Collaborative Representation Classifier based on K Nearest Neighbors for Classifi- cation

The sparse representation based classifier (SRC) is a classical representation method for classification. The solution of SRC is obtained by l1 norm minimization, which can not obtain the closed form solution. Thus, the computational complexity of SRC is a little high. The collaborative representation classifier (CRC) is another classical method for classification. The solution of CRC is obtained by l2 norm minimization, from the l2 norm minimization, it can obtain the closed form solution, which makes the computational complexity of CRC is much lower than SRC. Although CRC is effective for classification, there are also some problems about CRC. Under some conditions, some test samples may be misclassified by CRC. This paper proposes a local CRC method, which is called KNN-CRC. This method firstly chooses K nearest neighbors of a test sample from all the training samples, then given a test sample, the test sample is represented by these K training samples. The solution of KNN-CRC is obtained by l2 norm minimization, and the size of K is much smaller than the total number of all training samples. Thus, the computational complexity of KNN-CRC is much lower than SRC and CRC. Furthermore, the extensive experiments show that the proposed KNN-CRC can obtain very competitive classification results compared with other methods.