Iterative tighter nonparallel hyperplane support vector clustering with simultaneous feature selection

In this paper, we propose a novel clustering method with feature selection in a synchronized manner, called iterative tighter nonparallel support vector clustering with simultaneous feature selection (IT-NHSVC-SFS). A certain iterative (alternating) optimization strategy for clustering is applied to a learning model with twin hyperplanes, in which two types of regularizers, namely the Euclidean and infinite norms, are introduced to achieve the enhancement of clustering generalization performance and coordinated feature selection. The L-infinite norm actually conducts implicit feature elimination process to reduce clustering noises resulting from irrelevant features, thus guaranteeing clustering accuracy. Meanwhile, since the formulation of the proposed model embodies the large-margin spirit,good generalization can also be ensured.Unlike twin support vector machine and its variants, nonparallel hyperplane SVM (NHSVM) is chosen to be a baseline model,thus only a single quadratic programming problem is needed to solve for the optimal twin hyperplanes, making it convenient to design a synchronized feature selection process in two hyperplanes. Additionally, two more groups of equality constraints are enforced into the original constraint set of NHSVM, thus the inverse operation of two large matrices can be avoided to reduce the computational complexity. Furthermore,the hinge loss function of NHSVM is replaced by the Laplacian loss measure to prevent the premature convergence. Numerical experiments are performed on benchmark datasets to investigate the validity of the proposed algorithm. The experimental results indicate that IT-NHSVC-SFS has better performance than other existing clustering methods mainly in terms of clustering accuracy.