Minimum Distribution Support Vector Clustering

Support vector clustering (SVC) is a boundary-based algorithm, which has several advantages over other clustering methods, including identifying clusters of arbitrary shapes and numbers. Leveraged by the high generalization ability of the large margin distribution machine (LDM) and the optimal margin distribution clustering (ODMC), we propose a new clustering method: minimum distribution for support vector clustering (MDSVC), for improving the robustness of boundary point recognition, which characterizes the optimal hypersphere by the first-order and second-order statistics and tries to minimize the mean and variance simultaneously. In addition, we further prove, theoretically, that our algorithm can obtain better generalization performance. Some instructive insights for adjusting the number of support vector points are gained. For the optimization problem of MDSVC, we propose a double coordinate descent algorithm for small and medium samples. The experimental results on both artificial and real datasets indicate that our MDSVC has a significant improvement in generalization performance compared to SVC.

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.