A Trace Lasso Regularized Robust Nonparallel Proximal Support Vector Machine for Noisy Classification

Abstract

Generalized eigenvalue proximal support vector machine (GEPSVM) and its improvement IGEPSVM are excellent nonparallel classification methods due to their excellent generalization. However, all of them adopt the square L2-norm metric to implement their empirical risk or penalty, which is sensitive to noise and outliers. Moreover, in many real-world learning tasks, it is a significant challenge for GEPSVMs when the data appears highly correlated. To alleviate the above issues, in this paper, we propose a novel trace lasso regularized robust nonparallel proximal support vector machine (RNPSVM) for noisy classification. Compared with GEPSVMs, our RNPSVM enjoys the following advantages. First, the empirical risk of RNPSVM is implemented by the robust L1-norm metric with a maximum margin criterion. Namely, it aims to maximize the L1-norm inter-class distance dispersion while minimizing the L1-norm intra-class distance dispersion simultaneously. Second, to capture the sparsity and the underlying correlation of data, a trace lasso (adaptive norm-based training data) is further introduced to regularize RNPSVM. Third, an iterative algorithm is designed to solve the maximization optimization problem of RNPSVM, whose convergence is guaranteed theoretically. The extensive experimental results on both synthetic and real-world noisy datasets demonstrate the effectiveness of RNPSVM.

Keywords

• Support vector machines
• L₁-norm%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">L</italic>₁-norm
• regularization
• robustness
• classification algorithms