Robust Multi-Weight Vector Projection Support Vector Machine

Abstract

Abstract.Recently proposed Multi-weight vector projection support vector machines (MVSVM) is an outstanding algorithm for binary classification. However, it measuring distance in the objective function by squared L2-norm, which is easy to find that the impact of outliers is exaggerated. To alleviate this, we propose an effective algorithm, termed as Robust MVSVM based on the L1-norm distance (L1-MVSVM). The distance in the objective of L1-MVSVM is measured by L1-norm. Besides, we design a powerful iterative algorithm to solve the optimal problem of L1-norm, whose convergence is theoretically ensured. Finally, the effectiveness of L1-MVSVM has been verified through extensive experiments.

Weighted Linear Loss Projection Twin Support Vector Machine for Pattern Classification

“…Inspired by MVSVM and TWSVM, in 2011, Chen et al proposed the projection twin support vector machine (PTSVM) [11], which aims at seeking two projection directions by solving a pair of SVM-type problems rather than eigenvalue problems. From then on, various improved algorithms based on PTSVM are proposed [24]- [34], e.g. RPTSVM [24], LSPTSVM [25], [26], IPTSVM [27], LIWLSPTSVM [28], PNPSVM [29], NPTSVM [30], PTSVR [31] and other variants PTSVM algorithms [32]- [34].…”

“…From then on, various improved algorithms based on PTSVM are proposed [24]- [34], e.g. RPTSVM [24], LSPTSVM [25], [26], IPTSVM [27], LIWLSPTSVM [28], PNPSVM [29], NPTSVM [30], PTSVR [31] and other variants PTSVM algorithms [32]- [34]. Although LSTSVM has been presented by using the squared loss function instead of hinge loss function in TWSVM and obtains very fast training speed since two QPPs are replaced by two systems of linear equations, but may result in the reduction of classification ability and the characteristic of constructing two nonparallel hyperplanes may be weakened [35].…”