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To overcome the low efficiency of Least Squares Twin Support Vector Machine (LSTSVM) in classifying, a new method called Sample Reduction LSTSVM (SR-LSTSVM) is proposed. The method greatly reduces the training samples and so improves the speed of LSTSVM, while the ability of LSTSVM to classify is unaffected. Our experiment results show remarkable improvement of the speed of LSTSVM on hyperspectral image, supporting our idea. Introduction The hyperspectral remote sensing technology, which appeared early in 1980s, has become an important technique in map cartography, vegetation investigation, ocean remote sensing, agriculture remote sensing, atmosphere research, environment monitoring and military information acquiring [1]. Support Vector Machine (SVM) [2] is an excellent kernel-based tool for Hyperspectral Image Classification [3] [4]. The central idea of SVM is to find the optimal separating hyperplane between the positive and negative examples. The optimal hyperplane is defined as the one giving maximum margin between the training examples that are closest to the hyperplane. In 2007, Jayadeva et al proposed Twin SVM (TSVM) [5]. TSVM generates two nonparallel hyperplanes by solving two smaller-sized QPPs such that each hyperplane is close to one class and as far as possible from the other. The strategy of solving two smaller-sized QPPs, rather than a single large-sized QPP, makes the TSVM is approximately four times faster than the usual SVM. TSVM has become one of the popular methods because of its low computational complexity. LSTSVM [6] is one of the variants of TSVM, it has better classification performance than TSVM and SVM [6] [7] [8]. Many variants of LSTSVM have been proposed, such as Knowledge based LSTSVM [9], Laplacian LSTSVM for semi-supervised classification [10], Weighted LSTSVM [11]. However, the low classification efficiency of LSTSVM has seldom been mentioned. In this paper, a novel LSTSVM algorithm based on sample reduction is proposed. The experimental results on two data sets confirm the feasibility and effectiveness of the proposed method. The remainder of this paper is organized as follows. In Section 2, we explain the method of LSTSVM and SR-LSTSVM, we discuss linear and nonlinear sample reduction methods respectively corresponding to linear and nonlinear LSTSVM. The experiments and their results are given in Section 3 and discussed in Section 4. Methods A. LSTSVM LSTSVM is a useful extended of TSVM. It modified the primal QPPs of TSVM in least squares sense and solved them with equality constraints instead of inequalities of TSVM. As a result, the solution of LSTSVM follows directly from solving two systems of linear equations as opposed to International Conference on Advances in Mechanical Engineering and Industrial Informatics (AMEII 2015) © 2015. The authors Published by Atlantis Press 1203

Least Squares Twin Support Vector Machines Based on Sample Reduction for Hyperspectral Image Classification