Collaborative-Representation-Based Nearest Neighbor Classifier for Hyperspectral Imagery

Abstract

Novel collaborative representation (CR)-based nearest neighbor (NN) algorithms are proposed for hyperspectral image classification. The proposed methods are based on a CR computed by an ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm minimization with a Tikhonov regularization 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 ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -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 residual. 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.