A NOVEL RANDOM SUBSPACE METHOD USING SPECTRAL AND SPATIAL INFORMATION FOR HYPERSPECTRAL IMAGE CLASSIFICATION Bor-Chen Kuo 1 Chun-Hsiang Chuang 1 Chih-Cheng Hung 2 Szu-Wei Yang 1 kbc@mail.ntcu.edu.tw cch.chuang@gmail.com chung@spsu.edu swyang@mail.ntcu.edu.tw 1 Graduate School of Educational Measurement and Statistics, National Taichung University, Taiwan 2 School of Computing and Software Engineering, Southern Polytechnic State University, GA, USA 1. INTRODUCTION In this study, a novel random subspace method (RSM) using both spectral and spatial information has been proposed for hyperspectral image classification. This scheme could be regarded as a dynamically statistic dimension reduction procedure in which weak classifiers are constructed based on features weighting distribution and subspace dimensionality distribution. Among the classification, spatial information is acquired on the basis of Markov random field (MRF) and then joined with Bayesian formula. The results of real data experiments show that the proposed method obtains the considerably exceptional performance. In the following, the dynamic RSM and Bayesian classifier with MRF will be introduced, and then the proposed framework of the classification is described. 2. RANDOM SUBSPACE METHODS WITH DYNAMIC DIMENSIONS SELECTION Random subspace method is the process of constructing the lower-dimensional system with multiple classifiers. In the improved RSM [1], weak classifiers are sequentially made up in the respectively specific subspaces, and the dimensionality of each subspace is dynamically selected based on an important distribution R which probability density is evaluated by the re-substitution performance of the preceding classifiers and updated by the next one. In terms of the initial distribution R 0 applied to the first classifier, it is estimated by the particular b 0 points and a kernel smoothing technique. Subsequently the distribution R would be updated every time later than obtained the re-substitution result from the current classifier. The formula is stated as the following: , ) ( ) ( ) ( 1 ) ,..., ), ( | ( 0 1 0 Â Â ? ? / ? ? i b j j j p i j j r r K h ACC h ACC i b j h ACC r f u u where u is the bandwidth parameter, ACC(h j ) is the re-substitution accuracy of classifier h j , and ). 2 ) ( exp( 2 1 ) ( 2 2 2 u ru u j j r r r r K / / ? / The component dimensions of each subspace are made up according to another distribution W representing the importance of all inclusively raw features. In original RSM, W is a discrete-type uniform distribution, and there are two estimation methods for W proposed in [1], which is defined by the normalized re-substitution classification accuracy and the separability of Fisher’s linear discriminant analysis respectively. Hence, relying on these two distributions the component dimensions and the number of them would gradually tend to be more adaptive to the trait of the classifier we used. Generally speaking, the whole subspace selection process could be regarded as a statistical dimension reduction approach, and the reduced data are given as the input to train a classifier. Finally, the simple majority voting is used for combining all decisions of each weak classifier to give a final result. In this study, we propose a novel RSM incorporating the original one with spatial information. The Bayesian classification based on the spatial model are introduced in next section. 3. BAYESIAN CLASSIFICATION BASED ON MARKOV RANDOM FIELDS As a result of the difficulty for a conventional classifier to distinguish the pixels that derive from different land-cover classes but have similar spectral attributes, there is the more significant information about the relative assignments of the classes of