Stochastic Subgradient for Large-Scale Support Vector Machine Using the Generalized Pinball Loss Function

In this paper, we propose a stochastic gradient descent algorithm, called stochastic gradient descent method-based generalized pinball support vector machine (SG-GPSVM), to solve data classification problems. This approach was developed by replacing the hinge loss function in the conventional support vector machine (SVM) with a generalized pinball loss function. We show that SG-GPSVM is convergent and that it approximates the conventional generalized pinball support vector machine (GPSVM). Further, the symmetric kernel method was adopted to evaluate the performance of SG-GPSVM as a nonlinear classifier. Our suggested algorithm surpasses existing methods in terms of noise insensitivity, resampling stability, and accuracy for large-scale data scenarios, according to the experimental results.

Pinball Loss Twin Support Vector Clustering

Twin Support Vector Clustering (TWSVC) is a clustering algorithm inspired by the principles of Twin Support Vector Machine (TWSVM). TWSVC has already outperformed other traditional plane based clustering algorithms. However, TWSVC uses hinge loss, which maximizes shortest distance between clusters and hence suffers from noise-sensitivity and low re-sampling stability. In this article, we propose Pinball loss Twin Support Vector Clustering (pinTSVC) as a clustering algorithm. The proposed pinTSVC model incorporates the pinball loss function in the plane clustering formulation. Pinball loss function introduces favorable properties such as noise-insensitivity and re-sampling stability. The time complexity of the proposed pinTSVC remains equivalent to that of TWSVC. Extensive numerical experiments on noise-corrupted benchmark UCI and artificial datasets have been provided. Results of the proposed pinTSVC model are compared with TWSVC, Twin Bounded Support Vector Clustering (TBSVC) and Fuzzy c-means clustering (FCM). Detailed and exhaustive comparisons demonstrate the better performance and generalization of the proposed pinTSVC for noise-corrupted datasets. Further experiments and analysis on the performance of the above-mentioned clustering algorithms on structural MRI (sMRI) images taken from the ADNI database, face clustering, and facial expression clustering have been done to demonstrate the effectiveness and feasibility of the proposed pinTSVC model.