144 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO. 1, JANUARY 2015 Extended Random Walker-Based Classification of Hyperspectral Images Xudong Kang, Student Member, IEEE, Shutao Li, Member, IEEE, Leyuan Fang, Student Member, IEEE, Meixiu Li, and Jón Atli Benediktsson, Fellow, IEEE Abstract—This paper introduces a novel spectral–spatial clas- sification method for hyperspectral images based on extended random walkers (ERWs), which consists of two main steps. First, a widely used pixelwise classifier, i.e., the support vector machine (SVM), is adopted to obtain classification probability maps for a hyperspectral image, which reflect the probabilities that each hyperspectral pixel belongs to different classes. Then, the obtained pixelwise probability maps are optimized with the ERW algo- rithm that encodes the spatial information of the hyperspectral image in a weighted graph. Specifically, the class of a test pixel is determined based on three factors, i.e., the pixelwise statistics information learned by a SVM classifier, the spatial correlation among adjacent pixels modeled by the weights of graph edges, and the connectedness between the training and test samples modeled by random walkers. Since the three factors are all well considered in the ERW-based global optimization framework, the proposed method shows very good classification performances for three widely used real hyperspectral data sets even when the number of training samples is relatively small. Index Terms—Extended random walkers (ERWs), graph, hyperspectral image, optimization, spectral–spatial image classification. I. I NTRODUCTION H YPERSPECTRAL image classification gives a high-level understanding of remotely sensed scenes and is therefore now widely used in different application domains such as envi- ronment monitoring [1], precision agriculture [2], and national defense [3]. However, because of the special characteristics of hyperspectral data sets, image classification in the hyperspectral domain still has many unresolved problems [4]. For instance, the high dimensionality of hyperspectral data sets involves the “Hughes” phenomenon in classification [5]. The “Hughes” phenomenon refers to the fact that, if the number of training samples is fixed, the classification accuracy may de- Manuscript received January 28, 2014; revised March 24, 2014; accepted April 18, 2014. Date of publication May 14, 2014; date of current version August 4, 2014. This paper was supported in part by the National Natural Science Foundation for Distinguished Young Scholars of China under Grant 61325007, by the National Natural Science Foundation of China under Grant 61172161, by the Fundamental Research Funds for the Central Universities, by Hunan University, and by the Chinese Scholarship Award for Excellent Doctoral Student. X. Kang, S. Li, L. Fang, and M. Li are with the College of Electrical and Information Engineering, Hunan University, Changsha 410082, China (e-mail: xudong_kang@hnu.edu.cn; shutao_li@hnu.edu.cn; fangleyuan@gmail.com). J. A. Benediktsson is with the Faculty of Electrical and Computer Engineer- ing, University of Iceland, 107 Reykjavik, Iceland (e-mail: benedikt@hi.is). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TGRS.2014.2319373 crease significantly for some supervised classification methods as the data dimensionality increases beyond a certain number of features. In order to deal with this difficulty, several solutions have been developed such as feature extraction [6]–[8] and discriminative learning [9], [10]. Feature extraction methods such as principal component analysis (PCA) [7], independent component analysis [6], and linear discriminant analysis [8], [11], [12] project the high-dimensional data into a low di- mensional feature space while preserving the discriminative information of different classes. Furthermore, discriminative learning approaches such as support vector machines (SVMs) [9], multinomial logistic regression [10], and artificial immune networks [13] learn the class distributions in high-dimensional spaces by inferring the nonlinear boundaries between classes in feature space. These methods can effectively tackle the aforementioned difficulties caused by high dimensionality. In addition to research on how to overcome the “Hughes” phenomenon, another active research topic for hyperspectral image classification is how to make full use of the spatial infor- mation of the data in order to further improve the classification accuracy [14]. To achieve this objective, intensive work has been performed in the last decade to develop spectral–spatial hyperspectral image classification methods. For example, spa- tial feature extraction methods [15]–[21] have been proposed to define an adaptive neighborhood for each pixel by local filtering operations so that the adaptive local neighborhood information could be preserved in the resulting features for classification. Furthermore, an optimal set of the resulting spatial features can be selected to further improve the performance of feature extraction [22]. In addition to spatial feature extraction, image segmentation is a widely used technique for spectral–spatial image classifi- cation. Specifically, segmentation-based methods perform the decision fusion of image segmentation and pixelwise classifica- tion to make full use of the spatial information of hyperspectral images. For this kind of methods, the automatic segmentation of hyperspectral images is a challenging task, and thus, many different hyperspectral image segmentation methods have been proposed such as watershed [23], partitional clustering [24], hierarchical segmentation [25], and stochastic minimum span- ning forest [26], [27]. In recent years, other types of spectral–spatial methods such as nonlocal joint collaborative representation [28], spatial kernel-based methods [29], [30], and probabilistic modeling- based methods [10], [31]–[34] have also been successfully applied for hyperspectral image classification. For instance, probabilistic modeling-based methods first estimate the 0196-2892 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.