Single Versus Union: Non-parallel Support Vector Machine Frameworks

JOURNAL OF L A T EX CLASS FILES, VOL., NO., 1 Single V ersus Union: Nonparallel Support V ector Machine Frameworks Chun-Na Li, Y uan-Hai Shao, Huajun Wang, Y u-Ting Zhao, Ling-Wei Huang, Naihua Xiu and Nai-Y ang Deng Abstract --Considering the classification problem, we summarize the nonparallel support vector machines with the nonparallel hyperplanes to two types of frameworks. It solves a series of small optimization problems to obtain a series of hyperplanes, but is hard to measure the loss of each sample. The other type constructs all the hyperplanes simultaneously, and it solves one big optimization problem with the ascertained loss of each sample. We give the characteristics of each framework and compare them carefully. In addition, based on the second framework, we construct a max-min distance-based nonparallel support vector machine for multiclass classification problem, called NSVM. Experimental results on benchmark data sets and human face databases show the advantages of our NSVM. I NTRODUCTION F OR binary classification problem, the generalized eigenvalue proximal support vector machine (GEPSVM) was proposed by Mangasarian and Wild [1] in 2006, which is the first nonparallel support vector machine. It aims at generating two nonparallel hyperplanes such that each hyperplane is closer to its class and as far as possible from the other class. GEPSVM is effective, particularly when dealing with the "Xor"-type data [1]. This leads to extensive studies on nonparallel support vector machines (NSVMs) [2]-[5].