one in every 1000 women has been suffering from breast cancer during 1974 - 1978 .
this means that effective preventive actions must be taken to reduce the rate of this dangerous cancer ( 1 ) .
the commonly used diagnostic techniques for breast cancer screening is mammography , thermography and ultrasound imaging . among these techniques , mammography is the gold standard approach for early detection . in early stage , the detection of microcalcifications appears in the breast tissue .
microcalcifications are small calcium deposits and appear as groups of radio - opaque spots in most cancerous mammograms .
there are different techniques for breast cancer detection , such as neural network , fuzzy logic and wavelet based algorithms ( 2 , 3 ) .
mammography is the best screening tool for the detection of breast cancer in early stages , before appearance in physical examination .
there are several features in mammography that help physicians to detect abnormalities in early stage , and these features can be directly extracted by image processing methods ( 4 ) .
the cancerous breast symptoms comprise of mass , changes in shape , color and dimension of breast .
if the cancer is detected in earlier stage , a better treatment can be provided .
recently , computer aided diagnosis ( cad ) systems have been developed to detect breast cancer automatically .
normal tissues typically have smooth boundary and surface , whereas abnormal tissue presents rough surfaces and jagged boundaries ( 5 ) .
for this purpose , there are several methods available that we can use for features extraction from the digital image , such as : region - based features , shape - based features , texture based features and position based features . in digital mammography , the most common used feature for classifying normal and abnormal pattern is texture feature . in this paper
, we used the texture based gray - level co - occurrence matrices ( glcm ) features for this purpose . for breast cancer classification
, we should select several features with special criteria . for breast cancer detection and classification ,
( 6 ) used a hypothesis test to determine if the feature can discriminate or not .
( 7 ) developed a diagnosis algorithm based on a neural - genetic algorithm feature selection method for digital mammograms and the obtained accuracy was 85% .
huang et al . ( 11 ) used a support vector machine based feature selection and obtained accuracy was of 86% .
( 12 ) used the sequential floating forward selection ( sffs ) to reduce the feature dimensionality .
luo et al . ( 13 ) used two well - known feature selection techniques , including forward selection and backward selection , and two classifiers for ensemble classification .
they have used a decision tree and supper vector machine , as an initial classifier .
wei et al . ( 14 ) used a sequential backward selection method for the purpose of selecting the most relevant features . in their work ,
18 features were extracted , out of which 12 features were finally selected for the classification of benign and malignant pattern .
to overcome the problem of overfitting and underfitting encountered in other studies , we present the ensemble supervised classification method with simple voting policy for the detection of normal and abnormal pattern in the mammogram data , with reasonable accuracy .
the proposed method consists of three main steps , as follows : 1- feature extraction , 2- feature selection and 3- the classification process using ensemble supervised classification technique . in brief
we obtained the required data from the digital database for screening mammography ( ddsm ) .
the resolution of obtained images was 42 microns with 4964  2900 pixels and breast density rating was up to 3 in the breast imaging - reporting and data system ( bi - rads ) .
feature extraction is a crucial step in the mammograms classification . if the extracted features are not proper , overfitting , underfitting and misclassification occurs . for obtaining relevant features , after reading the image , we restricted ourselves to the region of mammograms with highest probability of cancer occurrence .
we selected a region of interest ( roi ) rectangular window with 512  512 pixels in size and then we extracted the features from this region .
the glcm features are calculated in four directions , which are 0 , 45 , 90 , 145 , and four distances ( 1 , 2 , 3 , 4 ) .
these features are more redundant for classification and several of them are unnecessary ; therefore , we applied the feature selection method . where x and y are the coordinates of an entry in the co - occurrence matrix , x , y , x , and y are the mean and standard deviation , and the partial probability function , px+y(i ) is the probability of co - occurrence matrix coordinating summing to x + y. the hx and hy are the entropies of px and py : hxy=-ijp(i , j)log(p(i , j ) ) , 
 hxy1=-ijp(i , j)log(px(i)py(j ) ) 
  hxy2=-ijpx(i)py(j)log(px(i)py(j ) ) .
therefore , the selected features show more differences between normal and abnormal data . at the end ,
six dominant features of 20 features were selected , as shown in table 3 . in the next step ,
the classification process includes two steps : 1 ) initial classification and 2 ) ensemble . in the initial step , the k
- nearest neighbors ( knn ) , naive bayes and support vector machine ( svm ) algorithms have been used as supervised classifiers for classification of normal and abnormal data .
the knn algorithm is a method for classifying objects on closed training data in the feature space . in knn algorithm ,
classification of an object enrolled by a majority vote of its neighbors is performed . in this paper
naive bayes classifier can handle an arbitrary number of independent variables , whether continuous or categorical .
, xd } , we want to construct the posterior probability for the given cj among a set of possible outcomes c={c1,c2,c3 , 
bayes assumes that the conditional probabilities of the independent variables are statistically independent , we can decompose the likelihood to a product of terms : and rewrite the posterior as : using the bayes rule above , we label a new case x with a class level cj , that achieves the highest posterior probability .
the svms construct a decision surface in the feature space that bisects the two categories and maximizes the margin of separation between two classes of points .
this decision surface can then be used as a basis for classifying points of unknown class ( 18 ) .
suppose we have n training data points f ( x1 ; y1 ) ; ( x2 ; y2 ) ; ( xn ; yn ) g , where xi 
  r and yi 
  
 , { + 1 : -1 } . the problem of finding a maximal margin separating hyperplane plane can be written as : this is a convex quadratic programming problem .
introducing lagrange multipliers and solving to get the wolfe dual , we obtain : the solution of the primal problem is given by : to train the svm , we search through the feasible region of the dual problem and maximize the objective function . to classify the mammograms , the first 200 data features have been used for classifier training , and the remaining data was used for classifier evaluation . to obtain acceptable accuracy ,
, we initially classify the data by three classification algorithms . in the next step ,
we assign a label to data , as temporary label . after assigning temporary labels to all data ,
the final label for each pixel will be the one that obtains the maximum number of votes between the temporary labels of its surrounding neighbors . equation 8 presents this process for each data set . where the final_class ( i ) is the final label allocated to data ( i ) , l=(1 , 2 ) is a set of associated labels to two normal and abnormal , s is variable for defining neighborhood around data ( i ) and is (s ) defined by equation 9 . in this equation ,
argmaxq(k=13k(s ) ) determines temporary label for data ( i ) and k(s ) is defined through equation 10 . in equation 10 , the label is a matrix with the size of m multiply 3 ( m3 ) , where m is the length of data .
for example , label can be defined for data ( m ) as follow : label ( m , 1 ) = knn_label ( m ) label ( m , 2 ) = bayes_label ( m ) label ( m , 3 ) = svm_label ( m ) .
we obtained the required data from the digital database for screening mammography ( ddsm ) .
the resolution of obtained images was 42 microns with 4964  2900 pixels and breast density rating was up to 3 in the breast imaging - reporting and data system ( bi - rads ) .
feature extraction is a crucial step in the mammograms classification . if the extracted features are not proper , overfitting , underfitting and misclassification occurs . for obtaining relevant features , after reading the image , we restricted ourselves to the region of mammograms with highest probability of cancer occurrence .
we selected a region of interest ( roi ) rectangular window with 512  512 pixels in size and then we extracted the features from this region .
the glcm features are calculated in four directions , which are 0 , 45 , 90 , 145 , and four distances ( 1 , 2 , 3 , 4 ) .
these features are more redundant for classification and several of them are unnecessary ; therefore , we applied the feature selection method . where x and y are the coordinates of an entry in the co - occurrence matrix , x , y , x , and y are the mean and standard deviation , and the partial probability function , px+y(i ) is the probability of co - occurrence matrix coordinating summing to x + y. the hx and hy are the entropies of px and py : hxy=-ijp(i , j)log(p(i , j ) ) , 
 hxy1=-ijp(i , j)log(px(i)py(j ) ) 
  hxy2=-ijpx(i)py(j)log(px(i)py(j ) ) .
feature selection is an important step for feature dimension reduction in the classification procedure . after feature extraction ,
therefore , the selected features show more differences between normal and abnormal data . at the end ,
six dominant features of 20 features were selected , as shown in table 3 . in the next step ,
the classification process includes two steps : 1 ) initial classification and 2 ) ensemble . in the initial step , the k - nearest neighbors ( knn ) , naive bayes and support vector machine ( svm ) algorithms have been used as supervised classifiers for classification of normal and abnormal data .
the knn algorithm is a method for classifying objects on closed training data in the feature space . in knn algorithm ,
classification of an object enrolled by a majority vote of its neighbors is performed . in this paper , we used the knn algorithm with k = 5 ( 16 ) .
naive bayes classifier can handle an arbitrary number of independent variables , whether continuous or categorical .
, xd } , we want to construct the posterior probability for the given cj among a set of possible outcomes c={c1,c2,c3 , 
since naive bayes assumes that the conditional probabilities of the independent variables are statistically independent , we can decompose the likelihood to a product of terms : and rewrite the posterior as : using the bayes rule above , we label a new case x with a class level cj , that achieves the highest posterior probability .
the svms construct a decision surface in the feature space that bisects the two categories and maximizes the margin of separation between two classes of points .
this decision surface can then be used as a basis for classifying points of unknown class ( 18 ) .
suppose we have n training data points f ( x1 ; y1 ) ; ( x2 ; y2 ) ; ( xn ; yn ) g , where xi 
  r and yi 
  
 , { + 1 : -1 } . the problem of finding a maximal margin separating hyperplane plane can be written as : this is a convex quadratic programming problem .
introducing lagrange multipliers and solving to get the wolfe dual , we obtain : the solution of the primal problem is given by : to train the svm , we search through the feasible region of the dual problem and maximize the objective function . to classify the mammograms , the first 200 data features have been used for classifier training , and the remaining data was used for classifier evaluation . to obtain acceptable accuracy ,
we assign a label to data , as temporary label . after assigning temporary labels to all data ,
the final label for each pixel will be the one that obtains the maximum number of votes between the temporary labels of its surrounding neighbors .
equation 8 presents this process for each data set . where the final_class ( i ) is the final label allocated to data ( i ) , l=(1 , 2 ) is a set of associated labels to two normal and abnormal , s is variable for defining neighborhood around data ( i ) and is (s ) defined by equation 9 . in this equation ,
argmaxq(k=13k(s ) ) determines temporary label for data ( i ) and k(s ) is defined through equation 10 . in equation 10 , the label is a matrix with the size of m multiply 3 ( m3 ) , where m is the length of data .
for example , label can be defined for data ( m ) as follow : label ( m , 1 ) = knn_label ( m ) label ( m , 2 ) = bayes_label ( m ) label ( m , 3 ) = svm_label ( m ) .
in this section , the performance of our ensemble - supervised classifier is investigated using the ddsm dataset provided by massachusetts general hospital , boston , ma , usa , the university of south florida , tampa , fl , usa , and sandia national laboratories , albuquerque , nm , usa . here
, we used 200 data sets for training process , of which 100 data sets are chosen randomly for evaluation of classifier .
finally , the evaluation of data consists of sixty abnormal and forty normal data sets . by applying feature extraction and selection method on roi in training data ,
six salience features were selected , which lead to appropriate accuracy . in the evaluation step ,
we only extracted these features from roi in the test data and fed them to classifier . finally , the obtained results were compared with the gold standards that were labeled as normal or abnormal by an expert .
sensitivity and specificity were used to investigate classifier performance ; where tp = true positive , tn = true negative , fp = false positive , and fn = false negative , a 100% sensitivity is the theoretical desired prediction for the cancerous data .
also , a 100% specificity is the theoretical desired prediction for the non - cancerous data .
the sensitivity and specificity of the proposed system are shown in table 4 . to verify that our selected features are robust and our feature selection method is acceptable , we compared the obtained results from the proposed method with the results of random feature selection method . in random selection method , we assume that the data distribution is normal and therefore , by using  randm 
abbreviations : pv , predictive value ; tp , true positive ; fp , false positive ; fn , false negative ; tn , true negative ; ppv , positive predictive value ; npv , negative predictive value .
in this paper , we have proposed a new cad method to classify the tumoral mammogram .
this method is fully automatic and does not need operator manipulation . at first , we select the area of mammograms with high cancer probability .
the extracted features are classified into normal and abnormal , using ensemble supervised classification method .
the performance of the proposed method is evaluated by the perfect test method , which gives the sensitivity and specificity of the result .
the proposed classification method gave the correct classification of 97% for the division into two categories according to bi - rads standard on the ddsm .
the obtained accuracy of the proposed method , 97% , is comparable with knn ( 96% ) , svm ( 87% ) and naive bayes ( 89% ) . in this paper , by assembling three classifiers and applying single voting policy , we improve the classification results in comparison to the method proposed by luo et al .
( 13 ) the obtained results show that our method has a slight improvement over the other proposed methods on the dataset , which is publicly available .
therefore , the proposed method is more reliable in order to assist the radiologist in the detection of abnormal data and to improve the diagnostic accuracy .
 background : breast cancer is one of the most encountered cancers in women . 
 detection and classification of the cancer into malignant or benign is one of the challenging fields of the pathology.objectives:our aim was to classify the mammogram data into normal and abnormal by ensemble classification method.patients and methods : in this method , we first extract texture features from cancerous and normal breasts , using the gray - level co - occurrence matrices ( glcm ) method . to obtain better results , 
 we select a region of breast with high probability of cancer occurrence before feature extraction . after features extraction 
 , we use the maximum difference method to select the features that have predominant difference between normal and abnormal data sets . 
 six selected features served as the classifying tool for classification purpose by the proposed ensemble supervised algorithm . for classification 
 , the data were first classified by three supervised classifiers , and then by simple voting policy , we finalized the classification process.results:after classification with the ensemble supervised algorithm , the performance of the proposed method was evaluated by perfect test method , which gave the sensitivity and specificity of 96.66% and 97.50% , respectively.conclusions:in this study , we proposed a new computer aided diagnostic tool for the detection and classification of breast cancer . 
 the obtained results showed that the proposed method is more reliable in diagnostic to assist the radiologists in the detection of abnormal data and to improve the diagnostic accuracy . 
1. Background
2. Objectives
3. Patients and Methods
3.1. Data
3.2. Feature Extraction
3.3. Feature Selection
3.4. Classification
4. Results
5. Discussion