BITS Faculty Publications
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Item An unconstrained primal based twin parametric insensitive support vector regression(World Scientific, 2025) Richhariya, BharatIn this paper, we propose an efficient regression algorithm based on primal formulation of twin support vector machine. This is an efficient approach to solve the optimization problem leading to reduced computation time. The proposed method is termed as twin parametric insensitive support vector regression (UPTPISVR). The optimization problems of the proposed (UPTPISVR) are a pair of unconstrained convex minimization problems. Moreover, the objective functions of UPTPISVR are strongly convex, differentiable and piecewise quadratic. Therefore, an approximate solution is obtained in primal variables instead of solving the dual formulation. Further, an absolute value equation problem is solved by using a functional iterative algorithm for UPTPISVR, termed as FUPTPISVR. The objective function of the proposed formulation involves the plus function which is non-smooth and therefore, smooth approximation functions are used to replace the plus function, termed as SUPTPISVR. The Newton-Armijo algorithm is then used to iteratively obtain the solutions, thus eliminates the requirement of any optimization toolbox. Various numerical experiments on synthetic and benchmark real-world datasets are presented for justifying the applicability and effectiveness of the proposed UPTPISVR. The results clearly indicate that the proposed algorithms outperform the existing algorithms in terms of root mean square error (RMSE) on most datasets.Item Enhancing class imbalance solutions: A projection-based fuzzy LS-TSVM approach(Elsevier, 2024-07) Richhariya, BharatClass imbalance and noise present significant challenges in numerous real-world classification tasks. The prevalence of an uneven distribution of samples typically results in a bias towards the majority class in Support Vector Machine (SVM) classifiers, compounded by the often inherent noise within these samples. Addressing both class imbalance and noise, we introduce two fuzzy-based methodologies. The first method employs intuitionistic fuzzy membership, resulting in the development of the Robust Energy-based Intuitionistic Fuzzy Least Squares Twin Support Vector Machine (IF-RELSTSVM), a model specifically designed for class imbalance learning. The IF-RELSTSVM model is distinguished by its use of intuitionistic fuzzy scores for both classes, significantly attenuating the detrimental effects of noise and outliers. A distinctive attribute of IF-RELSTSVM is its proficiency in processing noisy data points, whether proximate to or distant from the hyperplane. Additionally, we introduce a novel concept of hyperplane-based fuzzy membership, calculating fuzzy memberships through a projection-based approach. This foundation supports the formulation of a Robust Energy-based Fuzzy Least Squares Twin Support Vector Machine (F-RELSTSVM), also aimed at class imbalance learning. The efficacy of the proposed IF-RELSTSVM and F-RELSTSVM algorithms is rigorously evaluated across several benchmark and synthetic datasets, employing the Area Under the ROC Curve (AUC) as a performance metric. Experimental findings indicate that these algorithms surpass baseline models in the majority of datasets tested. Statistical analyses further validate the significance of our proposed methods, demonstrating their suitability for application in environments characterized by noise and class imbalance. A case study in credit card fraud detection showcases the F-RELSTSVM algorithm achieving an impressive average AUC of 90.84%, thereby outperforming comparable algorithms and highlighting the practical applicability of our approaches in tackling challenging datasets.Item Efficient implicit Lagrangian twin parametric insensitive support vector regression via unconstrained minimization problems(Springer, 2020-11) Richhariya, BharatIn this paper, an efficient implicit Lagrangian twin parametric insensitive support vector regression is proposed which leads to a pair of unconstrained minimization problems, motivated by the works on twin parametric insensitive support vector regression (Peng: Neurocomputing. 79, 26–38, 2012), and Lagrangian twin support vector regression (Balasundaram and Tanveer: Neural Comput. Applic. 22(1), 257–267, 2013). Since its objective function is strongly convex, piece-wise quadratic and differentiable, it can be solved by gradient-based iterative methods. Notice that its objective function having non-smooth ‘plus’ function, so one can consider either generalized Hessian, or smooth approximation function to replace the ‘plus’ function and further apply the simple Newton-Armijo step size algorithm. These algorithms can be easily implemented in MATLAB and do not require any optimization toolbox. The advantage of this method is that proposed algorithms take less training time and can deal with data having heteroscedastic noise structure. To demonstrate the effectiveness of the proposed method, computational results are obtained on synthetic and real-world datasets which clearly show comparable generalization performance and improved learning speed in accordance with support vector regression, twin support vector regression, and twin parametric insensitive support vector regression.Item Universum least squares twin parametric-margin support vector machine(IEEE, 2020-07) Richhariya, BharatUniversum based algorithms involve universum samples in the classification problem to improve the generalization performance. In order to provide prior information about data, we utilized universum data to propose a novel classification algorithm. In this paper, a novel parametric model for universum based twin support vector machine is presented for classification problems. The proposed model is termed as universum least squares twin parametric-margin support vector machine (ULSTPMSVM). The solution of ULSTPMSVM involves a system of linear equations. This makes the ULSTPMSVM efficient w.r.t. training time. In order to verify the performance of the proposed model, various experiments are carried out on real world benchmark datasets. Statistical tests are performed to verify the significance of the proposed method. The proposed ULSTPMSVM performed better than existing algorithms in terms of classification accuracy and training time for most of the datasets. Moreover, an application of proposed ULSTPMSVM is presented for classification of Alzheimer's disease data.Item A Fuzzy Universum Support Vector Machine Based on Information Entropy(Springer, 2018-08) Richhariya, BharatUniversum-based support vector machines (USVMs) are known to give better generalization performance than standard SVM methods by incorporating prior information about the data. In datasets involving noise and outliers, this universum-based scheme is not so effective because the generated universum data points do not lie in between the two classes. In this paper, we propose a fuzzy universum support vector machine (FUSVM) by introducing the weights to the universum data points based on their information entropy. Since there is no standard approach of selecting the universum, our information entropy based approach is helpful in giving less weight to the outlier universum points and thus gives prior information about the data in an appropriate manner. In addition, we also propose a fuzzy-based approach for universum twin support vector machine named as fuzzy universum twin support vector machine (FUTSVM). Experimental results on several benchmark datasets indicate that, comparing to SVM, USVM, TWSVM and UTSVM our proposed FUSVM and FUTSVM have shown better generalization performanceItem Lagrangian twin parametric insensitive support vector regression (LTPISVR)(Springer, 2019-03) Richhariya, BharatIn this paper, motivated by the works on twin parametric insensitive support vector regression (TPISVR) (Peng in Neurocomputing 79(1):26–38, 2012), and Lagrangian twin support vector regression (Balasundaram and Tanveer in Neural Comput Appl 22(1):257–267, 2013), a new efficient approach is proposed as Lagrangian twin parametric insensitive support vector regression (LTPISVR). In order to make the objective function strongly convex, we consider square of 2-norm of slack variables in the optimization problem. To reduce the computation cost, the solution of proposed LTPISVR is obtained by solving simple linearly convergent iterative schemes, instead of quadratic programming problems as in TPISVR. There is no requirement of any optimization toolbox for proposed LTPISVR. To demonstrate the effectiveness of proposed method, we present numerical results on well-known synthetic and real-world datasets. The results clearly show similar or better generalization performance of proposed method with lesser training time in comparison with support vector regression, twin support vector regression and twin parametric insensitive support vector regression.Item Sparse Twin Support Vector Clustering Using Pinball Loss(IEEE, 2021-10) Richhariya, BharatClustering is a widely used machine learning technique for unlabelled data. One of the recently proposed techniques is the twin support vector clustering (TWSVC) algorithm. The idea of TWSVC is to generate hyperplanes for each cluster. TWSVC utilizes the hinge loss function to penalize the misclassification. However, the hinge loss relies on shortest distance between different clusters, and is unstable for noise-corrupted datasets, and for re-sampling. In this paper, we propose a novel Sparse Pinball loss Twin Support Vector Clustering (SPTSVC). The proposed SPTSVC involves the ϵ -insensitive pinball loss function to formulate a sparse solution. Pinball loss function provides noise-insensitivity and re-sampling stability. The ϵ -insensitive zone provides sparsity to the model and improves testing time. Numerical experiments on synthetic as well as real world benchmark datasets are performed to show the efficacy of the proposed model. An analysis on the sparsity of various clustering algorithms is presented in this work. In order to show the feasibility and applicability of the proposed SPTSVC on biomedical data, experiments have been performed on epilepsy and breast cancer datasets.Item Least squares projection twin support vector clustering (LSPTSVC)(Elsevier, 2020-09) Richhariya, BharatClustering is a prominent unsupervised learning technique. In the literature, many plane based clustering algorithms are proposed, such as the twin support vector clustering (TWSVC) algorithm. In this work, we propose an alternative algorithm based on projection axes termed as least squares projection twin support vector clustering (LSPTSVC). The proposed LSPTSVC finds projection axis for every cluster in a manner that minimizes the within class scatter, and keeps the clusters of other classes far away. To solve the optimization problem, the concave-convex procedure (CCCP) is utilized in the proposed method. Moreover, the solution of proposed LSPTSVC involves a set of linear equations leading to very less training time. To verify the performance of the proposed algorithm, several experiments are performed on synthetic and real world benchmark datasets. Experimental results and statistical analysis show that the proposed LSPTSVC performs better than existing algorithms w.r.t. clustering accuracy as well as training time. Moreover, a comparison of the proposed method with existing algorithms is presented on biometric and biomedical applications. Better generalization performance is achieved by proposed LSPTSVC on clustering of facial images, and Alzheimer’s disease data.Item A fuzzy universum least squares twin support vector machine (FULSTSVM)(Springer, 2021-01) Richhariya, BharatUniversum based twin support vector machines give prior information about the distribution of data to the classifier. This leads to better generalization performance of the model, due to the universum. However, in many applications the data points are not equally useful for the classification task. This leads to the use of fuzzy membership functions for the datasets. Similarly, in universum based algorithms, all the universum data points are not equally important for the classifier. To solve these problems, a novel fuzzy universum least squares twin support vector machine (FULSTSVM) is proposed in this work. In FULSTSVM, the membership values are used to provide weights for the data samples of the classes, as well as to the universum data. Further, the optimization problem of proposed FULSTSVM is obtained by solving a system of linear equations. This leads to an efficient fuzzy based algorithm. Numerical experiments are performed on various benchmark datasets, with discussions on generalization performance, and computational cost of the algorithms. The proposed FULSTSVM outperformed the existing algorithms on most datasets. A comparison is presented for the performance of the proposed and other baseline algorithms using statistical significance tests. To show the applicability of FULSTSVM, applications are also presented, such as detection of Alzheimer’s disease, and breast cancer.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.