Collaborative-Representation-Based Nearest Neighbor Classifier for Hyperspectral Imagery

Abstract—Novel collaborative representation (CR)-based near-est neighbor (NN) algorithms are proposed for hyperspectral image classification. The proposed methods are based on a CR computed by an 2-norm minimization with a Tikhonov regular-ization matrix. More specific, a testing sample is represented as a linear combination of all the training samples, and the weights for representation are estimated by an 2-norm minimization-derived closed-form solution. In the first strategy, the label of a testing sample is determined by majority voting of those with k largest representation weights. In the second strategy, local within-class CR is considered as an alternative, and the testing sample is assigned to the class producing the minimum representation resid-ual. The experimental results show that the proposed algorithms achieve better performance than several previous algorithms, such as the original k-NN classifier and the local mean-based NN classifier. Index Terms—Collaborative representation (CR), hyperspec-tral data, nearest neighbors (NNs), pattern classification. I