A generalized representation-based approach for hyperspectral image classification

Sparse representation-based classifier (SRC) is of great interest recently for hyperspectral image classification. It is assumed that a testing pixel is linearly combined with atoms of a dictionary. Under this circumstance, the dictionary includes all the training samples. The objective is to find a weight vector that yields a minimum L2 representation error with the constraint that the weight vector is sparse with a minimum L1 norm. The pixel is assigned to the class whose training samples yield the minimum error. In addition, collaborative representation-based classifier (CRC) is also proposed, where the weight vector has a minimum L2 norm. The CRC has a closed-form solution; when using class-specific representation it can yield even better performance than the SRC. Compared to traditional classifiers such as support vector machine (SVM), SRC and CRC do not have a traditional training-testing fashion as in supervised learning, while their performance is similar to or even better than SVM. In this paper, we investigate a generalized representation-based classifier which uses Lq representation error, Lp weight norm, and adaptive regularization. The classification performance of Lq and Lp combinations is evaluated with several real hyperspectral datasets. Based on these experiments, recommendation is provide for practical implementation.