DIMENSION REDUCTION FOR HYPERSPECTRAL IMAGE CLASSIFICATION VIA SUPPORT VECTOR BASED FEATURE EXTRACTION Cheng-Hsuan Li 1 Bor-Chen Kuo 2 Chin-Teng Lin 1 Chih-Cheng Hung 3 ChengHsuanLi@gmail.com kbc@mail.ntcu.edu.tw ctlin@mail.nctu.edu.tw chung@spsu.edu 1 Department of Electrical and Control Engineering, National Chiao Tung University, Taiwan, R.O.C. 2 Graduate School of Educational Measurement and Statistics, National Taichung University, Taiwan, R.O.C. 3 Hendri Purnawan Southern Polytechnic State University Marietta, GA 30067 USA 1. INTRODUCTION Usually feature extraction is applied for dimension reduction in hyperspectral data classification problems. Many studies show that nonparametric weighted feature extraction (NWFE) is a powerful tool for extracting hyperspectral image features. The detection of class boundary is an important part in NWFE and the weighted mean was defined for this purpose. In this paper, a kernel-based feature extraction is proposed based on a new class boundary detection mechanism. The soft-margin support vector machine (SVM) binary classifier and the support vector domain description (SVDD) are applied to detect the boundaries between two classes and one class, respectively. The results of real data experiments show that the proposed method outperforms original NWFE. 2. NONPARAMETRIC WEIGHTED FEATURE EXTRACTION In this paper, NWFE is modified to form a new feature extraction method and before introducing the new method a brief introduction of NWFE is stated in the following. Suppose a data set of samples is partitioned into N L classes and are the samples in class i , , ) ( ) ( 1 ,..., i N i i x x L i ,..., 1 ? L N N N - - ? 5 1 . Let i P denote the prior probability of class i and be the Euclidean distance from ) z , ( dist x x to z . The between-class scatter matrix and the within-class scatter matrix in NWFE [1] are NW b S NW w S T i j i L i L i j j N i j i i j i i NW b x M x x M x N P S i ) ) ( ( ) ) ( ( ) ( ) ( 1 1 1 ) ( ) ( ) , ( A A A A A A / / ?  Â ? ” ? ? n and T i i i L i N i i i i i i i NW w x M x x M x N P S i ) ) ( ( ) ) ( ( ) ( ) ( 1 1 ) ( ) ( ) , ( A A A A A A / / ?  ? ? n where the scatter matrix weight is defined by ) , ( j i A n  ? / / ? i N t i t j i t i j i j i x M x x M x 1 1 ) ( ) ( 1 ) ( ) ( ) , ( ) ) ( , dist( ) ) ( , dist( A A A n , and  ? ? j N k j k j i k i j x w x M 1 ) ( ) , ( ) ( ) ( A A ,  ? / / ? j N t j t i j k i j i k x x x x w 1 1 ) ( ) ( 1 ) ( ) ( ) , ( ) , dist( ) , dist( A A A denotes the weighted mean with respect to in class ) (i x A j . 3. NONPARAMETRIC WEIGHTED FEATURE EXTRACTION WITH THE BOUNDARIES OF SVMS Let be a feature mapping from original space into a feature space H, a Hilbert space with higher dimensionality, and be the corresponding kernel function. H R d › : h d R d R z x z x z x Œ @ ?> , , ) ( ), ( ) , ( h h m For the between class scatter matrix, the boundary between class i and class j is determined by the decision function using the soft-margin SVM [2] binary classifier is