subspaces of a fixed dimension is proposed by Markiewicz et al. (2009). If the largest principal angle between an original and resampled subspace is very small, the PCA can be considered to be sufficiently independent of the underlying training set. Otherwise, abnormal large principal angles can indicate that too many PCs (i.e., too much noise) are included in the analysis, or that the sample was not selected carefully enough with respect to outliers.

In bootstrap resampling, *n* subjects are drawn with replacement from the original training set (Efron & Tibshirani (1993)). For better replication of the original set, AD and CTR cases are stratified in the bootstrap sample (Markiewicz et al. (2009)).

For every sample, PCA is performed and the subspace spanned by the first *i* PCs is compared to the *i*-dimensional PC-subspace of the original set. This is achieved by calculating the largest principal angle between the two subspaces (Golub & van Van Loan (1996); Knyazev et al. (2002)). For any number of PCs, the mean angle across all iterations is computed. Increased angles indicate the destabilization of the PCA.

The same method can be applied with leave-one-out resampling, i.e., one subject of each group is dropped in every iteration (Markiewicz et al. (2009)).

The computation of prinipal angles should be treated with caution, as round-off errors might cause inaccurate estimates for small angles. A solution to this problem is proposed by Knyazev et al. (2002), where a combined sine and cosine based approach is presented and generalized.

#### **6. Discussion**

For analysis of SPECT and PET data, PCA is widely applied and commonly reported to deliver stable and efficient results when used correctly. However, some limitations of PCA outlined in Section 6.1 remain, which might interfere strongly with the outcome of the statistical analyses. In some cases it might even be advisable to apply alternative methods to obtain more reliable results. In Section 6.2, examples are given where the performance of PCA on neuroimaging data was investigated and compared to other approaches.

#### **6.1 Limitations of the PCA in neuroimaging**

As PCA is based solely on the decomposition of the covariance matrix, the underlying data must be dealt with carefully. The preprocessing of the images has a crucial impact on the outcome of the analysis as pointed out by Fripp et al. (2008a), where PCA on 11C PiB PET data proved to be sensitive to inaccuracies originating from non-rigid registration and intensity normalization. On 99*m*Tc-ECD SPECT, the classification accuracy of AD and CTR subjects via PCA and subsequent FDA depends significantly on the data preprocessing method (Merhof

**6.2 Comparison to similar methods**

**6.2.1 Univariate analysis of neuroimaging data**

and even deteriorated accuracy results.

able to recognize these differences.

than the representative directions generated by PCA.

**6.2.2 Partial least squares**

In Section 4, different extensions to PCA such as linear regression or canonical variate analysis are presented, and also an outline of methods with similar properties or intentions as PCA is given. The decision which of these methods is best to employ always depends on the

Principal Component Analysis Applied to SPECT and PET Data of Dementia Patients – A Review 181

Sections 6.2.1 to 6.2.3 provide a review of the most important methods frequently applied to

Univariate analysis measures the voxel-by-voxel correlation between groups (e.g., by a voxel-wise T-test in Habeck et al. (2008)) and thereby merely focuses on the identification of significant shifts between voxel-values. In neuroimaging, univariate methods are commonly used during image preprocessing, e.g., in Dukart et al. (2010) or Scarmeas et al. (2004) for intensity normalization. Voxel-wise analysis can also be used for differentiation between groups, but it is unanimously reported that multivariate approaches outperfom univariate analysis in this matter, especially in the detection of early-onset cases of dementia (Habeck et al. (2008); Scarmeas et al. (2004)). Another drawback of voxel-wise analysis is the sensitivity regarding the preprocessing of the data, and even under the assumption that an optimized normalization factor was applied, the interpretion of the results must be addressed in a multivariate fashion (McCrory & Ford (1991)). In another approach, Higdon et al. (2004) tried to apply a between-group T-test for dimensionality reduction, but this proved to be ineffective

On the other hand, multivariate analysis is found to be more robust as it considers the entire covariance structure of the data (accounting for relations among regions) and withstands the deviation of individual voxel-values (Borroni et al. (2006); Habeck et al. (2008)). It thereby detects correlated alterations in a diseased brain, whereas univariate analysis might not be

When examining very high-dimensional data, and especially for the discrimination into groups within the dataset, PLS has been reported to perform better than PCA regarding the classification accuracy (Higdon et al. (2004); Kemsley (1996)). This is rather self-evident, as PCA does not take into account further behavioral data (e.g., neuropsychological data such as Mini-Mental State Examination (MMSE) scores, age, years of education). If PLS is applied for dimensionality reduction, Kemsley (1996) reports that fewer PLS dimensions than PCs were required for a successful subsequent differentiation of the groups. This implies that PLS will capture the most discriminative attributes of the subjects within the first dimensions, rather

Nevertheless, there are certain drawbacks in the application of PLS methods. PLS tends to overfit the data, so the determination of the number of PLS dimensions kept in the analysis is of decisive importance (Abdi (2010)). In addition, PLS may detect differences which are not characteristic of the examined groups but were produced randomly by noise within the underlying dataset (Kemsley (1996)). Furthermore, PLS only works under the assumption

that behavior relates linearly to neuroimaging data (McIntosh & Lobaugh (2004)).

underlying research question, on the data available and the selected sample.

neuroimaging data and compare them to results obtained from PCA.

et al. (2011)). Classification accuracy relies also on scanner type and reconstruction method of FDG-PET, if the data is aquired from a more heterogeneous dataset, e.g., from the ADNI database as in Markiewicz et al. (2011b).

Not only the preprocessing of the training set but also its composition is essential. This includes the stratification of groups, the sample sizes and the absence of outliers as described in Sections 6.1.1 and 6.1.2. Moreover, the number of PCs retained in the analysis is important and depends on the purpose of the study (see Section 6.1.3).

#### **6.1.1 Sample size**

The selection of subjects suited for training is constrained by many premisses, such as age- and gender-matched CTR cases, stage of AD, the absence of other neurodegenerative disorders and the quality of the scan. It is also preferable for all images to be aquired by the same scanner, as this improves comparability of the data. Therefore, most studies only include less than 30 subjects of each group, except for Markiewicz et al. (2011b) where previous results on a smaller and more homogeneously selected training set were validated on more than 160 AD and CTR cases obtained from the ADNI database. ADNI provides generally accessible data of patients diagnosed with AD or MCI and of normal controls collected from various clinical sites (Mueller et al. (2005)).

An under-sized training set might cause the extraction of instable features (Markiewicz et al. (2009)) resulting in overly optimistic results of subsequent analysis (Markiewicz et al. (2011a)). This might be remedied by bootstrap resampling of the training set but must rely on the assumption that the sample is representative of the population (Markiewicz et al. (2009)).

#### **6.1.2 Sensitivity to outliers**

As the covariance matrix is calculated empirically, the estimates of eigenvectors (PCs) are heavily influenced by outliers, i.e., pathologically abnormal cases within the training dataset. The variance caused by only one outlier may be captured within the first PC, which will thereby not regard the variance within regular cases and dramatically change further results. Approaches which substitute the original covariance matrix by a more robust estimate (e.g., in Debruyne & Hubert (2006)) exist, but these methods are not practical for datasets of high dimensionality. For this reason, it is highly recommended to determine outliers by additional testing when applying PCA to neuroimaging data.

#### **6.1.3 Number of PCs**

Although several approaches are presented in Section 4.2, the determination of how many and which PCs are best suited to represent the original images remains subject to interpretation. So far, much relies on the purpose of PCA and the further analysis of the data. An elaborate overview over criteria for estimating the number of significant PCs and their application is presented in Peres-Neto et al. (2005), and some of these apply to covariance matrices as well as correlation matrices. The application of such methods can be ambivalent, as reviewed by Franklin et al. (1995). In most studies, PCs are chosen according to their potential to explain data and their impact on robustness. It is therefore advisable to determine the number of retained PCs not only based on one criterion but also on the best possible trade-off between the resulting accuracy and robustness.

#### **6.2 Comparison to similar methods**

14 Will-be-set-by-IN-TECH

et al. (2011)). Classification accuracy relies also on scanner type and reconstruction method of FDG-PET, if the data is aquired from a more heterogeneous dataset, e.g., from the ADNI

Not only the preprocessing of the training set but also its composition is essential. This includes the stratification of groups, the sample sizes and the absence of outliers as described in Sections 6.1.1 and 6.1.2. Moreover, the number of PCs retained in the analysis is important

The selection of subjects suited for training is constrained by many premisses, such as age- and gender-matched CTR cases, stage of AD, the absence of other neurodegenerative disorders and the quality of the scan. It is also preferable for all images to be aquired by the same scanner, as this improves comparability of the data. Therefore, most studies only include less than 30 subjects of each group, except for Markiewicz et al. (2011b) where previous results on a smaller and more homogeneously selected training set were validated on more than 160 AD and CTR cases obtained from the ADNI database. ADNI provides generally accessible data of patients diagnosed with AD or MCI and of normal controls collected from various clinical

An under-sized training set might cause the extraction of instable features (Markiewicz et al. (2009)) resulting in overly optimistic results of subsequent analysis (Markiewicz et al. (2011a)). This might be remedied by bootstrap resampling of the training set but must rely on the assumption that the sample is representative of the population (Markiewicz et al. (2009)).

As the covariance matrix is calculated empirically, the estimates of eigenvectors (PCs) are heavily influenced by outliers, i.e., pathologically abnormal cases within the training dataset. The variance caused by only one outlier may be captured within the first PC, which will thereby not regard the variance within regular cases and dramatically change further results. Approaches which substitute the original covariance matrix by a more robust estimate (e.g., in Debruyne & Hubert (2006)) exist, but these methods are not practical for datasets of high dimensionality. For this reason, it is highly recommended to determine outliers by additional

Although several approaches are presented in Section 4.2, the determination of how many and which PCs are best suited to represent the original images remains subject to interpretation. So far, much relies on the purpose of PCA and the further analysis of the data. An elaborate overview over criteria for estimating the number of significant PCs and their application is presented in Peres-Neto et al. (2005), and some of these apply to covariance matrices as well as correlation matrices. The application of such methods can be ambivalent, as reviewed by Franklin et al. (1995). In most studies, PCs are chosen according to their potential to explain data and their impact on robustness. It is therefore advisable to determine the number of retained PCs not only based on one criterion but also on the best possible trade-off between

database as in Markiewicz et al. (2011b).

**6.1.1 Sample size**

sites (Mueller et al. (2005)).

**6.1.2 Sensitivity to outliers**

**6.1.3 Number of PCs**

testing when applying PCA to neuroimaging data.

the resulting accuracy and robustness.

and depends on the purpose of the study (see Section 6.1.3).

In Section 4, different extensions to PCA such as linear regression or canonical variate analysis are presented, and also an outline of methods with similar properties or intentions as PCA is given. The decision which of these methods is best to employ always depends on the underlying research question, on the data available and the selected sample.

Sections 6.2.1 to 6.2.3 provide a review of the most important methods frequently applied to neuroimaging data and compare them to results obtained from PCA.

#### **6.2.1 Univariate analysis of neuroimaging data**

Univariate analysis measures the voxel-by-voxel correlation between groups (e.g., by a voxel-wise T-test in Habeck et al. (2008)) and thereby merely focuses on the identification of significant shifts between voxel-values. In neuroimaging, univariate methods are commonly used during image preprocessing, e.g., in Dukart et al. (2010) or Scarmeas et al. (2004) for intensity normalization. Voxel-wise analysis can also be used for differentiation between groups, but it is unanimously reported that multivariate approaches outperfom univariate analysis in this matter, especially in the detection of early-onset cases of dementia (Habeck et al. (2008); Scarmeas et al. (2004)). Another drawback of voxel-wise analysis is the sensitivity regarding the preprocessing of the data, and even under the assumption that an optimized normalization factor was applied, the interpretion of the results must be addressed in a multivariate fashion (McCrory & Ford (1991)). In another approach, Higdon et al. (2004) tried to apply a between-group T-test for dimensionality reduction, but this proved to be ineffective and even deteriorated accuracy results.

On the other hand, multivariate analysis is found to be more robust as it considers the entire covariance structure of the data (accounting for relations among regions) and withstands the deviation of individual voxel-values (Borroni et al. (2006); Habeck et al. (2008)). It thereby detects correlated alterations in a diseased brain, whereas univariate analysis might not be able to recognize these differences.

#### **6.2.2 Partial least squares**

When examining very high-dimensional data, and especially for the discrimination into groups within the dataset, PLS has been reported to perform better than PCA regarding the classification accuracy (Higdon et al. (2004); Kemsley (1996)). This is rather self-evident, as PCA does not take into account further behavioral data (e.g., neuropsychological data such as Mini-Mental State Examination (MMSE) scores, age, years of education). If PLS is applied for dimensionality reduction, Kemsley (1996) reports that fewer PLS dimensions than PCs were required for a successful subsequent differentiation of the groups. This implies that PLS will capture the most discriminative attributes of the subjects within the first dimensions, rather than the representative directions generated by PCA.

Nevertheless, there are certain drawbacks in the application of PLS methods. PLS tends to overfit the data, so the determination of the number of PLS dimensions kept in the analysis is of decisive importance (Abdi (2010)). In addition, PLS may detect differences which are not characteristic of the examined groups but were produced randomly by noise within the underlying dataset (Kemsley (1996)). Furthermore, PLS only works under the assumption that behavior relates linearly to neuroimaging data (McIntosh & Lobaugh (2004)).

Burnham, K. P. & Anderson, D. R. (2002 2nd edn). *Model Selection and Multi-Model Inference. A*

Principal Component Analysis Applied to SPECT and PET Data of Dementia Patients – A Review 183

Caroli, A., Testa, C., Geroldi, C., Nobili, F., Barnden, L., Guerra, U., Bonetti, M. & Frisoni,

amnestic mild cognitive impairment, *Journal of Neurology* 254: 1698–1707. Carr, D., Goate, A., Phil, D. & Morris, J. (1997). Current Concepts in the Pathogenesis of

Debruyne, M. & Hubert, M. (2006). The Influence Function of Stahel-Donoho Type Methods

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impairment and healthy aging, *NeuroImage* 43(3): 430 – 439.

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10S.

Overall, if allowances are made for these effects and significant behavioral data is available, PLS can still be a favourable alternative to PCA.

#### **6.2.3 Linear discriminant analysis**

As explained above, performance of PCA (or any other dimensionality reduction method) prior to LDA is preferable in neuroimaging due to the high dimensionality of the data and the resulting expensive computation. To our knowlegde, LDA as described above in Section 4.3.5 has not yet been applied to discriminate AD from CTR using voxel-values of PET or SPECT images of the whole-brain region, although McEvoy et al. (2009) utilize a stepwise approach of LDA to identify brain regions significant for differentiation.

In other areas also dealing with high-dimensional data, such as object recognition in images, LDA is usually considered to perform superior to PCA. But this is not necessarily the case for small training sets, as pointed out by Martínez & Kak (2001). In the same study they also observe PCA to be less biased than LDA, i.e., less constrained to the training set.

The overall good results regarding accuracy and robustness of the PCA-LDA or PCA-FDA approach (e.g., as presented in Markiewicz et al. (2009)) also indicate, that a preceding PCA does not impair the discriminant analysis.

#### **7. Conclusion**

PCA applied to SPECT or PET data is well suited to reduce the high dimensionality of the original dataset containing voxel-values of the whole-brain region. It achieves best results when data is transformed into a subspace spanned by a well-chosen subset of PCs that represents the variability within all datasets and at the same time reduces noise and redundant information. PCA can also be used successfully to train discrimination between AD and a set of asymptomatic CTRs with the intention to enable an early detection of AD, or to provide a stable and effective basis for the subsequent application of discriminant analysis.

#### **8. References**

16 Will-be-set-by-IN-TECH

Overall, if allowances are made for these effects and significant behavioral data is available,

As explained above, performance of PCA (or any other dimensionality reduction method) prior to LDA is preferable in neuroimaging due to the high dimensionality of the data and the resulting expensive computation. To our knowlegde, LDA as described above in Section 4.3.5 has not yet been applied to discriminate AD from CTR using voxel-values of PET or SPECT images of the whole-brain region, although McEvoy et al. (2009) utilize a stepwise approach

In other areas also dealing with high-dimensional data, such as object recognition in images, LDA is usually considered to perform superior to PCA. But this is not necessarily the case for small training sets, as pointed out by Martínez & Kak (2001). In the same study they also

The overall good results regarding accuracy and robustness of the PCA-LDA or PCA-FDA approach (e.g., as presented in Markiewicz et al. (2009)) also indicate, that a preceding PCA

PCA applied to SPECT or PET data is well suited to reduce the high dimensionality of the original dataset containing voxel-values of the whole-brain region. It achieves best results when data is transformed into a subspace spanned by a well-chosen subset of PCs that represents the variability within all datasets and at the same time reduces noise and redundant information. PCA can also be used successfully to train discrimination between AD and a set of asymptomatic CTRs with the intention to enable an early detection of AD, or to provide a

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**11**

*Malaysia*

**Public Parks Aesthetic Value Index**

Aesthetics is a branch of philosophy dealing with the nature of beauty, art, and taste with the creation and appreciation of beauty. It is more scientifically defined as the study of sensory or sensory-emotional values. Broadly, scholars in the field define aesthetics as

Traditionally, aesthetics is specific to the philosophy of art on level of beauty of any object but later, it was expanded to include the sublime with careful analyses on the characteristics. Studies on the aesthetics level experience and its attitude being conducted had lead to a

According to Kant (1964), the theory of beauty has four clear aspects which are freedom from concepts, objectivity in the judgment, the disinterest of the viewer, and evenness in obligation. Freedom from concepts refers the cognitive powers of human understanding and imagination judge in identifying an object, such as stone. In this situation, the replacement of a certain individual object by a group of object would bring the experience of pure beauty when the cognitive powers are held to be in harmonious. Consequently, this results the second aspect that is the objectivity in the judgment since the cognitive powers are common to all who can classify that group of object. However, this was not the basis on which the apprehension of pure beauty was obligatory. According to Kant (1964), it derived from its disinterest because pure beauty not necessarily brings the fully agreement of the visitor to its aesthetic level nor does it raise any desire to possess the object but it just make

Aesthetics value can be defined as theory of the level of beauty of a certain natural resources (Slater, 2006). This term appear when there was some interest among researchers to assess the level of aesthetic quantitatively instead of just qualitatively. It is about the objectivity and universality of judgments of pure beauty. It can also be defined as the individual

The main debate over aesthetic value concerns on social and political matters, in many different points of view. The central question concerns whether there are existing aesthetics

survey of the scope of aesthetics together with an account of redefinition of the term.

**1. Introduction 1.1 Aesthetic**

critical reflection on art, culture and nature.

satisfaction in a distinctive intellectual way.

**1.1.1 Aesthetic value**

judgment of the quality of beauty.

M. K. Mohamad Roslan and M. I. Nurashikin

*Universiti Putra Malaysia*

Covariance PET patterns in early Alzheimer's disease and subjects with cognitive impairment but no dementia: utility in group discrimination and correlations with functional performance, *NeuroImage* 23(1): 35 – 45.

## **Public Parks Aesthetic Value Index**

M. K. Mohamad Roslan and M. I. Nurashikin

*Universiti Putra Malaysia Malaysia*

#### **1. Introduction**

#### **1.1 Aesthetic**

20 Will-be-set-by-IN-TECH

186 Principal Component Analysis – Multidisciplinary Applications

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Van Huffel, S. (1997). *Recent Advances in Total Least Squares Techniques and Errors-in-Variables*

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functional performance, *NeuroImage* 23(1): 35 – 45.

Impairment, *Arch Gen Psychiatry* 63(8): 916–924.

PLS-analysis, *Journal of Chemometrics* 1(1): 41–56.

*Modeling*, SIAM, Philadelphia, PA.

81(2): 741–766.

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Goodkind, M., Bell, K., Stern, Y. & Devanand, D. P. (2006). Neuropsychological Prediction of Conversion to Alzheimer Disease in Patients With Mild Cognitive

analysis for multivariate 3D voxel-based mapping of brain functional imaging data sets as applied to FDG-PET and normal aging, *Human Brain Mapping* 18(1): 13–21.

Aesthetics is a branch of philosophy dealing with the nature of beauty, art, and taste with the creation and appreciation of beauty. It is more scientifically defined as the study of sensory or sensory-emotional values. Broadly, scholars in the field define aesthetics as critical reflection on art, culture and nature.

Traditionally, aesthetics is specific to the philosophy of art on level of beauty of any object but later, it was expanded to include the sublime with careful analyses on the characteristics. Studies on the aesthetics level experience and its attitude being conducted had lead to a survey of the scope of aesthetics together with an account of redefinition of the term.

According to Kant (1964), the theory of beauty has four clear aspects which are freedom from concepts, objectivity in the judgment, the disinterest of the viewer, and evenness in obligation. Freedom from concepts refers the cognitive powers of human understanding and imagination judge in identifying an object, such as stone. In this situation, the replacement of a certain individual object by a group of object would bring the experience of pure beauty when the cognitive powers are held to be in harmonious. Consequently, this results the second aspect that is the objectivity in the judgment since the cognitive powers are common to all who can classify that group of object. However, this was not the basis on which the apprehension of pure beauty was obligatory. According to Kant (1964), it derived from its disinterest because pure beauty not necessarily brings the fully agreement of the visitor to its aesthetic level nor does it raise any desire to possess the object but it just make satisfaction in a distinctive intellectual way.

#### **1.1.1 Aesthetic value**

Aesthetics value can be defined as theory of the level of beauty of a certain natural resources (Slater, 2006). This term appear when there was some interest among researchers to assess the level of aesthetic quantitatively instead of just qualitatively. It is about the objectivity and universality of judgments of pure beauty. It can also be defined as the individual judgment of the quality of beauty.

The main debate over aesthetic value concerns on social and political matters, in many different points of view. The central question concerns whether there are existing aesthetics

Public Parks Aesthetic Value Index 189

reflective contemplation. In short, judgments of aesthetic involved sensory, emotional and

There are some factors that could contribute in viewer view or perception on aesthetic value level. Negative reaction such as disgust shows that sensory detection is linked to body language, facial expressions, and behaviors (Slote, 1971). Aesthetic judgments also linked to emotions that partially embodied in physical reactions. For example, watching a well-design landscape parks may give the viewer a reaction of awe and consequently, physical reactions. In the other hand, aesthetic judgments may be affected by culture or norm of the community. Other factors that could affect the judgments are desirability, economic,

Aesthetic judgments can be highly parallel or highly contradict between viewers (Mothersill, 2004). In the other hand, aesthetic judgments were partly intellectual and interpretative. Therefore aesthetic judgments were usually based on the senses, emotions, intellectual opinions, will, desires, culture, preferences, values, subconscious behavior,

Index is a numerical standardized value of evaluation of a variable that is in composite form, meaning that this variable was formed through the integration or combination of several other variables.. The evaluation process of this composite variable is not an easy process since there is no standard value used as a base of comparison of the evaluation. Therefore the indices are the best way to be introduced to determine that particular

A Public Parks Aesthetic Value Index, proposed in this paper is a measurement that aggregates numerous aesthetic value indicators into one consolidates and objective value representing the status of aesthetic value in public parks in relation to some specific use. The mode of assessment was carried out with a full consideration on certain criteria as suggested

Public parks is a bounded area of land, either in the form of natural or man-made state, dedicated to recreation use and generally characterized by its natural historic or landscape features. It is used for both passive and active forms of recreation and may be designated to serve the residents of a neighbourhood, community, region or province. This area is maintained by a local or private authority for recreation which can stimulate the morale and transform the cities to become more attractive and entertaining to visitors (Cranz, 1982).

Parks commonly resembles a certain formation of landscaping which any individuals who visit it would find more relaxing and feeling enjoyment of any recreation activities, for example picnics and sporting activities. Many smaller neighbourhood parks are receiving increased attention and valuation as significant community assets and places in heavily

conscious decision, training, instinct, sociological institutions, or combinations.

intellectual all at once.

political, or moral value.

**1.2 Index**

standard value.

by Haslina (2006).

**1.3 Public parks**

populated urban areas.

**1.1.4 Factors of aesthetic value judgment**

expertises that have aesthetic interests and whether their view represents a fair view since, from a sociological perspective, it only just a portion of the whole population.

#### **1.1.2 Environmental aesthetics**

This paper would explain on public parks which are related to environment. In this case, according to Fisher (2003), environmental aesthetics applies naturally in the study of the aesthetics of nature conducted under the influence of environmental aspects concerns. The rapid growth of concern for the natural environment over the last third of the 20th century has brought the welcome reintroduction of nature as a significant topic in aesthetics such as the aesthetic interactions with nature, the aesthetic value of nature, and the status of art about nature. Nature began to be seen as comprising landscapes compelling in their own wild beauty and objects valuable in their smallest natural detail.

Environmental aesthetics consists of two terms which are environmental roots that emphasize on the aesthetics of nature, and aesthetic appreciation that focusing on the notion of environments of all sorts as objects of appreciation (Fisher, 2003). Based on these, nature is regarded not as an object to be exploited, but as something with an autonomous and worthy existence in itself. A thing is right when it tends to preserve the integrity, stability, and beauty of the biotic community but is wrong if otherwise.

According to Berleant (1998), environmental aesthetics applies to the researches on the aesthetics of nature of all sorts of environments either human made or natural conducted under the influence of environmental concerns. This environmental aesthetics also incorporates city planning, landscape architecture and environmental design, and it is significant because, whether applied to nature or built environments because it directly associating the modern structure or design to the standard theories in aesthetics. In short, Thompson (1995) found that although the authorities have an obligation to preserve beautiful high aesthetic value parks, they also have an obligation to preserve aesthetically valuable nature areas.

#### **1.1.3 Aesthetic value judgment**

Judgments of aesthetic value rely on our ability to discriminate at a sensory level. Aesthetics examines our affective domain response to an object or phenomenon. According to Slote (1971), a personal view on the level of aesthetic cannot represent the view of the community because each individual in the community also have their own view unless all of them have the same perception.

Since beauty is not a tangible object, judgment of aesthetic value is subjective to any individual perception. For example, it can be related to desirability or expectation on certain aspects of the nature. This assessment would also be based on many other kinds of issues such as senses, emotions, intellectual opinions, culture, preferences, values and behavior (Slater, 2006).

Aesthetic judgment is not only focusing on sensory discrimination but also linked to capacity for pleasure (Kant, 1964). The sensory discrimination that raising the pleasure would results the enjoyment. However, in order to judge something as having high aesthetic value, it needs a third requirement, that is it must involve the viewer's capacities of

expertises that have aesthetic interests and whether their view represents a fair view since,

This paper would explain on public parks which are related to environment. In this case, according to Fisher (2003), environmental aesthetics applies naturally in the study of the aesthetics of nature conducted under the influence of environmental aspects concerns. The rapid growth of concern for the natural environment over the last third of the 20th century has brought the welcome reintroduction of nature as a significant topic in aesthetics such as the aesthetic interactions with nature, the aesthetic value of nature, and the status of art about nature. Nature began to be seen as comprising landscapes compelling in their own

Environmental aesthetics consists of two terms which are environmental roots that emphasize on the aesthetics of nature, and aesthetic appreciation that focusing on the notion of environments of all sorts as objects of appreciation (Fisher, 2003). Based on these, nature is regarded not as an object to be exploited, but as something with an autonomous and worthy existence in itself. A thing is right when it tends to preserve the integrity, stability,

According to Berleant (1998), environmental aesthetics applies to the researches on the aesthetics of nature of all sorts of environments either human made or natural conducted under the influence of environmental concerns. This environmental aesthetics also incorporates city planning, landscape architecture and environmental design, and it is significant because, whether applied to nature or built environments because it directly associating the modern structure or design to the standard theories in aesthetics. In short, Thompson (1995) found that although the authorities have an obligation to preserve beautiful high aesthetic value parks, they also have an obligation to preserve aesthetically

Judgments of aesthetic value rely on our ability to discriminate at a sensory level. Aesthetics examines our affective domain response to an object or phenomenon. According to Slote (1971), a personal view on the level of aesthetic cannot represent the view of the community because each individual in the community also have their own view unless all of them have

Since beauty is not a tangible object, judgment of aesthetic value is subjective to any individual perception. For example, it can be related to desirability or expectation on certain aspects of the nature. This assessment would also be based on many other kinds of issues such as senses, emotions, intellectual opinions, culture, preferences, values and behavior

Aesthetic judgment is not only focusing on sensory discrimination but also linked to capacity for pleasure (Kant, 1964). The sensory discrimination that raising the pleasure would results the enjoyment. However, in order to judge something as having high aesthetic value, it needs a third requirement, that is it must involve the viewer's capacities of

from a sociological perspective, it only just a portion of the whole population.

wild beauty and objects valuable in their smallest natural detail.

and beauty of the biotic community but is wrong if otherwise.

**1.1.2 Environmental aesthetics**

valuable nature areas.

the same perception.

(Slater, 2006).

**1.1.3 Aesthetic value judgment**

reflective contemplation. In short, judgments of aesthetic involved sensory, emotional and intellectual all at once.

#### **1.1.4 Factors of aesthetic value judgment**

There are some factors that could contribute in viewer view or perception on aesthetic value level. Negative reaction such as disgust shows that sensory detection is linked to body language, facial expressions, and behaviors (Slote, 1971). Aesthetic judgments also linked to emotions that partially embodied in physical reactions. For example, watching a well-design landscape parks may give the viewer a reaction of awe and consequently, physical reactions.

In the other hand, aesthetic judgments may be affected by culture or norm of the community. Other factors that could affect the judgments are desirability, economic, political, or moral value.

Aesthetic judgments can be highly parallel or highly contradict between viewers (Mothersill, 2004). In the other hand, aesthetic judgments were partly intellectual and interpretative. Therefore aesthetic judgments were usually based on the senses, emotions, intellectual opinions, will, desires, culture, preferences, values, subconscious behavior, conscious decision, training, instinct, sociological institutions, or combinations.

#### **1.2 Index**

Index is a numerical standardized value of evaluation of a variable that is in composite form, meaning that this variable was formed through the integration or combination of several other variables.. The evaluation process of this composite variable is not an easy process since there is no standard value used as a base of comparison of the evaluation. Therefore the indices are the best way to be introduced to determine that particular standard value.

A Public Parks Aesthetic Value Index, proposed in this paper is a measurement that aggregates numerous aesthetic value indicators into one consolidates and objective value representing the status of aesthetic value in public parks in relation to some specific use. The mode of assessment was carried out with a full consideration on certain criteria as suggested by Haslina (2006).

#### **1.3 Public parks**

Public parks is a bounded area of land, either in the form of natural or man-made state, dedicated to recreation use and generally characterized by its natural historic or landscape features. It is used for both passive and active forms of recreation and may be designated to serve the residents of a neighbourhood, community, region or province. This area is maintained by a local or private authority for recreation which can stimulate the morale and transform the cities to become more attractive and entertaining to visitors (Cranz, 1982).

Parks commonly resembles a certain formation of landscaping which any individuals who visit it would find more relaxing and feeling enjoyment of any recreation activities, for example picnics and sporting activities. Many smaller neighbourhood parks are receiving increased attention and valuation as significant community assets and places in heavily populated urban areas.

Public Parks Aesthetic Value Index 191

The function of flowers in public parks is well-documented. The evolving, flourishing process of civilization has increased the usage of flower in the form of civility, art and religion. For example, the Japanese people regarded flowers as materials for spiritual

Besides location, the appropriate design for the intended function of the building is one of the important elements of value The style and functional utility of a building are necessarily interrelated to create a success. In the valuation process, the aspects that are critical are functionality of the layout, design attractiveness, the appropriateness of the material and its

According to Janick (2010), there are four main design elements which become the visible

a. Colour – Refer to visual sensation produced by different light wavelength that may be

d. Line – Refer to one dimensional interpretation of form that delimits the shape and

Non-existence of this public parks aesthetic value index in Malaysia brings the issue of the uncertainty whether the existing public parks are functioning well in giving relaxation, enjoyment and pleasuring to the community and visitors. This study aims to introduce an index to assess the level of aesthetics value of public parks and applied it to assess the

This research had been conducted in Shah Alam Lake Garden, Selangor, Malaysia which is one of the popular recreational public parks among domestic tourists in Selangor (Fig. 1). This garden, consists of three man-made lakes is located in the city centre and provides the community and visitors with water-sports besides some basic leisure activities. This urban public parks, managed by government has a beautiful, green and unique landscape with the

Due to the assessment of aesthetics value is subjective to individual's perception as mention earlier, the first stage of this research is a qualitative study with questionnaire as a tool of

**<IP_ADDRESS> Flower**

**<IP_ADDRESS> Building**

structure

**1.5 Aim of study**

**2. Methodology 2.1 Study area**

**2.2 Data collection**

data collection.

expressions (Haslina, 2006).

quality and workmanship applied.

**1.4 Elements of design aesthetic value**

features of all objects. They are as follows.

described in term of its hue, intensity and chroma. b. Texture – Refer to the visual effect of tactile surface qualities.

aesthetic value level of a certain public parks in Malaysia.

presence of many different bird species.

c. Form – Refer to the shape and structure of a three dimensional object

Traditionally, public parks are classified by their horticulture design, recreational value and public friendliness. It often provide leisure and sports areas for children and teenagers. It may also equip with semi natural or man-made habitats such as woodlands, heaths and wetlands. The formal garden designs and high composition of flora species characterized the horticultural history of public parks.

Rapid population growth rate and prolonged economic expansion consequently results a high degree of urbanization which could led to serious degradation of living environment and public amenities including air and water pollution, expanding temperature diffusion and decrement of public open space areas.

In order to have the functioning public parks in giving relaxation, enjoyment and pleasuring to the community, besides a good management and proper location, public parks should have a good aesthetic value. Aesthetic value for public parks can be defined as the level of beauties of natural beauty of public parks. However, the assessment of aesthetic value cannot be done in a straight forward approach because as mention earlier, this term is subjective to qualitative variables which are in composite form that means it consists of several aspects that need to combine together. Therefore the index of aesthetics value needs to be applied and measure to assess the aesthetic value of the parks. Index is a numerical standardized value of the composite form.

#### **1.3.1 Characteristics of aesthetic values in public parks**

Aesthetic values in Public Parks are normally characterized with five scopes; tree, fauna, lake, flower and building (Haslina, 2006).

#### **<IP_ADDRESS> Tree**

The basic value of the tree in public parks could be based on emotion, aesthetic or strictly utilitarian. However, visitors seldom perceive the value as strictly aesthetic or monetary gain. In some areas, public used to spend on tree care and management which reflects the approximate value of trees. Trees may be selected to be planted in the public parks based on texture, fragrance, size, shape and colour. The replanting of best and cost effective tree species could create beauty environment and pull the visitors to come.

#### **<IP_ADDRESS> Fauna**

Fauna is one of the aesthetic aspects in public parks. The existing of fauna species such as birds and fish would make the parks more harmonious, relaxing and enjoyable. Fauna species could revitalized flora survival needs and hence support each other. In the other hand, the abundance of greens in public parks could cause a significant increment in wildlife population.

#### **<IP_ADDRESS> Lake**

Public parks, especially in urban areas are normally provides the visitors with lake as a choice for recreation. The physical attractiveness of a particular area contributes to its aesthetic value. The well-managed lake would provide the visitors not only the natural visual element but also a serene sound and smell. These aesthetic characteristics of the lake make up the reason that visitors might find lake as beautiful and attractive.

#### **<IP_ADDRESS> Flower**

190 Principal Component Analysis – Multidisciplinary Applications

Traditionally, public parks are classified by their horticulture design, recreational value and public friendliness. It often provide leisure and sports areas for children and teenagers. It may also equip with semi natural or man-made habitats such as woodlands, heaths and wetlands. The formal garden designs and high composition of flora species characterized

Rapid population growth rate and prolonged economic expansion consequently results a high degree of urbanization which could led to serious degradation of living environment and public amenities including air and water pollution, expanding temperature diffusion

In order to have the functioning public parks in giving relaxation, enjoyment and pleasuring to the community, besides a good management and proper location, public parks should have a good aesthetic value. Aesthetic value for public parks can be defined as the level of beauties of natural beauty of public parks. However, the assessment of aesthetic value cannot be done in a straight forward approach because as mention earlier, this term is subjective to qualitative variables which are in composite form that means it consists of several aspects that need to combine together. Therefore the index of aesthetics value needs to be applied and measure to assess the aesthetic value of the parks. Index is a numerical

Aesthetic values in Public Parks are normally characterized with five scopes; tree, fauna,

The basic value of the tree in public parks could be based on emotion, aesthetic or strictly utilitarian. However, visitors seldom perceive the value as strictly aesthetic or monetary gain. In some areas, public used to spend on tree care and management which reflects the approximate value of trees. Trees may be selected to be planted in the public parks based on texture, fragrance, size, shape and colour. The replanting of best and cost effective tree

Fauna is one of the aesthetic aspects in public parks. The existing of fauna species such as birds and fish would make the parks more harmonious, relaxing and enjoyable. Fauna species could revitalized flora survival needs and hence support each other. In the other hand, the abundance of greens in public parks could cause a significant increment in

Public parks, especially in urban areas are normally provides the visitors with lake as a choice for recreation. The physical attractiveness of a particular area contributes to its aesthetic value. The well-managed lake would provide the visitors not only the natural visual element but also a serene sound and smell. These aesthetic characteristics of the lake

the horticultural history of public parks.

and decrement of public open space areas.

standardized value of the composite form.

lake, flower and building (Haslina, 2006).

**<IP_ADDRESS> Tree**

**<IP_ADDRESS> Fauna**

**<IP_ADDRESS> Lake**

wildlife population.

**1.3.1 Characteristics of aesthetic values in public parks**

species could create beauty environment and pull the visitors to come.

make up the reason that visitors might find lake as beautiful and attractive.

The function of flowers in public parks is well-documented. The evolving, flourishing process of civilization has increased the usage of flower in the form of civility, art and religion. For example, the Japanese people regarded flowers as materials for spiritual expressions (Haslina, 2006).

#### **<IP_ADDRESS> Building**

Besides location, the appropriate design for the intended function of the building is one of the important elements of value The style and functional utility of a building are necessarily interrelated to create a success. In the valuation process, the aspects that are critical are functionality of the layout, design attractiveness, the appropriateness of the material and its quality and workmanship applied.

#### **1.4 Elements of design aesthetic value**

According to Janick (2010), there are four main design elements which become the visible features of all objects. They are as follows.

#### **1.5 Aim of study**

Non-existence of this public parks aesthetic value index in Malaysia brings the issue of the uncertainty whether the existing public parks are functioning well in giving relaxation, enjoyment and pleasuring to the community and visitors. This study aims to introduce an index to assess the level of aesthetics value of public parks and applied it to assess the aesthetic value level of a certain public parks in Malaysia.

#### **2. Methodology**

#### **2.1 Study area**

This research had been conducted in Shah Alam Lake Garden, Selangor, Malaysia which is one of the popular recreational public parks among domestic tourists in Selangor (Fig. 1). This garden, consists of three man-made lakes is located in the city centre and provides the community and visitors with water-sports besides some basic leisure activities. This urban public parks, managed by government has a beautiful, green and unique landscape with the presence of many different bird species.

#### **2.2 Data collection**

Due to the assessment of aesthetics value is subjective to individual's perception as mention earlier, the first stage of this research is a qualitative study with questionnaire as a tool of data collection.

Public Parks Aesthetic Value Index 193

After the final round of discussion with experts, this section focused on type of species,

After the final round of discussion with experts, this section focused on design, level of cleanliness, material quality, number of buildings, suitability of the location and its

Sampling was conducted using convenience sampling techniques. In convenience sampling, the sample selection is based on availability and accessibility. This technique is quite suitable in this study due to the high mobility of visitors and also unknown activities

After calculations of sample size based on the population size obtained, it was found that as many as 407 respondents need to be taken as a sample size from the whole population. Although convenience sampling technique was applied, the sample of respondents was still taken from the whole area of the lake to ensure that the results would represent the whole visitors of the lake from all areas. Although the likelihood of the sample being unrepresentative of the visitor population would be quite high, the information could still provide a fairly significant insight and become a good source of data in

Second stage of this research involved quantitative study where all the qualitative data being analyzed and quantify to give a certain value to indicate the aesthetic level. Descriptive analysis was first used to determine the importance of each aspect in determining the aesthetic level. Table 1 shows the results of the analysis. It was found that the most important aspect for the respondents to visit the parks was tree with mean value of 2.00 followed by lake, flower and fauna with mean value of 2.34, 3.06 and 3.33 respectively. The aspect of buildings was considered as not important to be including in the assessment with the mean of 4.25. From the observations and feedbacks from visitors, the buildings in the parks doesn't have any uniqueness that can be consider as important enough to attract them to visit. Therefore, the aspect of building would not be analyzed in

> Aspects Mean Median Tree 2.00 2.00 Fauna 3.33 3.00 Lake 2.34 2.00 Buildings 4.25 5.00 Flowers 3.06 3.00

shape, form, colour, sound, aroma, site selection, design, quantities and its function.

d. Aesthetic value of Flower

e. Aesthetic value of Buildings

**2.3 Sampling technique**

functionality.

among visitors.

exploratory research.

**2.4 Data analysis**

the second stage.

Table 1. Descriptive analysis of the aspects in study

Fig. 1. The map of Shah Alam Lake Garden

The field survey was conducted on weekdays, weekend and public holidays. The respondents involved those who were present at the lakes at the time when questionnaires were given. Besides that, the respondent age of above 16 years old was also been point out in order to ensure that the respondents could give the grading to the aspects fairly. The questionnaires were designed based on the information obtain through discussions with experts. The questions provided in the questionnaires were straight forward and highly focusing on the aim that was to assess the respondent perception on the aesthetic level of the parks.

This questionnaire has two parts, Part 1 and Part 2. Part 1 involved the ranking of importance of five aspects in study while Part 2 involved the ranking of aesthetic value of each aspects attribute. Likert scale was used as aesthetic value grading scale for each subaspect from 1 to 10 where 10 means very high value. Moreover, Likert scale was also used as importance scale for each aspect from 1 to 5 where 5 means not important at all. Five aspects in study were as follows.

a. Aesthetic value of Tree

After the final round of discussion with experts, this section focused on the form, colour, shape, scent, sound, appearance, function, site selection, and quantities and diversity of species that could influencing the visitors to visit the park.

b. Aesthetic value of Animal or Fauna

After the final round of discussion with experts, this section focused on the quantities and diversity of species, sound, disturbance, smell, colour, shape, habitat and its function in the parks.

c. Aesthetic value of Lake

After the final round of discussion with experts, this section focused on water quality in term of presence of fish, colour, lake design, sound, disturbance, odor, site selection and its function to visitors.

The field survey was conducted on weekdays, weekend and public holidays. The respondents involved those who were present at the lakes at the time when questionnaires were given. Besides that, the respondent age of above 16 years old was also been point out in order to ensure that the respondents could give the grading to the aspects fairly. The questionnaires were designed based on the information obtain through discussions with experts. The questions provided in the questionnaires were straight forward and highly focusing on the aim that was to assess the respondent perception on the aesthetic level of

This questionnaire has two parts, Part 1 and Part 2. Part 1 involved the ranking of importance of five aspects in study while Part 2 involved the ranking of aesthetic value of each aspects attribute. Likert scale was used as aesthetic value grading scale for each subaspect from 1 to 10 where 10 means very high value. Moreover, Likert scale was also used as importance scale for each aspect from 1 to 5 where 5 means not important at all. Five aspects

After the final round of discussion with experts, this section focused on the form, colour, shape, scent, sound, appearance, function, site selection, and quantities and diversity of

After the final round of discussion with experts, this section focused on the quantities and diversity of species, sound, disturbance, smell, colour, shape, habitat and its function in the

After the final round of discussion with experts, this section focused on water quality in term of presence of fish, colour, lake design, sound, disturbance, odor, site selection and its

species that could influencing the visitors to visit the park.

b. Aesthetic value of Animal or Fauna

Fig. 1. The map of Shah Alam Lake Garden

the parks.

parks.

in study were as follows. a. Aesthetic value of Tree

c. Aesthetic value of Lake

function to visitors.

#### d. Aesthetic value of Flower

After the final round of discussion with experts, this section focused on type of species, shape, form, colour, sound, aroma, site selection, design, quantities and its function.

e. Aesthetic value of Buildings

After the final round of discussion with experts, this section focused on design, level of cleanliness, material quality, number of buildings, suitability of the location and its functionality.

#### **2.3 Sampling technique**

Sampling was conducted using convenience sampling techniques. In convenience sampling, the sample selection is based on availability and accessibility. This technique is quite suitable in this study due to the high mobility of visitors and also unknown activities among visitors.

After calculations of sample size based on the population size obtained, it was found that as many as 407 respondents need to be taken as a sample size from the whole population. Although convenience sampling technique was applied, the sample of respondents was still taken from the whole area of the lake to ensure that the results would represent the whole visitors of the lake from all areas. Although the likelihood of the sample being unrepresentative of the visitor population would be quite high, the information could still provide a fairly significant insight and become a good source of data in exploratory research.

#### **2.4 Data analysis**

Second stage of this research involved quantitative study where all the qualitative data being analyzed and quantify to give a certain value to indicate the aesthetic level. Descriptive analysis was first used to determine the importance of each aspect in determining the aesthetic level. Table 1 shows the results of the analysis. It was found that the most important aspect for the respondents to visit the parks was tree with mean value of 2.00 followed by lake, flower and fauna with mean value of 2.34, 3.06 and 3.33 respectively. The aspect of buildings was considered as not important to be including in the assessment with the mean of 4.25. From the observations and feedbacks from visitors, the buildings in the parks doesn't have any uniqueness that can be consider as important enough to attract them to visit. Therefore, the aspect of building would not be analyzed in the second stage.

Table 1. Descriptive analysis of the aspects in study

Public Parks Aesthetic Value Index 195

From the feedback of the visitors, different form of trees can create an attractive view to the park while giving an aesthetic visual to them. At the same time, a proper tree maintenance

Table 3 shows the results of PCA analysis for the aspect of animal or fauna. It was found that higher factor loading recorded for habitat and selection of species with 0.872 and 0.839 respectively. From the feedback of visitors, the varieties of species play a pull factor to

Component 1 Component 2

Component 1 Component 2

Component 1 Component 2

Attributes Component

Table 2. Results of PCA analysis for the aspect of tree

attract them to the parks.

influencing their first impression.

existed in the park becomes an added value in term of aesthetic value.

Attributes Component

Attributes Component

Quality 0.903 0.136 Design 0.309 0.712 Colour 0.905 0.162 Cleanliness 0.575 0.524 Sound 0.261 0.650 Function -0.041 0.851

Table 3. Results of PCA analysis for the aspect of animal or fauna

Table 4. Results of PCA analysis for the aspect of lake

Species selection 0.839 -0.025 Quantity 0.503 0.490 Habitat 0.872 0.094 Sound 0.067 0.779 Cleanliness 0.663 0.260 Function 0.095 0.843

Table 4 shows the results of PCA analysis for the aspect of lake. There were two attributes that have the value of factor loading more than threshold, colour and quality with 0.905 and 0.903 respectively. From the feedback of the visitors, both attributes are important in

Form 0.741 -0.027 Colour 0.425 0.419 Maintenance 0.773 0.101 Quality 0.202 0.699 Species selection 0.766 0.031 Function 0.058 0.840 Quantity 0.499 0.376 Location -0.078 0.762

#### **2.4.1 Principal Component Analysis (PCA)**

PCA is a technique for simplifying a data set by reducing multidimensional data sets to lower dimensions for analysis. It is an orthogonal linear transformation that transforms the variance covariance matrices to a new coordinate system such that the greatest variance would lie on the first principal component and so on while at the same time still retaining the characteristics of the data set.

The correlation between variables or aspects and component, indicated by factor loading was used as a basic for classifying the dominant variables in each component. If the factor loading value is more than 0.7, the attribute can be considered as dominant and plays a main role in that component (Nunnally, 1978; Hair, 2009) because it would account for more than 50% of the variance in all variables.

The next step of analysis was the usage of Principal Component Analysis (PCA). The reason of applying this analysis was to extract the main attributes from all attributes of each aspect. This is important as in index development, the number of attributes must be optimum in order to represent a good indicator for assessment tools. The index with a lot of attributes would seldom represent a good status indicator. Moreover, another important step in developing or creating an index is the selection of only the most important or dominant attributes as these attributes play a big role in determining the status of the variable such as the status of aesthetic value of the public parks in this study. Since in PCA, the first component is always dominant compare to the other component, the selection of the main attributes was done only in first component.

However, this dominant component cannot be chose straight away as the indicator used in index as there is still some effect of correlation between components. According to Hair (2009), factor loading is the coefficient used to interpret the role of each variable and factor and the unrotated solution may not provide a true pattern of variable loadings due to the presence of this effect. In order to solve this problem, the whole extracted component need to be rotated. According to Rencher (2002), the most popular rotation technique is the varimax technique which seeks rotated loadings that maximize the variance of the squared loadings in each component. Indirectly, this varimax rotation could eliminate the effect of correlation between components.

As mention earlier, only four aspects were being considered after the aspect of building had been omitted. In the preliminary round, PCA was run separately for all five aspects to determine the main or dominant attributes in each aspect. As mention earlier, the index is the composite variable that was formed through the combination of several other variables. Mohamad Roslan et. al (2007) found that the index that can best explaining the real condition or situation is the index that focused on dominant variables in each scope or classification. In this study, it refers to dominant variables in the scope of tree, fauna, lake and flower.

Table 2 shows the component structure of trees after the varimax rotation process of PCA. The Table reports the factor loadings for each variable on the components between the item and the rotated factor. In this case, the factor loading value of 0.7 was chosen as as threshold value explained earlier. It was found that the attributes of maintenance, species selection and form has the factor loading value of 0.773, 0.766 and 0.741 respectively which are higher than the threshold value.

PCA is a technique for simplifying a data set by reducing multidimensional data sets to lower dimensions for analysis. It is an orthogonal linear transformation that transforms the variance covariance matrices to a new coordinate system such that the greatest variance would lie on the first principal component and so on while at the same time still retaining

The correlation between variables or aspects and component, indicated by factor loading was used as a basic for classifying the dominant variables in each component. If the factor loading value is more than 0.7, the attribute can be considered as dominant and plays a main role in that component (Nunnally, 1978; Hair, 2009) because it would account for more

The next step of analysis was the usage of Principal Component Analysis (PCA). The reason of applying this analysis was to extract the main attributes from all attributes of each aspect. This is important as in index development, the number of attributes must be optimum in order to represent a good indicator for assessment tools. The index with a lot of attributes would seldom represent a good status indicator. Moreover, another important step in developing or creating an index is the selection of only the most important or dominant attributes as these attributes play a big role in determining the status of the variable such as the status of aesthetic value of the public parks in this study. Since in PCA, the first component is always dominant compare to the other component, the selection of the main

However, this dominant component cannot be chose straight away as the indicator used in index as there is still some effect of correlation between components. According to Hair (2009), factor loading is the coefficient used to interpret the role of each variable and factor and the unrotated solution may not provide a true pattern of variable loadings due to the presence of this effect. In order to solve this problem, the whole extracted component need to be rotated. According to Rencher (2002), the most popular rotation technique is the varimax technique which seeks rotated loadings that maximize the variance of the squared loadings in each component. Indirectly, this varimax rotation could eliminate the effect of

As mention earlier, only four aspects were being considered after the aspect of building had been omitted. In the preliminary round, PCA was run separately for all five aspects to determine the main or dominant attributes in each aspect. As mention earlier, the index is the composite variable that was formed through the combination of several other variables. Mohamad Roslan et. al (2007) found that the index that can best explaining the real condition or situation is the index that focused on dominant variables in each scope or classification. In

Table 2 shows the component structure of trees after the varimax rotation process of PCA. The Table reports the factor loadings for each variable on the components between the item and the rotated factor. In this case, the factor loading value of 0.7 was chosen as as threshold value explained earlier. It was found that the attributes of maintenance, species selection and form has the factor loading value of 0.773, 0.766 and 0.741 respectively which are higher

this study, it refers to dominant variables in the scope of tree, fauna, lake and flower.

**2.4.1 Principal Component Analysis (PCA)**

the characteristics of the data set.

than 50% of the variance in all variables.

attributes was done only in first component.

correlation between components.

than the threshold value.

Table 2. Results of PCA analysis for the aspect of tree

From the feedback of the visitors, different form of trees can create an attractive view to the park while giving an aesthetic visual to them. At the same time, a proper tree maintenance existed in the park becomes an added value in term of aesthetic value.

Table 3 shows the results of PCA analysis for the aspect of animal or fauna. It was found that higher factor loading recorded for habitat and selection of species with 0.872 and 0.839 respectively. From the feedback of visitors, the varieties of species play a pull factor to attract them to the parks.

Table 3. Results of PCA analysis for the aspect of animal or fauna

Table 4 shows the results of PCA analysis for the aspect of lake. There were two attributes that have the value of factor loading more than threshold, colour and quality with 0.905 and 0.903 respectively. From the feedback of the visitors, both attributes are important in influencing their first impression.

Table 4. Results of PCA analysis for the aspect of lake

Public Parks Aesthetic Value Index 197

Table 6 shows that from the exploratory results, it was found that six attributes could be taken as aesthetic value index indicators from 26 attributes. They were odour of flower, colour of water, quality of flowers, quantity of flowers, water quality and colour of flowers following the order. This order or arrangement is important in the next stage of analysis. Consequently, running the same process for the validation data set gave the same

Benchmarking analysis is the analysis used in comparing the current project, methods or processes with the best practices in order to drive improvement. The objective of this analysis is to set an appropriate reliability and quality matrices for the output based on

This method had been used by Mohamad Roslan et. al (2007) in their study on the creation of ground water quality index. They found that this method is suitable and highly sensitive. However, in their study, they used the quantitative data of several prospect water

After the analysis of PCA, the next stage is to develop the index. This study would offer some uniqueness in the index formation; the index is not in statistical equation but in graphical feature (Figure 3). Each vertex represents the attributes, extracted from the PCA and arranged in clock-wise order. This graphical feature which is part of benchmarking analysis was drawn to calculate the index with the help of mean analysis. From this graphics, the index was calculated as the percentage of the polygon area drawn using the

1. Fix the value of analysis with the scale of 0 to 10 for each main attribute extracted from

3. Calculate each triangle (Fig 2) area inside the polygon drawn based on the value from

b

A=0.5 × a × b × sin θ (1)

IV=A/L × 100 (2)

arrangement of attributes though the factor loading value is not same.

data to the whole polygon area as shown in the green area in Figure 3.

Procedure of developing the index using Benchmarking Analysis is as follow.

θ

a

**2.4.2 Benchmarking analysis**

similar present products.

quality indicators.

PCA

2. Built the polygon

data using formula (1).

Fig. 2. Triangle in the polygon

4. Determine the ratio of the area using formula (2).

Table 5 shows the results of PCA analysis for the aspect of flower. It was found that only one component could be form from the analysis and from this component, five attributes were major attributes. They were quality, odour, quantity, colour and species selection. These five attributes were related to each other because if choices of species were good enough, it reflected the qualities, quantities, colour and odour. In short, a good quality species produced a good flower.

Table 5. Results of PCA analysis for the aspect of flower

From all these Table 2 to Table 5, it was found that most major attributes that could be a major pull factors for the visitors to visit were in the aspect of flower. In the final analysis of PCA, all main attributes in each aspect were analyzed together. In this stage, the data was separate into two parts, 300 of them in one part, used to determine the main attribute in exploratory while another 107 were used in validating the exploratory results. This process was done because the results of this stage would be use in creating the index and therefore need to be validating to ensure that the index is valid to be use. The data set of 300 respondents still covering the whole public parks areas and the same applied for the data set of 107 respondents.

Table 6 shows the results of PCA analysis for data set in determining the main attributes in exploratory. It was found that odour of flower, colour of water, quality of flower, quantity of flower, water quality and colour of flowers were the main attributes from all selection attributes, having the factor loading value of 0.805, 0.766, 0.756, 0.734, 0.704 and 0.700 respectively.

Table 6. Results of PCA analysis for data set to determine the main attrbutes

Table 5 shows the results of PCA analysis for the aspect of flower. It was found that only one component could be form from the analysis and from this component, five attributes were major attributes. They were quality, odour, quantity, colour and species selection. These five attributes were related to each other because if choices of species were good enough, it reflected the qualities, quantities, colour and odour. In short, a good quality

> Attributes Component Species selection 0.746 Quantity 0.773 Quality 0.810 Colour 0.754 Odour 0.796 Function 0.586

From all these Table 2 to Table 5, it was found that most major attributes that could be a major pull factors for the visitors to visit were in the aspect of flower. In the final analysis of PCA, all main attributes in each aspect were analyzed together. In this stage, the data was separate into two parts, 300 of them in one part, used to determine the main attribute in exploratory while another 107 were used in validating the exploratory results. This process was done because the results of this stage would be use in creating the index and therefore need to be validating to ensure that the index is valid to be use. The data set of 300 respondents still covering the whole

Table 6 shows the results of PCA analysis for data set in determining the main attributes in exploratory. It was found that odour of flower, colour of water, quality of flower, quantity of flower, water quality and colour of flowers were the main attributes from all selection attributes, having the factor loading value of 0.805, 0.766, 0.756, 0.734, 0.704 and

Component 1 Component 2

public parks areas and the same applied for the data set of 107 respondents.

Attributes Component

Table 6. Results of PCA analysis for data set to determine the main attrbutes

Tree formation 0.141 0.800 Tree maintenance 0.273 0.771 Tree species selection 0.175 0.727 Water quality 0.704 0.255 Colour of water 0.766 0.177 Flower species selection 0.679 0.164 Quantity of flower 0.734 0.186 Quality of flower 0.756 0.175 Colour of flower 0.700 0.172 Odour of flower 0.805 0.172

species produced a good flower.

0.700 respectively.

Table 5. Results of PCA analysis for the aspect of flower

Table 6 shows that from the exploratory results, it was found that six attributes could be taken as aesthetic value index indicators from 26 attributes. They were odour of flower, colour of water, quality of flowers, quantity of flowers, water quality and colour of flowers following the order. This order or arrangement is important in the next stage of analysis. Consequently, running the same process for the validation data set gave the same arrangement of attributes though the factor loading value is not same.

#### **2.4.2 Benchmarking analysis**

Benchmarking analysis is the analysis used in comparing the current project, methods or processes with the best practices in order to drive improvement. The objective of this analysis is to set an appropriate reliability and quality matrices for the output based on similar present products.

This method had been used by Mohamad Roslan et. al (2007) in their study on the creation of ground water quality index. They found that this method is suitable and highly sensitive. However, in their study, they used the quantitative data of several prospect water quality indicators.

After the analysis of PCA, the next stage is to develop the index. This study would offer some uniqueness in the index formation; the index is not in statistical equation but in graphical feature (Figure 3). Each vertex represents the attributes, extracted from the PCA and arranged in clock-wise order. This graphical feature which is part of benchmarking analysis was drawn to calculate the index with the help of mean analysis. From this graphics, the index was calculated as the percentage of the polygon area drawn using the data to the whole polygon area as shown in the green area in Figure 3.

Procedure of developing the index using Benchmarking Analysis is as follow.

$$\mathbf{A} = \mathbf{0}.5 \times \mathbf{a} \times \mathbf{b} \times \sin \theta \tag{1}$$

Fig. 2. Triangle in the polygon

4. Determine the ratio of the area using formula (2).

$$\text{IV} = \text{A/L} \times 100 \tag{2}$$

Public Parks Aesthetic Value Index 199

0 2 4 6 8 10 Odour of f l ower s

Quanti ty of f l ower s

Col our of water

Qual i ty of f l ower s

Grades Value range Excellence 81.00 – 100.00 Good 49.00 – 80.99 Satisfactory 25.00 – 48.99 Poor 9.00 – 24.99 Very poor 0.00 – 8.99

The final stage of this study is to apply the index to calculate the aesthetic value index of the study area. Based on the grading range (Table 8), the index value for Shah Alam Lake Garden Aesthetic Value Index of 20.44 can be classified as poor. From Figure 3 and Table 7, it was shown that almost all attributes were given grading scales less than 5 except the

Taking into considerations the five criteria related to the assessment of aesthetic value index as mentioned by Haslina (2006) which primarily focuses on the beauties and the 'in' thing, this index would be a valuable tool in the management of aesthetic value in tourist attraction sites such as public parks, lake gardens and recreational forests. The minimal constraint in

This index was created with the data gain during daylight. Therefore, the main indicator variables in the index became dominant during daylight. However, the assessment for the night session may refer to another set of indicator variables. This brings the potential of

Another potential scope of future study is to use the quantitative method in measuring the value or grading for each attribute in the index instead of just collecting the data through a large size of respondent perception's. This could be done with the utilization of several high

application made it suitably applied in assessing the aesthetic value under the sun.

Fig. 3. The index with the mean value for each variables

Water qual i ty

Col our of f l ower s

quality of flower. This contributes the overall grade level.

Table 8. Grading system

**3. Conclusion**

future study on this aspect.

technology equipments.

WhereIV=Index value

A= Total triangle area

L=Total polygon area

5. Evaluate the aesthetic value using the index.

#### **2.4.3 Sensitivity analysis**

This analysis was also conducted to the model to determine its sensitivity to the change of the value. For example, determine the changing rate of the index when any attribute fall from 10 to 9 in benchmarking scale. In this case, it was found that the index value would fall as much as 3.33% for any single attribute that fall as much as one unit in benchmarking scale.

#### **2.5 Creation and calculation of the index in the study**

Before the polygon can be drawn, the mean analysis for the main attributes extracted from PCA need to be conduct to determine the level of aesthetic level for each attribute within the Benchmarking scale of 0-10. This analysis involved all respondents without separation. Table 7 shows the mean analysis for six main attributes. It shows that during the study, the attribute of quality of flower has the highest ranking compare to the other five attributes with the value of 5.12.

Table 7. Mean analysis for six main attributes

The values in Table 7 were used in drawing the polygon and consequently the Public Parks Aesthetic Value Index. Fig. 3 shows the polygon used to calculate the index with the scale of 0-10. Using the procedure and formula as mentioned earlier, it was found that the value for Shah Alam Lake Garden Aesthetic Value Index is 20.44.

This study also furnished the index with the grading system; develop using the concept of the polygon area to help in grading the aesthetic value index through benchmarking analysis. Five grades were applied in this product that is excellence, good, satisfactory, poor and very poor (Table 8). These grades were set up using the benchmarking level scale of 9, 7, 5. 3 and 1 for all six attributes.

WhereIV=Index value

A= Total triangle area

L=Total polygon area

This analysis was also conducted to the model to determine its sensitivity to the change of the value. For example, determine the changing rate of the index when any attribute fall from 10 to 9 in benchmarking scale. In this case, it was found that the index value would fall as much as 3.33% for any single attribute that fall as much as one unit in

Before the polygon can be drawn, the mean analysis for the main attributes extracted from PCA need to be conduct to determine the level of aesthetic level for each attribute within the Benchmarking scale of 0-10. This analysis involved all respondents without separation. Table 7 shows the mean analysis for six main attributes. It shows that during the study, the attribute of quality of flower has the highest ranking compare to the other five attributes

The values in Table 7 were used in drawing the polygon and consequently the Public Parks Aesthetic Value Index. Fig. 3 shows the polygon used to calculate the index with the scale of 0-10. Using the procedure and formula as mentioned earlier, it was found that the value for

This study also furnished the index with the grading system; develop using the concept of the polygon area to help in grading the aesthetic value index through benchmarking analysis. Five grades were applied in this product that is excellence, good, satisfactory, poor and very poor (Table 8). These grades were set up using the benchmarking level scale of 9, 7,

Attributes Mean Water quality 4.13 Colour of water 3.99 Quantity of flower 4.75 Quality of flower 5.12 Colour of flower 4.90 Odour of flower 4.28

5. Evaluate the aesthetic value using the index.

**2.5 Creation and calculation of the index in the study**

Table 7. Mean analysis for six main attributes

5. 3 and 1 for all six attributes.

Shah Alam Lake Garden Aesthetic Value Index is 20.44.

**2.4.3 Sensitivity analysis**

benchmarking scale.

with the value of 5.12.

Fig. 3. The index with the mean value for each variables

Table 8. Grading system

The final stage of this study is to apply the index to calculate the aesthetic value index of the study area. Based on the grading range (Table 8), the index value for Shah Alam Lake Garden Aesthetic Value Index of 20.44 can be classified as poor. From Figure 3 and Table 7, it was shown that almost all attributes were given grading scales less than 5 except the quality of flower. This contributes the overall grade level.

#### **3. Conclusion**

Taking into considerations the five criteria related to the assessment of aesthetic value index as mentioned by Haslina (2006) which primarily focuses on the beauties and the 'in' thing, this index would be a valuable tool in the management of aesthetic value in tourist attraction sites such as public parks, lake gardens and recreational forests. The minimal constraint in application made it suitably applied in assessing the aesthetic value under the sun.

This index was created with the data gain during daylight. Therefore, the main indicator variables in the index became dominant during daylight. However, the assessment for the night session may refer to another set of indicator variables. This brings the potential of future study on this aspect.

Another potential scope of future study is to use the quantitative method in measuring the value or grading for each attribute in the index instead of just collecting the data through a large size of respondent perception's. This could be done with the utilization of several high technology equipments.

#### **4. References**

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Berleant, A. (1998). Environmental Aesthetics. In M. Kelly (Ed). *Encyclopedia of Aesthetics*.

Carlson, A. (2010). Environmental aesthetics. In E. Craig (Ed.), *Routledge Encyclopedia of*

Cranz, G. (1982). *The Politics of Park Design: A History of Urban Parks*. Cambridge Press:

Fisher, J. A. (2003). Environmental Aesthetics. In: the *Oxford Handbook of Aesthetics* ed.

Hair, J. F., Black, W. C., Banin, B. J. & Anderson, R.E. (2009). *Multivariate Data Analysis*. 7th

Haslina, H. (2006). *Visitors Perception on Aesthetic Function of Ornamental Plant in Taman Tasik Titiwangsa, Kuala Lumpur*. UPM Faculty of Forestry Bachelor Thesis. Hettinger, N. (2005). Allen Carlson's Environmental Aesthetics and the Protection of the

Janick, J. (2010). Plant iconography and art. *Source of information on horticultural technology, 1*. Kant, I. (1964), *The Critique of Judgement*, trans. J.C.Meredith, Oxford University Press,

Kent, A. J. (2005). Aesthetics: A Lost Cause in Cartographic Theory. *The Cartographic Journal*.

Lifestyle Information Network. (2007). Guidelines for Developing Public Recreation Facility

Mothersill, M. (2004). Beauty and the Critic's Judgment: Remapping Aesthetics. In *The*

Mohamad Roslan, M.K., Mohd Kamil, Y., Wan Nor Azmin, S. & Mat Yusoff, A. (2007).

Rencher, A.C. (2002). *Methods of Multivariate Analysis*. 2nd Edition. New York: John Wiley &

Slater, B.H. (2005). Aesthetics. Internet Encyclopedia of Philosophy. Date of access: 11 June

Slote, M. A. (1971). The Rationality of Aesthetic Value Judgments. *The Journal of Philosophy*.

Thompson, J. (1995). "Aesthetics and the value of nature," *Environmental Ethics* 17, 291-305

*Blackwell Guide to Aesthetics*. New Jersey: Blackwell Publishing Ltd

Nunnally, J. C. (1978). *Psychometric theory*. 2nd Edition. New York: McGraw-Hill.

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Standards. Date of access: 20th October 2011.. http://lin.ca/resource-details/1477.

Creation of a Ground Water Quality Index for an Open Municipal Landfill Area.

Camp, J.V. (2005). *Freedom of Expression*. New York: The National Endowment for the Arts. Carlson, A. (2000). *Aesthetics and the Environment: The Appreciation of Nature, Art and*

New York: Oxford University Press, 114-120.

Levinson, J. Oxford: Oxford University Press

Environment. *Environmental Ethics* 27(1): 57-76.

*Architecture*. New York: Routledge.

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*Philosophy*. London: Routledge.

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of New York

Cambridge

Oxford.

Sons.

68 (22): 821-839

42(2). Pg 182-188

### *Edited by Parinya Sanguansat*

This book is aimed at raising awareness of researchers, scientists and engineers on the benefits of Principal Component Analysis (PCA) in data analysis. In this book, the reader will find the applications of PCA in fields such as taxonomy, biology, pharmacy,finance, agriculture, ecology, health and architecture.

Photo by nevarpp / iStock

Principal Component Analysis - Multidisciplinary Applications

Principal Component

Analysis

Multidisciplinary Applications

*Edited by Parinya Sanguansat*