BITS Faculty Publications
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Item Improved universum twin support vector machine(IEEE, 2018) Richhariya, BharatUniversum based learning provides prior information about data in the optimization problem of support vector machine (SVM). Universum twin support vector machine (UTSVM) is a computationally efficient algorithm for classification problems. It solves a pair of quadratic programming problems (QPPs) to obtain the classifier. In order to include the structural risk minimization (SRM) principle in the formulation of UTSVM, we propose an improved universum twin support vector machine (IUTSVM). Our proposed IUTSVM implicitly makes the matrices non-singular in the optimization problem by adding a regularization term. Several numerical experiments are performed on benchmark real world datasets to verify the efficacy of our proposed IUTSVM. The experimental results justifies the better generalization performance of our proposed IUTSVM in comparison to existing algorithms.Item An Efficient Angle-based Universum Least Squares Twin Support Vector Machine for Classification(ACM Digital Library, 2021-08) Richhariya, BharatUniversum-based support vector machine incorporates prior information about the distribution of data in training of the classifier. This leads to better generalization performance but with increased computation cost. Various twin hyperplane-based models are proposed to reduce the computation cost of universum-based algorithms. In this work, we present an efficient angle-based universum least squares twin support vector machine (AULSTSVM) for classification. This is a novel approach of incorporating universum in the formulation of least squares-based twin SVM model. First, the proposed AULSTSVM constructs a universum hyperplane, which is proximal to universum data points. Then, the classifying hyperplane is constructed by minimizing the angle with the universum hyperplane. This gives prior information about data distribution to the classifier. In addition to the quadratic loss, we introduce linear loss in the optimization problem of the proposed AULSTSVM, which leads to lesser computation cost of the model. Numerical experiments are performed on several benchmark synthetic, real-world, and large-scale datasets. The results show that proposed AULSTSVM performs better than existing algorithms w.r.t. generalization performance as well as computation time. Moreover, an application to Alzheimer’s disease is presented, where AULSTSVM obtains accuracy of 95% for classification of healthy and Alzheimers subjects. The results imply that the proposed AULSTSVM is a better alternative for classification of large-scale datasets and biomedical applications.Item Entropy based fuzzy least squares twin support vector machine for class imbalance learning(Springer, 2018-06) Richhariya, BharatIn classification problems, the data samples belonging to different classes have different number of samples. Sometimes, the imbalance in the number of samples of each class is very high and the interest is to classify the samples belonging to the minority class. Support vector machine (SVM) is one of the widely used techniques for classification problems which have been applied for solving this problem by using fuzzy based approach. In this paper, motivated by the work of Fan et al. (Knowledge-Based Systems 115: 87–99 2017), we have proposed two efficient variants of entropy based fuzzy SVM (EFSVM). By considering the fuzzy membership value for each sample, we have proposed an entropy based fuzzy least squares support vector machine (EFLSSVM-CIL) and entropy based fuzzy least squares twin support vector machine (EFLSTWSVM-CIL) for class imbalanced datasets where fuzzy membership values are assigned based on entropy values of samples. It solves a system of linear equations as compared to the quadratic programming problem (QPP) as in EFSVM. The least square versions of the entropy based SVM are faster than EFSVM and give higher generalization performance which shows its applicability and efficiency. Experiments are performed on various real world class imbalanced datasets and compared the results of proposed methods with new fuzzy twin support vector machine for pattern classification (NFTWSVM), entropy based fuzzy support vector machine (EFSVM), fuzzy twin support vector machine (FTWSVM) and twin support vector machine (TWSVM) which clearly illustrate the superiority of the proposed EFLSTWSVM-CILItem A fuzzy twin support vector machine based on information entropy for class imbalance learning(Springer, 2018-05) Richhariya, BharatIn real-world binary class datasets, the total number of samples may not be the same in both the classes, i.e. size of the majority class is much larger than minority class which is called as imbalance problem. In various classification problems, the main interest is to correctly classify the samples belonging to the minority class. Since support vector machine (SVM) and twin support vector machine (TWSVM) obtain the resultant classifier by giving same importance to all the training samples, it results in a biased classifier towards the majority class in imbalanced datasets. In this paper, by considering the fuzzy membership value for each sample, we have proposed an efficient approach, entropy-based fuzzy twin support vector machine for class imbalanced datasets (EFTWSVM-CIL) where fuzzy membership values are assigned based on the entropy values of samples. Here, we give more importance to the minority class by assigning relatively larger fuzzy memberships to the minority class samples. Further, it solves a pair of smaller-size quadratic programming problems (QPPs) rather than a large one as in the case of SVM. Experiments are performed on various real-world imbalanced datasets, and results of our proposed EFTWSVM-CIL are compared with twin support vector machine (TWSVM), fuzzy twin support vector machine (FTWSVM) and entropy-based fuzzy SVM (EFSVM) for imbalanced datasets.