Fuzzy multi-category proximal support vector classification via generalized eigenvalues

Abstract

Given a dataset, where each point is labeled with one of M labels, we propose a technique for multicategory proximal support vector classification via generalized eigenvalues (MGEPSVMs). Unlike Support Vector Machines that classify points by assigning them to one of M disjoint half-spaces, here points are classified by assigning them to the closest of M non-parallel planes that are close to their respective classes. When the data contains samples belonging to several classes, classes often overlap, and classifiers that solve for several nonparallel planes may often be able to better resolve test samples. In multicategory classification tasks, a training point may have similarities with prototypes of more than one class. This information can be used in a fuzzy setting. We propose a fuzzy multi-category classifier that utilizes information about the membership of training samples, to improve the generalization ability of the classifier. The desired classifier is obtained by using one-from-rest (OFR) separation for each class, i.e. 1 : M − 1 classification. Experimental results demonstrate the efficacy of the proposed classifier over MGEPSVMs.

Review on: Twin Support Vector Machines

“…Compared with the straightforward multiclass extension of TWSVM or GEPSVM [107][108][109], MBSVM took into account the computational complexity, the "min" decision criterion of TWSVM is changed into the "max" one of MBSVM. The geometric interpretation of MBSVM with x ∈ R 2 is shown in Fig.…”

A weighted twin support vector regression

“…At present, TSVM has become one of the popular methods because of its low computational complexity. Many variants of TSVM have been proposed by Peng [12], Kumar and Gopal [7], Jayadeva et al [6], Khemchandani et al [9]. Certainly, the above algorithms are suitable to the classification problems.…”

Differential Search Algorithm-based Parametric Optimization of Fuzzy Generalized Eigenvalue Proximal Support Vector Machine

“…In real world applications data may affected by noise or error which significantly influences on the performance of GEPSVM. There are many approaches have been proposed by researchers for this problem [13][14][15][16][17][18][19]. More efforts are needed in order to improve the performance of the classification task in this type of data.…”

“…The works of many researches carried out by adding fuzzy values to the standard SVM [13,14,17,18]. Many attempts for adding fuzzy to GEPSVM have been illustrated as in [15,16,19]. A first attempt to obtain a fuzzy version of the GEPSVM classification is presented in [15,16].…”