 Advances in Technology Innovation, vol. 2, no. 3, 2016, pp. 68 - 72 68 Spatial and Spectral Nonparametric Linear Feature Extrac- tion Method for Hyperspectral Image Classification Jinn-Min Yang*, Shih-Hsuan Wei Department of Mathematics Education, National Taichung University of Education, Taichung, Taiwan. Received 02 May 2016; received in revised form 21 June 2016; accepted 21 June 2016 Abstract Feature extraction (FE) or dimensionality re- duction (DR) plays quite an important role in the field of pattern recognition. Feature extraction aims to reduce the d imens ionality of the high-d imens ional dataset to enhance the clas- sification accuracy and foster the classification speed, particularly when the training sample size is small, namely the small sample size (SSS) problem. Remotely sensed hyperspectral images (HSIs) are often with hundreds of measured features (bands) which potentially provides more accurate and de- tailed information for classification, but it generally needs more samples to estimate parameters to achieve a satisfactory result. The cost of collect ing ground-t ruth o f remotely sensed hyperspectral scene can be considerably difficult and expensive. Therefore, FE techniques have been an important part for hyperspectral image classification. Unlike lots of feature extraction methods are based only on the spectral (band) information of the training sam- ples, some feature extraction methods integrating both spatial and spectral information of training samples show more effective results in recent years. Spatial contexture information has been proven to be useful to improve the HSI data representation and to increase classification accuracy. In this paper, we propose a spatial and spectral nonparametric linear feature extraction method for hyperspectral image classification. The spatial and spectral in- formation is extracted for each training sample and used to design the within-class and between-class scatter matrices for constructing the feature extrac- tion model. The experimental results on one benchmark hyperspectral image demonstrate that the proposed method obtains stable and satisfactory results than some existing spectral-based feature extraction. Keywords: feature extraction, hyperspectral image, dimensionality reduction, classification, small sample size problem 1. Introduction Remotely sensed hyperspectral images (HSIs) are often with hundreds of measured features (spectral bands) potentially provides more accurate and detailed informat ion for classification and widely used in environmental mapping, geological research, and mineral identification in recent years. The cost of col- lecting ground-truth of remotely sensed hyper- spectral image can be considerably d if f icu lt and e xpens ive. Ther efo re, F E techniques have been an important part for hyperspectral image classification. In general feature extraction (FE) or dimen- sionality reduction (DR) plays quite an im- portant role in the field of pattern recognition. Linear discriminant analysis (LDA) [1] is one of the most well-known linear feature extraction methods and has been successfully applied to many fields. The purpose of LDA is to find a linear t ransformat ion matrix that can be used to project data from a h igh-dimensional space into a low-dimensional subspace to mitigate the so-called curse of dimensionality [2], [3] or the Hughes phenomenon [4], [5]. The Hughes phenomenon describes that the ratio of the number of train ing samples and the number of features must be maintained at or above some minimum value to achieve statistical confidence [5]. Otherwise, the classification accuracy will decline with an increase in the dimensionality of data to some extent. However, it is not necessary to have sufficient training samples to keep the ratio in a high-dimensional classification task. Therefore, by featu re ext ract ion, the rat io can be relat ively en larged and the curs e o f dimensionality can therefore be improved, this will result in an enhancement of classification accuracy. Meanwhile, the computational time can be reduced as well. * Corresponding author, Email: jinnminyang@mail.ntcu.edu.tw Advances in Technology Innovation, vol. 2, no. 3, 2016, pp. 68 - 72 69 Copyright © TAETI Bas ically , LDA has th ree inherent defi- ciencies in dealing with classificat ion problems. First, LDA is only well-suited for normally distributed data [1]. If the distributions are sig- nificantly non-normal, the use of LDA cannot be expected to accurately indicate which features should be extracted to preserve complex struc- tures needed for classification. Second, since the rank of between-class scatter matrix is the number o f classes minus one [1], the number of features can be extracted at most remains the same. Third, the singularity problem arises when dealing with high-dimensional and small sample size (SSS) data [1, 3, 6-7]. Nonparametric linear discriminant analysis such as nonparametric discriminant analysis (NDA) [1], nonparametric weighted feature extract ion (NWFE) [6] and cosine-based feature extraction (CNFE) [7] provide solutions for circumventing the previ- ously mentioned problems. The aforementioned FE methods are spec- tral-based algorithms; in other words, they measure similarity in the spectral space. Using only spectral informat ion to classification tasks is insufficient. Spatial contexture information has been proven to be useful to improve the classification of HSI data in recent years [8]-[9]. In the paper, a nonparametric feature extraction method, integrating both spectral and spatial information, is proposed. The rest of this paper is organized as follows. The proposed method and its experiment are described in Section 2. The experimental results and discussion are provided in Section 3. Finally, Section 4 gives some conclusions of the paper. 2. Method The goal of FE is to find a transformation matrix A which maximizes the class separab ility in the transformed space, where and denote the within-class and between-class scatter matrices, respectively. That is (1) The maximizat ion of (1) is equivalent to solving the generalized eigenvalue decomposition problem where denotes the dimensionality of the trans- formed space, represent the eigen-pair of , and . Thus, the trans- formation matrix A = [v1,… , v𝑃 ] can be obtained. The proposed spatial and spectral feature e x- traction method includes two parts, one idea is to incorporate the spatial information into the within -class and scatter matrix design, and the other idea is to incorporate another scatter ma- trix to regularize the within -class scatter matrix. 2.1. The Nonparametric Linear Discriminate Analysis The within-class matrix and between-class scatter matrix o f the nonparametric linear dis- criminant feature extract ion (NLDA) are defined as follows, respectively. (2) (3) where and denote the local mean of training sample corresponding to the th class and th class, respectively. The local mean of is computed by its -nearest neighbors ( NNs) in the same class or in the different classes as shown in (4). (4) 2.2. The Spatial and Spectral Nonparametric Linear Discriminate Analysis The within-class matrix and between-class scatter matrix o f the spatial and spectral non- parametric linear d iscriminan t featu re ex- traction (SSNLDA) are defined as follows, re- spectively.             1 1 i T L S S i i I iw i N i i iS x x x xP M M       (5)             1 1 1 iNL L T S S i i i i i j jb i j j i S x x x xP M M         (6) where and denote the local mean of training sample corresponding to the th class and th class, respectively. The local mean of is computed by utilizing the Advances in Technology Innovation, vol. 2, no. 3, 2016, pp. 68 - 72 70 Copyright © TAETI spectral weighted local mean and spa- tial weighted local mean , as shown in (7). (7) where (8) with (9) and (10) with (11) and denotes the coordinate of training sample , the parameter . Another part of is the distance scatter matrix introduce in [8]. Based on a window, a training sample and its pixel neighbors form a local patch , where the odd number is the width of the neighborhood window. The scatter matrix and (12) where s = 𝑧2 − 1 , and . Parameter re- flects the degree of filtering. Regularization is employed to improve the singularity problem in SSNLDA. The within-class scatter matrix is replaced by (13) where denotes the diagonal parts of a matrix and . 2.3. Dataset The Indian Pines image, mounted from an aircraft flown at 65000-ft altitude and operated by the NASA/Jet Propulsion Laboratory, with the size of 145 × 145 pixels has 220 spectral bands measuring approximately 20 m across the ground. We have also reduced the number of bands to 200 by removing bands covering the region of water absorption: 104-108, 150-163, and 220. There are 16 classes in the data set. The total number of samples is 10249, ranging from 20 to 2455 in each class. In figure 1, the left and right images depict the false color composition of three sample bands 50, 27 and 17 and its ground truth of the Indian Pines dataset, respec- tively. Fig. 1 The left figure depicts Indian Pines image of band 50, 27 and 17; the right one shows its ground truth. 2.4. Experiment Design Three different cases, each class with 5 (case I), 10 (case II), and 20 (case III) training samples are investigated to discover the effect on the sizes of training samples in the experiments. The remain ing samples are employed as the test samples. The cases I and II are the so-called il l-posed and poorly pos ed class ificat ion problems [7], respectively. They are challenging cases in the field of pattern recognition. In each case, the training and testing datasets are ran- domly selected. We will repeat each case for 10 times and report the averaged overall accuracy (OA) and standard deviation. Two other linear feature extraction methods, CNFE and NWFE, are utilized to compare the classification performance with the proposed SSNLDA. The 1-nearest neighbor (1NN) clas- sifier is employed. In SSNLDA, we adopt a window to form a local patch and the val- ues of , and  are set as 0.5. Advances in Technology Innovation, vol. 2, no. 3, 2016, pp. 68 - 72 71 Copyright © TAETI Table 1 Graph representations class # pixels class name 1 46 Alfalfa 2 1428 Corn-notill 3 830 Corn-mintill 4 237 Corn 5 483 Grass-pasture 6 730 Grass-trees 7 28 Grass-pasture-mowed 8 478 Hay-windrowed 9 20 Oats 10 972 Soybean-notill 11 2455 Soybean-mintill 12 593 Soybean-clean 13 205 Wheat 14 1265 Woods 15 386 Buildings-Grass-Trees-Drives 16 93 Stone-Steel-Towers 3. Results and Discussion Table 2 lists the best classification accuracies of the three cases of the Indian Pines dataset. As we can see from the table, 1NN classifier with SSNLDA features can achieve better results than with CNFE and NWFE features. SSNLDA pro- vides about 6% improvement as compared with the other two methods. Meanwhile, the standard devia- tions is smaller as well. Fig. 2 demonstrates the variations of OAs with the reduced dimensions where 5, 10 and 20 training samples are utilized. The proposed SSNLDA significantly outperform the other two methods. Fig. 3 shows the classifica- tion map of the Indian Pines scene using 1NN clas- sifier for 20 training samples case. The dimension- ality of the reduced space is 30. As shown in Fig. 3, the 1NN classifier with SSNLDA feature can get better results. Table 2 Classification accuracies (in percent) in Indian Pines scene Case FE OA±std (#features) NWFE 63.03±4.68(28) CNFE 65.10±4.91(15) SSNLDA 71.05±3.28(28) NWFE 72.82±2.28(29) CNFE 75.67±1.77(29) SSNLDA 81.79±1.81(30) NWFE 80.15±1.76(28) CNFE 81.93±2.17(28) SSNLDA 88.08±1.21(30) Fig. 2 Classification results on the Indian Pines dataset for the three feature extraction method. (a) NWFE (b) CNFE (c) SSNLDA (d) Ground-truth Fig. 3 Classification maps of the Indian Pines scene using 1NN classifier for 20 training samples case. 4. Conclusions In this paper, a spectral and spatial infor- mation-based nonparametric feature extraction SSNLDA is proposed. From the above results, we find SSNLDA can achieve more stable and effec- tive results. In most of cases, 1NN classifier with SSNLDA features can obtain better results than other spectral-based FE, CNFE and NLDA, partic- ularly when the training sample size is quite small. Acknowledgement This study is supported by Ministry of Sci- ence and Technology, R.O.C., under the contract number of MOST 104-2221-E-142- 005. References [1] K. Fukunaga, Introduction to statistical pattern recognition, 2nd ed., New York: Academic Press, 1990. Advances in Technology Innovation, vol. 2, no. 3, 2016, pp. 68 - 72 72 Copyright © TAETI [2] R. O. Duda, P. E. Hart, and D. G. 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