Instead , one mathematically ensures that the fewest possible assumptions about unmeasured data are made by choosing the spectrum that maximizes the entropy for the process . The use of the maximum entropy approach to spectral analysis was introduced by Burg [ 1 ] . In this correspondence , the authors derive the maximum-entropy spectrum by obtaining a spectrum that is forced to maximize the entropy of a stationary random process . MaxEnt is a popular maximum entropy-based algorithm originally developed for modelling species distribution , but increasingly used for land-cover classification . In this article , we used MaxEnt as a single-class land-cover classification and explored if recommended procedures for generating high-quality species distribution models also apply for generating high-accuracy land-cover classification . To solve a class of non-differentiable multi-objective optimization problems , this paper proposed a new method called maximum-entropy social cognitive optimization algorithm . First , used the maximum-entropy function , transformed the constrained non-differentiable multi-objective optimization problem to the approximation unconstrained differentiable optimization problem , then used the social cognitive optimization algorithm to solve this problem . The algorithm was based on social cognitive theory , through a series of learning agents to simulate human social and intelligent thereby completing the optimization of the target . Recently , an alternative measure of total uncertainty in Dempster – Shafer theory of evidence ( DST ) has been proposed in place of the maximum entropy measure . It is based on the pignistic probability of a basic probability assignment and it is proved that this measure verifies a set of needed properties for such a type of measure . The profilogram of FAE ( fuel-air explosive ) fuel explosion image is the important base to analyze the explosion process . In this article , the double peak method , the iteration method , the OTSU method , and the maximum entropy criterion method are respectively used to confirm the threshold , and extract and compare the profilograms of the FAE fuel explosion image , which could establish the base for the further experiment analysis . We examine several entropic thresholding methods which are the most popular in the literature . These methods are minimum cross entropy , maximum entropy sum method , Renyi ’s entropy and Havrda&Charvat entropy . We perform experiments for demonstrating the effectiveness of the examined methods on image thresholding . . At the microscopic level , the evolution of the knowledge base is divided into the iterative sequence of the enterprisepsilas knowledge basepsilas border in the information-flow process and the process is modeled with the help of the fractal theory . At the macroscopic level , the correlation is discussed among the information output of the enterprises as the information sources and the entropy character of the knowledge base evolution , by making use of the information-flow cycle with the maximum entropy equation . The conclusion can be reference for the knowledge base of the techno-innovation process and the management of the enterprisespsila knowledge . First , based on the global distance of evidence and the global belief entropy , the α value of IOWA is obtained . Simultaneously , a weight vector is given based on the maximum entropy method model . Then , according to IOWA operator , the evidence are modified before applying the Dempster ’s combination rule . The system employs a machine-learning technique to classify joint stiffness . A maximum-entropy-rate method is developed to select the most relevant features . Experimental results demonstrate that distance travelled and energy expended can be estimated from observed changes in knee and ankle motions during 5-km runs . The aim of this paper is to compare , in the domain of the Bearings-only Target Motion Analysis ( BTMA ) with two observers , three approaches in terms of tracking performances : the Interacting Multiple Models ( IMM ) based on the Extended Kalman Filtering , the Hidden Markov Models ( HMM ) and the approximated densities filtering based on the maximum of entropy . Second , we reinterpret and adjust the standard vae objective , which we argue is over - regularized . We draw connections between the learning algorithm resulting from our proposed regularization and the information - bottleneck principle and maximum - entropy discrimination . The result is a recipe that makes vaes practical solutions to this important problem . Xing et al . proposed two algorithms named LDLogitBoost and AOSO - LDLogitBoost to learn general models to relax the maximum entropy model in traditional LDL methods . Furthermore , He et al . generated age label distributions through weighted linear combination of the input image ’s label and its context - neighboring samples . Firstly , due to the soft clustering , entropy alone could be maximised trivially by setting all prediction vectors to uniform distributions , resulting in no clustering . This is corrected by the conditional entropy component , which encourages deterministic one - hot predictions . For example , even for the degenerate case of identical pairs , the IIC objective encourages a deterministic clustering function ( i.e. is a one - hot vector ) as this results in null conditional entropy . However , the regularization term K ( p gen ) in the training objective ( 1 ) requires the generator distribution . Faced with this problem , we focus on the max - entropy formulation , and exploit two different approximations of the regularization term K ( p gen ) = −H ( p gen ) . section : NEAREST - NEIGHBOR ENTROPY GRADIENT APPROXIMATION For practical reasons we only consider the first two polynomials , that is , the first two moments : mean and covariance . The Gaussian is the maximum entropy distribution for given mean and covariance , therefore we assume the coding units to follow a multidimensional Gaussian . The difference of two Gaussians ( synthetic and real - world images ) is measured by the Fréchet distance also known as Wasserstein - 2 distance . Consequently , the distance between samples and model ’s boundary can be enlarged accordingly , so that significant perturbations are required to fool the model . Then , based on the distance comparison , we propose a two-step classification algorithm that performs efficiently for multi-class classification . DunDi can not only build and train a new customized model but also support the incorporation of the available pre-trained neural network models to take full advantage of their capabilities . Abstract This paper presents a laboratory study of multi-class classification problem for multiple indoor air contaminants which belongs to a completely linear-inseparable case . Six kinds of indoor air contaminations ( formaldehyde , benzene , toluene , carbon monoxide , ammonia and nitrogen dioxide ) were recognized as indicators of air quality in this project . However , random forests are black-box ensemble models which lack a capability of explanation for the reasoning behind their prediction . Therefore , in this paper , we define a rule extraction algorithm named ExtractingRuleRF to derive an interpretable refined classification rule set from a random forest for a multi-class data classification task . The proposed algorithm follows a greedy approach with two phases : rule refinement and rule extraction . The method of multi-class classification based support vector machines is researched . After comparing some common multi-class SVMS , and proposes a multi-class classified method based on similar binary tree . The constructing algorithm of similar binary tree is given and its effectivity is discussed . Voxel-level fitting of the MRI data was performed on the classical mono-exponential model , and four anomalous diffusion models , namely , the stretched exponential model , the sub-diffusion model , the continuous time random walk model and the fractional Bloch-Torrey equation . The performance of the anomalous diffusion parameters for differentiating the three-concentric layers of tumour tissue ( i.e. , core ; intermediate zone ; peripheral and hyper-vascularised tumour layer ) was evaluated with multinomial logistic regression and multi-class classification analysis . We found that parameter ( \alpha ) from the stretched exponential model , parameter ( \beta ) from the subdiffusion model and parameter ( \beta ) from the continuous time random walk model provide a clear delineation of the three layers of tumour tissue . On the other hand , label ambiguity can also happen if we are not confident in the labels we provide for an image . In the multi - label classification task , some objects are clearly visible but difficult to recognize . This type of objects are annotated as Difficult in the PASCAL Visual Object Classes ( VOC ) classification challenge , e.g. , the chair in the third image of the first row in Fig . Intuitively , encodes a vector of latent features derived from the concatenation of both graph and node features , and can be used to predict the label of the th node . For multi - class classification , we can decode using the softmax activation function to learn a probability distribution over node labels . More precisely , we predict node labels via the following transformation : , where and . Accordingly , two classes of variations can be defined : the intrapersonal variations and the extrapersonal variations . Therefore , in this way the multi - class classification problem can be solved by distinguishing the above two classes . Moghaddam et al . proposed to model each of the two classes with a multivariate Gaussian distribution . Then , the subcategory conv layer consists of conv filters with one additional conv filter for a special “ background ” category . For multi - class detection ( e.g. , car , pedestrian , cyclist , etc . ) , the subcategories are the aggregation of all the subcategories from all the classes . These conv filters operate on the extrapolated conv feature maps and output heat maps that indicate the confidences of the presence of objects in the input image . subsection : Multi - label classification In the multi - label classification setting , every node is assigned one or more labels from a finite set . During the training phase , we observe a certain fraction of nodes and all their labels . The question text is then used to compute the top - down attention , , task specific attention , for each object in the image . Multi - modal fusion is done through a simple Hadamard product followed by a multi - label classifier using a sigmoid activation function to predict the answer scores . Their performance reached 70.34 % on VQA 2.0 test - std split with an ensemble of 30 models trained with different seeds . In this paper , a modified Cyclostationary Feature Detection ( CFD ) algorithm based on softmax regression model is proposed , which targets for improving the sensing performance under low signal-to-noise ratio ( SNR ) . The softmax regression model provides excellent classification performance ; moreover , it is simple and runs fast compared with other classification algorithms in machine learning . We build a model architecture of multi-view convolutional neural network ( MV-CNN ) containing multiple networks to deal with three DMMs ( DMMf , DMMs , DMMt ) . The output of full-connected layer under each view is integrated as feature representation , which is then learned in the last softmax regression layer to predict human actions . Experimental results on MSR-Action3D dataset and UTD-MHAD dataset indicate that the proposed approach achieves state-of-the-art recognition performance and is appropriate for real-time recognition . In this paper , we formulate the generalized softmax learning ( GSL ) problem , as a symmetric extension of the softmax regression problem . We further study the geometric structure of GSL and demonstrate the equivalence of GSL and the original softmax regression problem . Besides , this geometric structure indicates the symmetry between a neural network and its reverse network , and the symmetric roles of the weights and feature in a neural network . Joint distribution of the global ( scene ) and local ( face ) features is modeled using long short-term memory networks . This joint distribution is converted into class scores using softmax regression-based model . Inspired by its excellent performance in extracting universal and discriminative features , in this paper , we propose a deep learning approach for realizing DFLAR . Specifically , we design a sparse autoencoder network to automatically learn discriminative features from the wireless signals and merge the learned features into a softmax-regression-based machine learning framework to realize location , activity , and gesture recognition simultaneously . Extensive experiments performed in a clutter indoor laboratory and an apartment with eight wireless nodes demonstrate that the DFLAR system using the learned features could achieve 0.85 or higher accuracy , which is better than the systems utilizing traditional handcraft features . In our proposed network architecture , we first model the randomness of aging with the Gaussian distribution which is used to calculate the Gaussian integral of an age interval . Then , we present a soft softmax regression function used in the network . The new function applies the aging modeling to compute the function loss . In the current SoftMax regression algorithm model , a linear combination of features is used , and the resulting separated hyperplane belongs to a linear model . Aiming at the nonlinear characteristics of text categorization , an improved nonlinear SoftMax regression algorithm is proposed . This paper demonstrates an implementation of k-means clustering and softmax regression classification for movie recommendation based on the hetrec2011-movielens-2k dataset . Root-MeansSquare Error ( RMSE ) is used for evaluation of results . The framework constructs a feature learning network ( e.g. a CNN ) to project the face images into a target representation space , and the network is trained towards the goal that the set covariance matrix calculated in the target space has maximum discriminative ability . To encode the discriminative ability of set covariance matrices , we elaborately design two different loss functions , which respectively lead to two different representation learning schemes , i.e. , the Graph Embedding scheme and the Softmax Regression scheme . Both schemes optimize the whole network containing both image representation mapping and set model classification in a joint learning manner . Previous explanations for adversarial examples invoked hypothesized properties of neural networks , such as their supposed highly non - linear nature . Our hypothesis based on linearity is simpler , and can also explain why softmax regression is vulnerable to adversarial examples . section : Linear perturbation of non - linear models We can thus view weight decay as being more “ worst case ” than adversarial training , because it fails to deactivate in the case of good margin . If we move beyond logistic regression to multiclass softmax regression , weight decay becomes even more pessimistic , because it treats each of the softmax ’s outputs as independently perturbable , when in fact it is usually not possible to find a single that aligns with all of the class ’s weight vectors . Weight decay overestimates the damage achievable with perturbation even more in the case of a deep network with multiple hidden units . Results from this experiment are shown in Table [ reference ] . Nearly all of the parameters of the deep fried network reside in the final softmax regression layer , which still uses a dense linear transformation , and accounts for more than 99 % of the parameters of the network . This is a side effect of the large number of classes in ImageNet . Application examples are given using data from a longitudinal study of domestic violence . It is illustrated that CFA is able to yield results that are not redundant with results from log-linear modeling or multinomial regression . It is concluded that CFA is particularly useful in the context of person-oriented research . Furthermore the oxygenation process and which factors play a role in a membrane oxygenator were investigated . The second section entails development of an IPK control system and an oxygenator model based on multivariate polynomial regression . The developed prototype IPK control system was able to pump a kidney at a desired pressure pattern and has been used in a multitude of IPK experiments . In total , 1288 vignettes were judged . Multinomial regression analysis showed that Weight Loss , Trauma , and Nocturnal Pain are the three most significant predictive variables . A decision tree was generated that showed the same conclusion . These variables are used to estimate MOS in a reliable and robust way . We compare three techniques such as Artificial Neural Networks ( ANN ) , Factor Analysis ( FA ) and Multinomial Linear Regression , at different time scales and with Full Reference and Non Reference approaches . We carry out a performance evaluation of these techniques , concluding that the behavior of MOS estimation based on FA is more accurate , unless we had a lossless scenario related to Guaranteed Bit Rate services , where ANN performs better . This article introduces a straightforward framework of sentiment-sufficient dimension reduction for text data . Multinomial inverse regression is introduced as a general tool for simplifying predictor sets that can be represented as draws from a multinomial distribution , and we show that logistic regression of phrase counts onto document annotations can be used to obtain low-dimensional document representations that are rich in sentiment information . To facilitate this modeling , a novel estimation technique is developed for multinomial logistic regression with very high-dimensional response . We present a novel approach for probabilistic clustering of white matter fibre pathways using curve-based regression mixture modelling techniques in 3D curve space . The clustering algorithm is based on a principled method for probabilistic modelling of a set of fibre trajectories as individual sequences of points generated from a finite mixture model consisting of multivariate polynomial regression model components . Unsupervised learning is carried out using maximum likelihood principles . The course will present a number of model-estimation methods that are used in transportation data analysis and other subject areas that deal with data analysis . The students will be able to utilize various model development techniques discussed in the class in a number of applications such as ( 1 ) statistical model development , ( 2 ) multinomial regression estimation with examining various properties , ( 3 ) cross-sectional and panel data analysis , ( 4 ) ordinary least squares and maximum likelihood estimation , ( 5 ) time series analysis , ( 6 ) cluster analysis , ( 7 ) simultaneous model estimation techniques , and ( 8) discrete choice models . Econometric methods are vital to travel demand model development , travel behavior analysis , traffic safety studies , and economic decision making . Following the usage-based assumption that linguistic knowledge is both item-specific and schematic in nature and based on recent psycholinguistic work showing learners ' difficulties to produce native-like constructions ( Ellis and Sagarra 2011 ) , this study proposes a multifactorial way of exploring learners ' knowledge of constructions at concrete and schematic levels , simultaneously . Specifically , 1903 constructions are investigated using a comprehensive corpus annotation scheme and multinomial regression modelling . This work reveals different patterns of central tendency of constructions across IL and native English . We develop fast algorithms for estimation of generalized linear models with convex penalties . The models include linear regression , two-class logistic regression , and multinomial regression problems while the penalties include ℓ(1 ) ( the lasso ) , ℓ(2 ) ( ridge regression ) and mixtures of the two ( the elastic net ) . The algorithms use cyclical coordinate descent , computed along a regularization path . A set of available data for different operating conditions is used to empirically determine the parameters of this model and a different set of test data is used to verify its predictive accuracy . This DC model is used to express the drain current as a single multivariate regression polynomial with its validity spanning across different possible operating regions as long as the chosen independent variables lie within the range of data set used to develop the model . The continuity of the polynomial model and its derivatives makes it particularly suitable for implementation in a circuit simulator . GUESS simply selects the modal answer from the training set for each of 4 question types . VIS + BOW performs multinomial logistic regression based on image features and a BOW vector obtained by summing all the word vectors of the question . VIS + LSTM has one LSTM to encode the image and question , while 2 - VIS + BLSTM has two image feature inputs , at the start and the end . subsection : Objective function Our networks maximize the multinomial logistic regression objective , which is equivalent to minimizing the average across training cases of the cross - entropy between the true label distribution and the model ’s predicted label distribution . subsection : Weight initialization ( 6 ) The first sum is the objective function of a multinomial logistic regression problem with input - target pairs ( ĝi , ei ) . This objective falls back to the transformation - free instance classification problem L ( X ) = One of the well-known data balancing technique is the artificial oversampling , which increase the size of datasets . In this research , multinomial classification was applied to classify some recorded features obtained from a single ECG ( electrocardiograph ) sensor . Therefore , a Dirichlet process , a dirichlet distribution of cumulative distribution function of each data partition , was needed to model the distribution of the new generated data by also considering the statistical properties of the previous data . In discrete models , prediction of a targetgene value is given via a function of some predictor-gene values . This function is a multinomial classifier . Expression-based microarrays phenotype classification requires designing a classifier that takes a vector of gene expression levels as input and outputs a class label to predict the class containing the input vector . Predicting crime patterns is a significant task to develop more efficient strategies either to prevent crimes or to improve the investigation efforts . In this research , we use machine learning techniques to solve a multinomial classification problem where the goal is to predict the crime categories with spatiotemporal data . As a case study , we use San Francisco crime data from San Francisco Police Department ( SFPD ) . The semi-trained crossbar architecture is applicable to a broad class of neural networks . System level verification is performed with an extreme learning machine for binomial and multinomial classification . The total power for a single 4 × 4 layer network , when implemented in IBM 65 nm node , is estimated to be ≈42.16μW and the area is estimated to be 26.48μm × 22.35μm . Classification is a popular technique used to predict group membership for data samples in datasets . A multi-class or multinomial classification is the problem of classifying instances into more than two classes . With the emerging technology , the complexity of multi-class data has also increased thereby leading to class imbalance problem . We also used this method not only for binary but also multinomial categorization and empirically validate the ability of metrics to predict fault prone classes in different category using fault data . We conclude that this proposed metric is as effective as the traditional metrics in identifying fault-prone classes in binary categorization and also showing most efficient result for multinomial categorization . We also find that Univariate model for these metrics have same performance as the individual metric with no any learning technique in prediction of fault-proneness . Depending on the number of defects , class level information is classified into one of three defined multiclass class 0 , class 1 , and class 2 . RESULTS & CONCLUSION : Major outcome of the paper concludes that multinomial/multiclass classification is applicable on cross project data and has comparable results to within project defect data .
Instead , one mathematically ensures that the fewest possible assumptions about unmeasured data are made by choosing the spectrum that maximizes the entropy for the process . The use of the maximum entropy approach to spectral analysis was introduced by Burg [ 1 ] . In this correspondence , the authors derive the maximum-entropy spectrum by obtaining a spectrum that is forced to maximize the entropy of a stationary random process .
MaxEnt is a popular maximum entropy-based algorithm originally developed for modelling species distribution , but increasingly used for land-cover classification . In this article , we used MaxEnt as a single-class land-cover classification and explored if recommended procedures for generating high-quality species distribution models also apply for generating high-accuracy land-cover classification .
To solve a class of non-differentiable multi-objective optimization problems , this paper proposed a new method called maximum-entropy social cognitive optimization algorithm . First , used the maximum-entropy function , transformed the constrained non-differentiable multi-objective optimization problem to the approximation unconstrained differentiable optimization problem , then used the social cognitive optimization algorithm to solve this problem . The algorithm was based on social cognitive theory , through a series of learning agents to simulate human social and intelligent thereby completing the optimization of the target .
Recently , an alternative measure of total uncertainty in Dempster – Shafer theory of evidence ( DST ) has been proposed in place of the maximum entropy measure . It is based on the pignistic probability of a basic probability assignment and it is proved that this measure verifies a set of needed properties for such a type of measure .
The profilogram of FAE ( fuel-air explosive ) fuel explosion image is the important base to analyze the explosion process . In this article , the double peak method , the iteration method , the OTSU method , and the maximum entropy criterion method are respectively used to confirm the threshold , and extract and compare the profilograms of the FAE fuel explosion image , which could establish the base for the further experiment analysis .
We examine several entropic thresholding methods which are the most popular in the literature . These methods are minimum cross entropy , maximum entropy sum method , Renyi ’s entropy and Havrda&Charvat entropy . We perform experiments for demonstrating the effectiveness of the examined methods on image thresholding . .
At the microscopic level , the evolution of the knowledge base is divided into the iterative sequence of the enterprisepsilas knowledge basepsilas border in the information-flow process and the process is modeled with the help of the fractal theory . At the macroscopic level , the correlation is discussed among the information output of the enterprises as the information sources and the entropy character of the knowledge base evolution , by making use of the information-flow cycle with the maximum entropy equation . The conclusion can be reference for the knowledge base of the techno-innovation process and the management of the enterprisespsila knowledge .
First , based on the global distance of evidence and the global belief entropy , the α value of IOWA is obtained . Simultaneously , a weight vector is given based on the maximum entropy method model . Then , according to IOWA operator , the evidence are modified before applying the Dempster ’s combination rule .
The system employs a machine-learning technique to classify joint stiffness . A maximum-entropy-rate method is developed to select the most relevant features . Experimental results demonstrate that distance travelled and energy expended can be estimated from observed changes in knee and ankle motions during 5-km runs .
The aim of this paper is to compare , in the domain of the Bearings-only Target Motion Analysis ( BTMA ) with two observers , three approaches in terms of tracking performances : the Interacting Multiple Models ( IMM ) based on the Extended Kalman Filtering , the Hidden Markov Models ( HMM ) and the approximated densities filtering based on the maximum of entropy .
Second , we reinterpret and adjust the standard vae objective , which we argue is over - regularized . We draw connections between the learning algorithm resulting from our proposed regularization and the information - bottleneck principle and maximum - entropy discrimination . The result is a recipe that makes vaes practical solutions to this important problem .
Xing et al . proposed two algorithms named LDLogitBoost and AOSO - LDLogitBoost to learn general models to relax the maximum entropy model in traditional LDL methods . Furthermore , He et al . generated age label distributions through weighted linear combination of the input image ’s label and its context - neighboring samples .
Firstly , due to the soft clustering , entropy alone could be maximised trivially by setting all prediction vectors to uniform distributions , resulting in no clustering . This is corrected by the conditional entropy component , which encourages deterministic one - hot predictions . For example , even for the degenerate case of identical pairs , the IIC objective encourages a deterministic clustering function ( i.e. is a one - hot vector ) as this results in null conditional entropy .
However , the regularization term K ( p gen ) in the training objective ( 1 ) requires the generator distribution . Faced with this problem , we focus on the max - entropy formulation , and exploit two different approximations of the regularization term K ( p gen ) = −H ( p gen ) . section : NEAREST - NEIGHBOR ENTROPY GRADIENT APPROXIMATION
For practical reasons we only consider the first two polynomials , that is , the first two moments : mean and covariance . The Gaussian is the maximum entropy distribution for given mean and covariance , therefore we assume the coding units to follow a multidimensional Gaussian . The difference of two Gaussians ( synthetic and real - world images ) is measured by the Fréchet distance also known as Wasserstein - 2 distance .
Consequently , the distance between samples and model ’s boundary can be enlarged accordingly , so that significant perturbations are required to fool the model . Then , based on the distance comparison , we propose a two-step classification algorithm that performs efficiently for multi-class classification . DunDi can not only build and train a new customized model but also support the incorporation of the available pre-trained neural network models to take full advantage of their capabilities .
Abstract This paper presents a laboratory study of multi-class classification problem for multiple indoor air contaminants which belongs to a completely linear-inseparable case . Six kinds of indoor air contaminations ( formaldehyde , benzene , toluene , carbon monoxide , ammonia and nitrogen dioxide ) were recognized as indicators of air quality in this project .
However , random forests are black-box ensemble models which lack a capability of explanation for the reasoning behind their prediction . Therefore , in this paper , we define a rule extraction algorithm named ExtractingRuleRF to derive an interpretable refined classification rule set from a random forest for a multi-class data classification task . The proposed algorithm follows a greedy approach with two phases : rule refinement and rule extraction .
The method of multi-class classification based support vector machines is researched . After comparing some common multi-class SVMS , and proposes a multi-class classified method based on similar binary tree . The constructing algorithm of similar binary tree is given and its effectivity is discussed .
Voxel-level fitting of the MRI data was performed on the classical mono-exponential model , and four anomalous diffusion models , namely , the stretched exponential model , the sub-diffusion model , the continuous time random walk model and the fractional Bloch-Torrey equation . The performance of the anomalous diffusion parameters for differentiating the three-concentric layers of tumour tissue ( i.e. , core ; intermediate zone ; peripheral and hyper-vascularised tumour layer ) was evaluated with multinomial logistic regression and multi-class classification analysis . We found that parameter ( \alpha ) from the stretched exponential model , parameter ( \beta ) from the subdiffusion model and parameter ( \beta ) from the continuous time random walk model provide a clear delineation of the three layers of tumour tissue .
On the other hand , label ambiguity can also happen if we are not confident in the labels we provide for an image . In the multi - label classification task , some objects are clearly visible but difficult to recognize . This type of objects are annotated as Difficult in the PASCAL Visual Object Classes ( VOC ) classification challenge , e.g. , the chair in the third image of the first row in Fig .
Intuitively , encodes a vector of latent features derived from the concatenation of both graph and node features , and can be used to predict the label of the th node . For multi - class classification , we can decode using the softmax activation function to learn a probability distribution over node labels . More precisely , we predict node labels via the following transformation : , where and .
Accordingly , two classes of variations can be defined : the intrapersonal variations and the extrapersonal variations . Therefore , in this way the multi - class classification problem can be solved by distinguishing the above two classes . Moghaddam et al . proposed to model each of the two classes with a multivariate Gaussian distribution .
Then , the subcategory conv layer consists of conv filters with one additional conv filter for a special “ background ” category . For multi - class detection ( e.g. , car , pedestrian , cyclist , etc . ) , the subcategories are the aggregation of all the subcategories from all the classes . These conv filters operate on the extrapolated conv feature maps and output heat maps that indicate the confidences of the presence of objects in the input image .
subsection : Multi - label classification In the multi - label classification setting , every node is assigned one or more labels from a finite set . During the training phase , we observe a certain fraction of nodes and all their labels .
The question text is then used to compute the top - down attention , , task specific attention , for each object in the image . Multi - modal fusion is done through a simple Hadamard product followed by a multi - label classifier using a sigmoid activation function to predict the answer scores . Their performance reached 70.34 % on VQA 2.0 test - std split with an ensemble of 30 models trained with different seeds .
In this paper , a modified Cyclostationary Feature Detection ( CFD ) algorithm based on softmax regression model is proposed , which targets for improving the sensing performance under low signal-to-noise ratio ( SNR ) . The softmax regression model provides excellent classification performance ; moreover , it is simple and runs fast compared with other classification algorithms in machine learning .
We build a model architecture of multi-view convolutional neural network ( MV-CNN ) containing multiple networks to deal with three DMMs ( DMMf , DMMs , DMMt ) . The output of full-connected layer under each view is integrated as feature representation , which is then learned in the last softmax regression layer to predict human actions . Experimental results on MSR-Action3D dataset and UTD-MHAD dataset indicate that the proposed approach achieves state-of-the-art recognition performance and is appropriate for real-time recognition .
In this paper , we formulate the generalized softmax learning ( GSL ) problem , as a symmetric extension of the softmax regression problem . We further study the geometric structure of GSL and demonstrate the equivalence of GSL and the original softmax regression problem . Besides , this geometric structure indicates the symmetry between a neural network and its reverse network , and the symmetric roles of the weights and feature in a neural network .
Joint distribution of the global ( scene ) and local ( face ) features is modeled using long short-term memory networks . This joint distribution is converted into class scores using softmax regression-based model .
Inspired by its excellent performance in extracting universal and discriminative features , in this paper , we propose a deep learning approach for realizing DFLAR . Specifically , we design a sparse autoencoder network to automatically learn discriminative features from the wireless signals and merge the learned features into a softmax-regression-based machine learning framework to realize location , activity , and gesture recognition simultaneously . Extensive experiments performed in a clutter indoor laboratory and an apartment with eight wireless nodes demonstrate that the DFLAR system using the learned features could achieve 0.85 or higher accuracy , which is better than the systems utilizing traditional handcraft features .
In our proposed network architecture , we first model the randomness of aging with the Gaussian distribution which is used to calculate the Gaussian integral of an age interval . Then , we present a soft softmax regression function used in the network . The new function applies the aging modeling to compute the function loss .
In the current SoftMax regression algorithm model , a linear combination of features is used , and the resulting separated hyperplane belongs to a linear model . Aiming at the nonlinear characteristics of text categorization , an improved nonlinear SoftMax regression algorithm is proposed .
This paper demonstrates an implementation of k-means clustering and softmax regression classification for movie recommendation based on the hetrec2011-movielens-2k dataset . Root-MeansSquare Error ( RMSE ) is used for evaluation of results .
The framework constructs a feature learning network ( e.g. a CNN ) to project the face images into a target representation space , and the network is trained towards the goal that the set covariance matrix calculated in the target space has maximum discriminative ability . To encode the discriminative ability of set covariance matrices , we elaborately design two different loss functions , which respectively lead to two different representation learning schemes , i.e. , the Graph Embedding scheme and the Softmax Regression scheme . Both schemes optimize the whole network containing both image representation mapping and set model classification in a joint learning manner .
Previous explanations for adversarial examples invoked hypothesized properties of neural networks , such as their supposed highly non - linear nature . Our hypothesis based on linearity is simpler , and can also explain why softmax regression is vulnerable to adversarial examples . section : Linear perturbation of non - linear models
We can thus view weight decay as being more “ worst case ” than adversarial training , because it fails to deactivate in the case of good margin . If we move beyond logistic regression to multiclass softmax regression , weight decay becomes even more pessimistic , because it treats each of the softmax ’s outputs as independently perturbable , when in fact it is usually not possible to find a single that aligns with all of the class ’s weight vectors . Weight decay overestimates the damage achievable with perturbation even more in the case of a deep network with multiple hidden units .
Results from this experiment are shown in Table [ reference ] . Nearly all of the parameters of the deep fried network reside in the final softmax regression layer , which still uses a dense linear transformation , and accounts for more than 99 % of the parameters of the network . This is a side effect of the large number of classes in ImageNet .
Application examples are given using data from a longitudinal study of domestic violence . It is illustrated that CFA is able to yield results that are not redundant with results from log-linear modeling or multinomial regression . It is concluded that CFA is particularly useful in the context of person-oriented research .
Furthermore the oxygenation process and which factors play a role in a membrane oxygenator were investigated . The second section entails development of an IPK control system and an oxygenator model based on multivariate polynomial regression . The developed prototype IPK control system was able to pump a kidney at a desired pressure pattern and has been used in a multitude of IPK experiments .
In total , 1288 vignettes were judged . Multinomial regression analysis showed that Weight Loss , Trauma , and Nocturnal Pain are the three most significant predictive variables . A decision tree was generated that showed the same conclusion .
These variables are used to estimate MOS in a reliable and robust way . We compare three techniques such as Artificial Neural Networks ( ANN ) , Factor Analysis ( FA ) and Multinomial Linear Regression , at different time scales and with Full Reference and Non Reference approaches . We carry out a performance evaluation of these techniques , concluding that the behavior of MOS estimation based on FA is more accurate , unless we had a lossless scenario related to Guaranteed Bit Rate services , where ANN performs better .
This article introduces a straightforward framework of sentiment-sufficient dimension reduction for text data . Multinomial inverse regression is introduced as a general tool for simplifying predictor sets that can be represented as draws from a multinomial distribution , and we show that logistic regression of phrase counts onto document annotations can be used to obtain low-dimensional document representations that are rich in sentiment information . To facilitate this modeling , a novel estimation technique is developed for multinomial logistic regression with very high-dimensional response .
We present a novel approach for probabilistic clustering of white matter fibre pathways using curve-based regression mixture modelling techniques in 3D curve space . The clustering algorithm is based on a principled method for probabilistic modelling of a set of fibre trajectories as individual sequences of points generated from a finite mixture model consisting of multivariate polynomial regression model components . Unsupervised learning is carried out using maximum likelihood principles .
The course will present a number of model-estimation methods that are used in transportation data analysis and other subject areas that deal with data analysis . The students will be able to utilize various model development techniques discussed in the class in a number of applications such as ( 1 ) statistical model development , ( 2 ) multinomial regression estimation with examining various properties , ( 3 ) cross-sectional and panel data analysis , ( 4 ) ordinary least squares and maximum likelihood estimation , ( 5 ) time series analysis , ( 6 ) cluster analysis , ( 7 ) simultaneous model estimation techniques , and ( 8) discrete choice models . Econometric methods are vital to travel demand model development , travel behavior analysis , traffic safety studies , and economic decision making .
Following the usage-based assumption that linguistic knowledge is both item-specific and schematic in nature and based on recent psycholinguistic work showing learners ' difficulties to produce native-like constructions ( Ellis and Sagarra 2011 ) , this study proposes a multifactorial way of exploring learners ' knowledge of constructions at concrete and schematic levels , simultaneously . Specifically , 1903 constructions are investigated using a comprehensive corpus annotation scheme and multinomial regression modelling . This work reveals different patterns of central tendency of constructions across IL and native English .
We develop fast algorithms for estimation of generalized linear models with convex penalties . The models include linear regression , two-class logistic regression , and multinomial regression problems while the penalties include ℓ(1 ) ( the lasso ) , ℓ(2 ) ( ridge regression ) and mixtures of the two ( the elastic net ) . The algorithms use cyclical coordinate descent , computed along a regularization path .
A set of available data for different operating conditions is used to empirically determine the parameters of this model and a different set of test data is used to verify its predictive accuracy . This DC model is used to express the drain current as a single multivariate regression polynomial with its validity spanning across different possible operating regions as long as the chosen independent variables lie within the range of data set used to develop the model . The continuity of the polynomial model and its derivatives makes it particularly suitable for implementation in a circuit simulator .
GUESS simply selects the modal answer from the training set for each of 4 question types . VIS + BOW performs multinomial logistic regression based on image features and a BOW vector obtained by summing all the word vectors of the question . VIS + LSTM has one LSTM to encode the image and question , while 2 - VIS + BLSTM has two image feature inputs , at the start and the end .
subsection : Objective function Our networks maximize the multinomial logistic regression objective , which is equivalent to minimizing the average across training cases of the cross - entropy between the true label distribution and the model ’s predicted label distribution . subsection : Weight initialization
( 6 ) The first sum is the objective function of a multinomial logistic regression problem with input - target pairs ( ĝi , ei ) . This objective falls back to the transformation - free instance classification problem L ( X ) =
One of the well-known data balancing technique is the artificial oversampling , which increase the size of datasets . In this research , multinomial classification was applied to classify some recorded features obtained from a single ECG ( electrocardiograph ) sensor . Therefore , a Dirichlet process , a dirichlet distribution of cumulative distribution function of each data partition , was needed to model the distribution of the new generated data by also considering the statistical properties of the previous data .
In discrete models , prediction of a targetgene value is given via a function of some predictor-gene values . This function is a multinomial classifier . Expression-based microarrays phenotype classification requires designing a classifier that takes a vector of gene expression levels as input and outputs a class label to predict the class containing the input vector .
Predicting crime patterns is a significant task to develop more efficient strategies either to prevent crimes or to improve the investigation efforts . In this research , we use machine learning techniques to solve a multinomial classification problem where the goal is to predict the crime categories with spatiotemporal data . As a case study , we use San Francisco crime data from San Francisco Police Department ( SFPD ) .
The semi-trained crossbar architecture is applicable to a broad class of neural networks . System level verification is performed with an extreme learning machine for binomial and multinomial classification . The total power for a single 4 × 4 layer network , when implemented in IBM 65 nm node , is estimated to be ≈42.16μW and the area is estimated to be 26.48μm × 22.35μm .
Classification is a popular technique used to predict group membership for data samples in datasets . A multi-class or multinomial classification is the problem of classifying instances into more than two classes . With the emerging technology , the complexity of multi-class data has also increased thereby leading to class imbalance problem .
We also used this method not only for binary but also multinomial categorization and empirically validate the ability of metrics to predict fault prone classes in different category using fault data . We conclude that this proposed metric is as effective as the traditional metrics in identifying fault-prone classes in binary categorization and also showing most efficient result for multinomial categorization . We also find that Univariate model for these metrics have same performance as the individual metric with no any learning technique in prediction of fault-proneness .
Depending on the number of defects , class level information is classified into one of three defined multiclass class 0 , class 1 , and class 2 . RESULTS & CONCLUSION : Major outcome of the paper concludes that multinomial/multiclass classification is applicable on cross project data and has comparable results to within project defect data .
Notes on maximum-entropy processing (Corresp.) Land-Cover Classification Using MaxEnt: Can We Trust in Model Quality Metrics for Estimating Classification Accuracy? Social cognitive optimization algorithm for class of non-differentiable multi-objective optimization problems Requirements for total uncertainty measures in Dempster–Shafer theory of evidence The Extraction of the FAE Image Profilogram Based on the Grey Level Thresholding A COMPARATIVE STUDY ON ENTROPIC THRESHOLDING METHODS Research on the evolution of enterprises’ knowledge space-time in the techno-innovation process under the network environment An Improved Evidential-IOWA Sensor Data Fusion Approach in Fault Diagnosis Maximum-Entropy-Rate Selection of Features for Classifying Changes in Knee and Ankle Dynamics During Running Bearings-only target motion analysis by estimation of densities Variational Autoencoders for Collaborative Filtering Deep Label Distribution Learning With Label Ambiguity Invariant Information Clustering for Unsupervised Image Classification and Segmentation Calibrating Energy-based Generative Adversarial Networks GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium DunDi: Improving Robustness of Neural Networks Using Distance Metric Learning Classification of multiple indoor air contaminants by an electronic nose and a hybrid support vector machine Extracting Rule RF in Educational Data Classification: From a Random Forest to Interpretable Refined Rules Multi-class Classifier Based on Support Vector Machines and Similar Binary Tree Investigation of changes in anomalous diffusion parameters in a mouse model of brain tumour Deep Label Distribution Learning With Label Ambiguity Learning to Make Predictions on Graphs with Autoencoders Person re-identification by Local Maximal Occurrence representation and metric learning Subcategory-Aware Convolutional Neural Networks for Object Proposals and Detection node2vec: Scalable Feature Learning for Networks Pythia v0.1: the Winning Entry to the VQA Challenge 2018 A modified cyclostationary spectrum sensing based on softmax regression model Real-time human action recognition using depth motion maps and convolutional neural networks The Geometric Structure of Generalized Softmax Learning Emotional sentiment analysis for a group of people based on transfer learning with a multi-modal system Device-Free Wireless Localization and Activity Recognition: A Deep Learning Approach Age Estimation Based on a Single Network with Soft Softmax of Aging Modeling Text Classification Research Based on Improved SoftMax Regression Algorithm Movie Recommendations from User Ratings Discriminative Covariance Oriented Representation Learning for Face Recognition with Image Sets Explaining and Harnessing Adversarial Examples Deep Fried Convnets Temporal Patterns of Variable Relationships in Person-Oriented Research: Prediction and Auto-Association Models of Configural Frequency Analysis Development of an IPK control system and oxygenator model Should I see a Healthcare Professional or can I perform Self-care: Self-Referral Decision Support for Patients with Low Back Pain Performance evaluation of different techniques to estimate subjective quality in live video streaming applications over LTE-Advance mobile networks Multinomial Inverse Regression for Text Analysis Probabilistic Clustering and Shape Modelling of White Matter Fibre Bundles Using Regression Mixtures Statistical and Econometric Methods for Transportation Data Analysis Towards an identification of prototypical non-native modal constructions in EFL: A corpus-based approach Regularization Paths for Generalized Linear Models via Coordinate Descent. DC modelling of SOI four-gate transistor (G4FET) for implementation in circuit simulator using multivariate regression polynomial Image Captioning and Visual Question Answering Based on Attributes and External Knowledge Improving neural networks by preventing co-adaptation of feature detectors Discriminative Unsupervised Feature Learning with Convolutional Neural Networks Maintaining imbalance highly dependent medical data using dirichlet process data generation The fundamental role of pattern recognition for gene-expression/microarray data in bioinformatics Predicting Metropolitan Crime Rates Using Machine Learning Techniques Semi-Trained Memristive Crossbar Computing Engine with In Situ Learning Accelerator Hellinger distance based oversampling method to solve multi-class imbalance problem Investigating the Effect of Object-oriented Metrics on Fault Proneness Using Empirical Analysis Prediction of Cross Project Defects using Ensemble based Multinomial Classifier
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