A Discriminant Sparse Representation Graph-Based Semi-Supervised Learning for Hyperspectral Image Classification
The classification of hyperspectral image with a paucity of labeled samples is a challenging task. In this paper, we present a discriminant sparse representation (DSR) graph for semi-supervised learning (SSL) to address this problem. For graph-based metho
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Abstract. The classification of hyperspectral image with a paucity of labeled samples is a challenging task. In this paper, we present a discriminant sparse representation (DSR) graph for semi-supervised learning (SSL) to address this problem. For graph-based methods, how to construct a graph among the pixels is the key to a successful classification. Our graph construction method contains two steps. Sparse representation (SR) method is first employed to estimate the probability matrix of the pairwise pixels belonging to the same class, and then this probability matrix is integrated into the SR graph, which can be obtained by solving an 1 optimization problem, to form a DSR graph. Experiments on Hyperion and AVIRIS hyperspectral data show that our proposed method outperforms state of the art. Keywords: Hyperspectral image classification · Graph Semi-Supervised Learning (SSl) · Sparse Representation (SR)
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Introduction
Hyperspectral image data contains high-resolution spectral information on land covers, which is attractive for discriminating the subtle differences between classes with similar spectral signatures. However, hyperspectral image classification often faces the issue of limited number of labeled samples, as it is labor intensive and time-consuming to collect large number of training samples [1–3]. Semi-supervised learning (SSL) , which can utilize both small amount of labeled samples and abundant yet unlabeled samples, has recently been proposed to tackle the challenge [4,5]. Due to its practical success and its computational efficiency, graph-based SSL is pretty appealing among the semi-supervised methods. Graph-based SSL is dependent on a graph to represent the data structures, where each vertex corresponding to one sample and the edge weight denotes the similarity between the pairwise samples. Label information of labeled instances can then be efficiently propagated to the unlabeled samples through the graph. In order to expect desired result, it is critical to construct a good graph for all c Springer-Verlag Berlin Heidelberg 2015 H. Zha et al. (Eds.): CCCV 2015, Part I, CCIS 546, pp. 160–167, 2015. DOI: 10.1007/978-3-662-48558-3 16
A Discriminant SR Graph-Based SSL
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graph-based SSL methods. Nevertheless, it is still an open problem about how to construct such a good graph [6–8]. Recently, Cheng and Yan [9,10] proposed an 1 -graph structure based on sparse representation(SR).The latent philosophy is that each sample can be encoded as a sparse linear superposition of the remaining samples via solving an 1 optimization problem. In this way, the adjacency relationship and the weights of graph are derived automatically and simultaneously. Comparing with the traditional methods, e.g., k -nearest neighbors (k NN) graph and local linear embedding (LLE) graph [8,11], 1 -graph (SR graph) explores higher order relationships among data points, and hence has the natural discriminating powerful. However, it finds the sparse representation of each sample in an unsupervised manner, encoding the similarity b
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