Collaborative Representation Classifier based on K Nearest Neighbors for Classification
Jiangshu Wei, Xiangjun Qi, Mantao Wang
Journal of Intelligent Computing, Vol. 7, No. 1, 2016.
DOI: 
Link: http://www.dline.info/jic/fulltext/v7n1/jicv7n1_3.pdf
Abstract:
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.