WO2014195782A2 - Differential evolution-based feature selection - Google Patents

Differential evolution-based feature selection Download PDF

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Publication number
WO2014195782A2
WO2014195782A2 PCT/IB2014/000939 IB2014000939W WO2014195782A2 WO 2014195782 A2 WO2014195782 A2 WO 2014195782A2 IB 2014000939 W IB2014000939 W IB 2014000939W WO 2014195782 A2 WO2014195782 A2 WO 2014195782A2
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features
variation factor
class variation
feature
class
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PCT/IB2014/000939
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English (en)
French (fr)
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WO2014195782A3 (en
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Kingshuk CHAKRAVARTY
Diptesh DAS
Aniruddha Sinha
Amit Konar
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Tata Consultancy Services Limited
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Publication of WO2014195782A3 publication Critical patent/WO2014195782A3/en

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    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00Measuring for diagnostic purposes; Identification of persons
    • A61B5/72Signal processing specially adapted for physiological signals or for diagnostic purposes
    • A61B5/7235Details of waveform analysis
    • A61B5/7264Classification of physiological signals or data, e.g. using neural networks, statistical classifiers, expert systems or fuzzy systems
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00Measuring for diagnostic purposes; Identification of persons
    • A61B5/24Detecting, measuring or recording bioelectric or biomagnetic signals of the body or parts thereof
    • A61B5/316Modalities, i.e. specific diagnostic methods
    • A61B5/369Electroencephalography [EEG]
    • GPHYSICS
    • G06COMPUTING OR CALCULATING; COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00Pattern recognition
    • G06F18/20Analysing
    • G06F18/21Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/211Selection of the most significant subset of features
    • G06F18/2111Selection of the most significant subset of features by using evolutionary computational techniques, e.g. genetic algorithms
    • GPHYSICS
    • G06COMPUTING OR CALCULATING; COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00Pattern recognition
    • G06F18/20Analysing
    • G06F18/21Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/211Selection of the most significant subset of features
    • G06F18/2115Selection of the most significant subset of features by evaluating different subsets according to an optimisation criterion, e.g. class separability, forward selection or backward elimination
    • GPHYSICS
    • G06COMPUTING OR CALCULATING; COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/08Feature extraction
    • GPHYSICS
    • G16INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16HHEALTHCARE INFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR THE HANDLING OR PROCESSING OF MEDICAL OR HEALTHCARE DATA
    • G16H50/00ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics
    • G16H50/20ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics for computer-aided diagnosis, e.g. based on medical expert systems

Definitions

  • the present subject matter relates, in general, to selection of features and particularly to selection of optimum features using differential evolution.
  • Objects such as people, materials, diseases, etc.
  • the identification and classification of the objects into the classes requires knowledge and information of object features which correlate with their types or characteristics.
  • the kno wn features can be used for the purposes of identification and classification of the objects.
  • Figure 1 illustrates a system environment implementing an optimum feature selection system, in accordance with an implementation of the present subject matter.
  • Figure 2 illustrates a method for selection of an optimum feature subset, in accordance with an implementation of the present subject matter.
  • Figure 3 illustrates a method for identification and classification of objects into classes using an optimum feature subset, in accordance with an implementation of the present subject matter.
  • feature selection refers to selection of a feature subset for identification and classification of objects into classes
  • the optimum feature subset is a feature subset having a number of independent features, substantially sufficient for identification and classification of objects into classes.
  • the identification and classification of objects into the different classes using features that characterize the objects is known.
  • data sets of the objects are gathered, and a plurality of features is extracted from the gathered data sets.
  • biometric data such as skeleton data
  • various gait features are extracted from the obtained biometric data.
  • the plurality of features extracted is mapped to various possible classes, which is then used to train a supervised learning algorithm, also referred to as classifier, for subsequent identification and classification of unknown objects into the classes.
  • the number of features extracted from the data sets of the objects is substantially large.
  • Some conventional classification methodologies utilize all the extracted features for the purpose of identification and classification of the objects. Such conventional methodologies thus require a large number of computational steps to identify and classify the objects, which makes them computationally expensive. Also, some of the extracted features may not be relevant or may be redundant for the classification of objects.
  • the extracted features which may not be relevant or may be redundant for the classification of objects, may contribute to misclassification of the objects.
  • a subset of features from the set of extracted features, is selected.
  • the selection of a subset of features using a classifier is also known. Conventionally, multiple random subsets of features are individually used in a classifier to identify an optimum feature subset, from amongst the subsets of features, which can identify and classify the objects. This optimum feature subset is then used to train the classifier to identify and classify the objects into the classes.
  • the feature selection technique is classifier dependent.
  • the present subject matter describes system(s) and method(s) for selection of optimum feature subset from a plurality of extracted features.
  • the selection of optimum feature subset in accordance with the present subject matter, is classifier independent.
  • For the selection of an optimum feature subset a plurality of features extracted from data sets associated with objects representing multiple classes is obtained. The obtained features are analyzed and an optimum feature subset is selected based on differential evolution process.
  • the selection of optimum feature subset is based on computation of an intra-class variation factor and an inter- class variation factor for a plurality of feature subsets.
  • the intra-class variation factor refers to variations of individual or combination of features within a class.
  • the inter- class variation factor refers to variations of individual or combination of features across multiple classes, i.e., variation of feature from one class with respect to another.
  • the intra- class variation factor is minimized and the inter-class variation factor is maximized using differential evolution process.
  • the differential evolution process refers to an optimization search process which iteratively generates a solution (for example, a feature subset) to a problem (for example, an objective function, a fitness function, etc.,) with regard to a given condition (for example, minimization, maximization, etc.).
  • a solution for example, a feature subset
  • a problem for example, an objective function, a fitness function, etc.,
  • a given condition for example, minimization, maximization, etc.
  • the methodology of present subject matter can be implemented for selection of an optimum feature subset, to identify and classify objects into different classes using the optimum feature subset.
  • the optimum feature subset With the optimum feature subset, the number of computations and size of storage space involved in the identification and classification stage is substantially less and the classification or recognition accuracy substantially improves.
  • the usage of the optimum feature subset also substantially reduces the runtime complexity of identifying and classifying the objects into the classes.
  • the methodology of the present subject matter may be implemented for people identification, where the objects may be individuals who are to be classified as distinct individuals.
  • the gait features extracted from skeleton data sets at different instances for the individuals, are obtained, and an optimum gait feature subset is selected based on differential evolution process of the present subject matter. The optimum gait feature subset is then used in a classifier for the classification of the individuals.
  • the methodology of the present subject matter may be implemented for classification of cognitive loads on individuals, where the objects may be cognitive loads to be classified in different classes.
  • the electroencephalography (EEG) features extracted from EEG signals at different instances for the individuals, are obtained, and an optimum EEG feature subset is selected based on differential evolution process of the present subject matter. The optimum EEG feature subset is then used in a classifier for the classification of the cognitive loads on the individuals.
  • the selection of the optimum feature subset does not involve a classifier and, thus, is independent of the classifier. This removes restrictions on the use of a particular classifier for which the optimum feature subset is obtained and which is trained to use the optimum feature subset for the identification and classification of the objects. Further, the optimum feature subset selected based on differential evolution by the minimization of intra- class variation factor and by the maximization of the inter-class variation factor is substantially accurate. With the optimum feature subset selection of the present subject matter, a substantially accurate identification and classification can be achieved.
  • FIG. 1 illustrates a system environment 100 implementing an optimum feature selection system 102, in accordance with an implementation of the present subject matter.
  • the optimum feature selection system 102 is hereinafter referred to as a system 102.
  • the system 102 can be implemented as a computing device, such as a laptop computer, a desktop computer, a notebook, a workstation, a mainframe computer, and the like.
  • the system 102 is enabled to select an optimum feature subset based on differential evolution process, in accordance with the present subject matter.
  • the system 102 includes processor(s) 104.
  • the processor(s) 104 may be implemented as one or more microprocessors, microcomputers, microcontrollers, digital signal processors, central processing units, state machines, logic circuitries, and /or any devices that manipulate signals based on operational instructions.
  • the processor(s) 104 is configured to fetch and execute computer-readable instructions stored in a memory.
  • the system 102 includes interface(s) 106.
  • the interface(s) 106 may include a variety of machine readable instruction-based and hardware-based interfaces that allow the system 102 to communicate with other devices, including servers, data sources, and external repositories. Further, the interface(s) 106 may enable the system 102 to communicate with other communication devices, such as network entities, over a communication network.
  • the system 102 includes a memory 108.
  • the memory 108 may be coupled to the processor(s) 104.
  • the memory 108 can include any computer-readable medium known in the art including, for example, volatile memory, such as static random access memory (SRAM) and dynamic random access memory (DRAM), and/or non-volatile memory, such as read only memory (ROM), erasable read only memory (ROM), erasable programmable ROM, flash memories, hard disks, optical disks, and magnetic tapes.
  • volatile memory such as static random access memory (SRAM) and dynamic random access memory (DRAM)
  • non-volatile memory such as read only memory (ROM), erasable read only memory (ROM), erasable programmable ROM, flash memories, hard disks, optical disks, and magnetic tapes.
  • the system 102 includes module(s) 110 and data 112.
  • the module(s) 110 and the data 112 may be coupled to the processor(s) 104.
  • the modules 1 10, amongst other things, include routines, programs, objects, components, data structures, etc., which perform particular tasks or implement particular abstract data types.
  • the modules 1 10 may also be implemented as, signal processor(s), state machine(s), logic circuitries, and /or any other device or component that manipulate signals based on operational instructions.
  • the data 1 12 serves, amongst other things, as a repository for storing data that may be fetched, processed, received, or generated by the module(s) 1 10.
  • the data 112 is shown internal to the system 102, it may be understood that the data 1 12 can reside in an external repository (not shown in the Figure), which may be coupled to the system 102.
  • the system 102 may communicate with the external repository through the interface(s) 106.
  • the module(s) 1 10 can be implemented in hardware, as instructions executed by a processing unit, or by a combination thereof.
  • the processing unit can comprise a computer, a processor, a state machine, a logic array or any other suitable devices capable of processing instructions.
  • the processing unit can be a general-purpose processor which executes instructions to cause the general- purpose processor to perform the required tasks or, the processing unit can be dedicated to perform the required functions.
  • the module(s) 1 10 may be machine-readable instructions (software) which, when executed by a processor/processing unit, perform any of the desired functionalities.
  • the machine-readable instructions may be stored on an electronic memory device, hard disk, optical disk or other machine-readable storage medium or non-transitory medium.
  • the machine-readable instructions can also be downloaded to the storage medium via a network connection.
  • the module(s) 1 10 include a differential evolution feature selection (DEFS) module 114, and other module(s) 116.
  • the other module(s) 1 16 may include programs or coded instructions that supplement applications or functions performed by the system 102.
  • the data 1 12 includes feature data 120, fitness function data 122, optimum feature data 124, and other data 126.
  • the other data 126 amongst other things, may serve as a repository for storing data that is processed, received, or generated as a result of the execution of one or more modules in the module(s) 1 10.
  • the system 102 is coupled to a data source 130 to obtain a plurality of features for the selection of an optimum feature subset.
  • the data source 130 refers to an entity that has the data associated with the plurality of features extracted from data sets for multiple objects representing different classes.
  • the system 102 is coupled to a classifier 132 for classification of objects under the classes using the optimum feature subset.
  • the classifier 132 may be trained for the optimum feature subset over different classes and, subsequently, used for the classification of unknown objects using the optimum feature subset.
  • the DEFS module 114 obtains the plurality of features from the data source 130.
  • the features are extracted from data sets of objects representing multiple classes, taken at multiple instances of time.
  • the data associated with plurality of features is stored in the feature data 120.
  • g is the size of data sets taken for class 1.
  • class 2 (2) where w is the size of data sets taken for class 2.
  • (x ⁇ ,)! denotes the value of the feature d p extracted at w th instance for class 2.
  • ( ⁇ ⁇ ) denotes the value of the feature d p extracted at t th instance for class c.
  • the DEFS module 1 14 may normalize the values of each of the plurality of features to zero mean and unit covariance. With this, the values of the features are substantially scaled for subsequent processing.
  • the DEFS module 1 14 identifies an optimum feature subset based on a differential evolution process, such that the intra-class variation factor is minimum and the inter-class variation factor is maximum.
  • the description below describes the procedure followed for identification of the optimum feature subset based on different evolution process.
  • a population set comprising multiple parameter vectors for the different evolution process is formulated.
  • Each of the parameter vectors comprises a feature subset and a Lagrange's multiplier ⁇ .
  • the feature subset represents and is indicative of features selected from amongst all the features obtained by the DEFS module 1 14.
  • Each feature subset may have a set of features randomly selected from all of the obtained features.
  • the Lagrange's multiplier ⁇ is obtained from a range determined by a ratio of an inter-class variation factor and an intra-class variation factor of each of the features. The procedure of obtaining the Lagrange's multiplier ⁇ is described later in the description.
  • each feature subset is in the form of a binary encoded decimal (BED) pattern indicative of those features which are selected to be a part of the feature subset.
  • the BED pattern is of a size equal to the number of feature obtained by the DEFS module 114.
  • the BED pattern is represented as a binary bit pattern, with the number of bits equal to the number of features obtained, where each bit corresponds to one feature and the value of the bits indicate the selection or the non-selection of the features in the feature subset.
  • the 1 's in the BED pattern represent the features which are selected to be the part of the feature subset and the 0's represent the features which are not selected to be the part of the feature subset.
  • each feature subset is a BED pattern of p bits.
  • the BED pattern for a feature subset may be ' 101 101100100 ⁇ . This indicates that the features ⁇ di, d 3 , d4, d 6 , d 7 , d 10 , d 13 ⁇ are selected to be the part of that feature subset.
  • the population set for the differential evolution includes N number of feature subsets, where N is usually at least three times the number of the obtained features p, i.e., N > 3*p. For example, if the total number of obtained features is 5, the total number of feature subsets N is at least equal to 15. N also denotes the number of parameter vectors in the population set.
  • a range of upper limits of the Lagrange's multiplier ⁇ is determined. For this, the intra-class variation factor and inter-class variation factor for each of the features is computed. The intra-class variation factor of the each feature is divided by the inter- class variation factor of the same feature to obtain the upper limit of the Lagrange's multiplier ⁇ for that feature.
  • the upper limit of the Lagrange's multiplier ⁇ for the j th feature is given by equation (4) below:
  • IntraVar ⁇ - C m+ i)f
  • k governs the data set at the k th instance, i.e., k th datapoint
  • i governs the class
  • c total number of classes
  • n size of data sets in class i
  • j governs the feature for which the intra-class variation factor is to be calculated.
  • InterVar j is the inter-class variation factor of the j th fea and is given by the equation (6) below:
  • k governs the data set at the k instance, i.e., k datapoint
  • i governs the class
  • c total number of classes
  • n size of data sets in class i
  • j governs the feature for which the inter-class variation factor is to be calculated.
  • the upper limits of the Lagrange's multiplier ⁇ ⁇ 5 ⁇ 2 . .. ⁇ ⁇ for all the p features are obtained.
  • the lower limits of the Lagrange's multiplier for the features are considered as significantly small values, let' say epsilon where epsilon is near equal to zero.
  • the Lagrange's multiplier for the parameter vectors are determined.
  • the Lagrange's multiplier for each parameter vector is determined as a random value between the range of lower limits and the range of upper limits as obtained above.
  • the BED pattern for each of the parameter vectors is randomly generated initially.
  • the total number of feature subsets that can be represented using the BED pattern is 2 4 -l, i.e., the range of the BED patterns is from '0001 ' to ⁇ 1 1 .
  • the population set has at least 12 parameter vectors with the BED patterns randomly generated and selected from within the range of possible BED patterns.
  • the BED pattern for the each of the parameter vectors is uniformly randomly generated initially.
  • the 12 BED patterns for the population set are initially generated and selected randomly from within different ranges within ⁇ 00 and ⁇ 11 .
  • the BED patterns selected uniformly may be from different ranges of '0001 ' to '0011 ', '0100' to ⁇ ⁇ ⁇ ', ' 1000' to ' 101 1 ' and ' 1100' to ' 11 1 1'.
  • a fitness function, denoted by J is formulated based on the intra- class variation factor, inter-class variation factor, and the Lagrange's multiplier.
  • the fitness function J is given by equation (9):
  • intra-class variation factor and inter-class variation factor for the each of the feature subsets, in the population set is computed to compute the value of fitness function.
  • the intra-class variation factor for the each of the feature subset is computed using the values of features, as represented by equations (1) to (3), in equation (10) below:
  • IntraVar "
  • the inter-class variation factor for the each of the feature subset is computed using the values of features, as represented by equations (1) to (3), in equation ( 1 1 ) below:
  • k governs the data set at the k instance
  • i governs the class
  • c total number of classes
  • n total size of data sets in class i
  • j governs the feature
  • p is total number of features.
  • j belongs to those features which are selected in the feature subset for which the inter-class variation is to be computed.
  • the intra-class variation factor of the optimum feature subset should be minimum. So the intra-class variation factor for the each of the feature subsets is to'be minimized. Also, the optimum feature subset of objects in each two classes should have minimum amount of similarities, the intra- class variation factor of the optimum feature subset should be maximum. So the inter- class variation factor for the each of the feature subsets is to be maximized. Since the intra-class variation factor has to be minimized and the inter-class variation factor has to be maximized for each of the feature subsets, the fitness function J given by equation (9) has to be minimized for the feature subsets. The feature subset, from amongst the feature subsets, which has minimum value of the fitness function J is considered as the optimum feature subset. The data related to the optimum feature subset is stored in the optimum feature data 124.
  • the DEFS module 114 follows the differential evolution process for the minimization of the fitness function of the feature subsets and, thereby, the identification of the optimum feature subset.
  • the differential evolution process involves four steps: initialization, mutation, recombination (also known as crossover), and selection.
  • a parameter vector from amongst the parameter vectors in the population set, is selected as a target vector.
  • the target vector be denoted by u m , where m may be from 1 to the number of feature subsets N (or the number of parameter vectors).
  • the BED pattern and the Lagrange's multiplier associated with the target vector u m be denoted by BED um and ⁇ ⁇ , respectively.
  • the mutation stage for the selected target . vector u m , three other parameter vectors u p , u q , and u r are randomly selected from amongst the population set such that p ⁇ q ⁇ r ⁇ m.
  • a donor vector v m is generated by adding a weighted difference of any two vectors, from amongst the parameter vectors u p , u q , and u r , to the remaining parameter vector as given by equation (14):
  • v m Up + m f *(u q - u r ) (14)
  • m f is mutation factor taking a value between 0 and 2.
  • the mutation factor controls the rate of evolution of the population set.
  • the mutation factor m f is 0.9.
  • a trial vector t m is generated, where each element of the trial vector t m is selected from the elements of the target vector u m or the donor vector v m , depending on value of a cross-over (CR) ratio.
  • the crossover ratio CR takes a value between 0 and 1. In an implementation, the crossover ratio CR is 0.7.
  • the trial vector t m is generated using equation (15) below:
  • rand(0,l) is a random number generator that generates a random number between 0 and 1.
  • the fitness function value of the trial vector t m is calculated and compared with the fitness function value for the target vector u m . If the fitness function value for the trial vector t m is a lower than that for the target vector u m , then the target vector u m and its corresponding fitness function value are replaced by the trial vector t m and its corresponding fitness value. Based on this revision, the target vector u m , the Lagrange's multiplier ⁇ ( ⁇ and the corresponding fitness function value are stored in the fitness function data 122. [0050] The above procedure of mutation, recombination, and selection is iteratively repeated for all the parameter vectors as the target vectors in the population set.
  • a new population set comprising the new set of target vectors as the parameter vectors and its corresponding fitness values are obtained.
  • the differential evolution process is again performed on the new population set in a manner as described above.
  • the differential evolution process is continued until a stopping criterion is reached.
  • the stopping criterion may be that the values of the fitness function J for the target vectors (or the parameter vectors) stops changing and has the minimum value.
  • the differential evolution process may be performed for a predefined number of times.
  • the optimum feature subset is identified. For this, the values of fitness function for all parameter vectors of population set are compared with each other to identify that parameter vector for which the fitness function value is minimum. The BED pattern associated with that identified parameter vector is considered as the optimum feature subset.
  • the DEFS module 1 14 selects the features in identified optimum feature subset as the optimum set of features. This optimum set of features is substantially sufficient for distinct identification and classification objects in different classes.
  • the data related to the optimum feature subset is stored in the optimum feature data 124.
  • the DEFS module 1 14 provides the optimum feature subset to the classifier 132 for training the classifier 132 for identification and classification of the objects into the classes.
  • the classifier 132 may include a supervised learning algorithm, such as a support vector machine, a naive bayes, a decision tree, linear discriminate analysis, a neural network, and the like.
  • the data source 130 that provides the plurality of features for the selection of the optimum feature subset, and the classifier 132 that receives the optimum feature subset from the system 102 for identification and classification of the objects into classes reside outside the system 102; it may be understood by a person skilled in the art that the system 102 may obtaining the data sets for objects under the classes from devices such as a skeleton recording device, an EEG acquisition device, and the like, extract the plurality of features from the obtained data sets, identify to select the optimum feature subset, and then classify the objects into classes using a classifier.
  • the system 102 may have modules, such as a data acquisition module, a feature extraction module, the DEFS module 114, and a classification module, coupled to the processor(s) 104.
  • Figure 2 illustrates a method for selection of an optimum feature subset, in accordance with an implementation of the present subject matter.
  • the method 200 can be implemented in the optimum feature selection system 102.
  • the order in which the method 200 is described is not intended to be construed as a limitation, and any number of the described method blocks can be combined in any order to implement the method 200, or any alternative methods. Additionally, individual blocks may be deleted from the method 200 without departing from the spirit and scope of the subject matter described herein.
  • the method 200 can be implemented in any suitable hardware.
  • the method 200 may be described in the general context of computer executable instructions.
  • computer executable instructions can include routines, programs, objects, components, data structures, procedures, modules, functions, etc., that perform particular functions or implement particular abstract data types.
  • the method 200 may be implemented in any computing device; in an example described in Figure 2, the method 200 is explained in context of the aforementioned optimum feature selection system 102, for the ease of explanation.
  • a plurality of features extracted from data sets associated with objects representing multiple classes is obtained.
  • the features are obtained by the system 102 from the data source 130.
  • the data source 130 may obtain data sets for the objects representing multiple classes, and may extract the plurality of features from the obtained data sets.
  • the values of the plurality of features are normalized to zero mean and unit covariance.
  • a population set comprising of parameter vectors is formulated for a differential evolution process.
  • Each of the parameter vectors has a feature subset and a Lagrange's multiplier ⁇ .
  • the formulation of the population set is as described earlier in the description.
  • an intra-class variation factor and an inter-class variation factor for multiple feature subsets are computed.
  • the multiple feature subsets are the feature subsets associated with the parameter vectors of the population set.
  • the intra-class variation factor and the inter-class variation factor for the feature subsets associated with the parameter vectors in the population set are computed as described earlier in the description. Using the intra-class variation factor, the inter-class variation factor and the Lagrange's multiplier, the values of the fitness function is obtained for the parameter vectors in the population set.
  • the optimum feature subset is identified, from amongst the multiple feature subsets, based on minimization of the intra-class variation factor and the maximization of the inter-class variation factor using differential evolution.
  • the multiple feature subsets are the feature subsets associated with the parameter vectors of the population set.
  • the minimization of the intra-class variation factor and the maximization of the inter- class variation factor are done through the differential evolution process as described earlier in the description and the optimum feature subset is based on the feature subset having minimum value of the fitness function.
  • the features in the identified optimum feature subset are selected as the optimum features for further processing.
  • the method 200 may include one of obtaining data sets for the objects representing multiple classes, extracting the plurality of features from the obtained data sets, classifying the objects into the classes based on the optimum feature subset, and a combination thereof.
  • Figure 3 illustrates a method 300 for identification and classification of objects into classes using an optimum feature subset, in accordance with an implementation of the present subject matter.
  • the method 300 can be implemented in the optimum feature selection system 102.
  • the order in which the method 300 is described is not intended to be construed as a limitation, and any number of the described method blocks can be combined in any order to implement the method 300, or any alternative methods. Additionally, individual blocks may be deleted from the method 300 without departing from the spirit and scope of the subject matter described herein.
  • the method 300 can be implemented in any suitable hardware.
  • the method 300 may be described in the general context of computer executable instructions.
  • computer executable instructions can include routines, programs, objects, components, data structures, procedures, modules, functions, etc., that perform particular functions or implement particular abstract data types.
  • data sets for the objects representing multiple classes are obtained from a data acquisition device.
  • the data acquisition device may be a skeleton recording device, an EEG acquisition device, and the like, depending on the application for which the method 300 is applied.
  • the data set may include skeleton points, of individuals, obtained using the skeleton recording device.
  • the data sets may include EEG signals, of the individuals, obtained using the EEG acquisition device.
  • a plurality of features is extracted from the data sets obtained at the block 302.
  • the plurality of features may include area-related gait features of the object, dynamic centroid distance-related gait features of the object, angle-related gait features of the object, other static and dynamic gait features of the object and a combination thereof, or the plurality of features may include EEG features.
  • the values of the plurality of features are normalized to zero mean and unit covariance.
  • an optimum feature subset is selected from amongst the plurality of features.
  • the optimum feature subset is identified and selected based on minimization of intra-class variation factor and maximization of inter-class variation factor for multiple feature subsets through differential evolution process, described earlier in the description.
  • a population set comprising of parameter vectors having feature subsets and Lagrange's multiplier ⁇ is formulated for a differential evolution process, as described earlier in the description.
  • a fitness function is formulated as described earlier in the description.
  • an intra-class variation factor and an inter-class variation factor for the feature subsets associated with the parameter vectors in the population set are computed as described earlier in the description.
  • the values of the fitness function is obtained for the parameter vectors in the population set.
  • the differential evolution process is iteratively performed on the population set to minimize the intra-class variation factor and maximizing the inter-class variation factor for each of the feature sub-sets.
  • the differential evolution process is iteratively carried out till a stopping criterion is reached as explained in the description earlier.
  • the optimum feature subset is selected based on the feature subset having minimum value of the fitness function.
  • the features in the identified optimum feature subset are selected as the optimum features for further processing.
  • the objects are classified into classes based on the optimum feature subset.
  • a classifier is used.
  • the classifier may include a supervised learning algorithm, such as a support vector machine, a naive bayes, a decision tree, linear discriminate analysis, a neural network, and the like.

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