Collaborative representation with k-nearest classes for classification

Abstract

Sparse representation based classification (SRC) and collaborative representation based classification (CRC), have been widely used in many fields such as face recognition and hyperspectral image classification. All known pattern classes of the training samples are used by SRC and CRC to collaborative represent a test sample, which may be time-consuming and unnecessary. This paper proposes the use of only a part of known pattern classes to collaboratively represent a test sample. Specifically, only the first k (a pre-given constant) classes that are nearest to the sample to be tested are used. With these k-nearest classes (KNCs), SRC and CRC, each can be generalized as KNCs based SRC (KNCSRC) and KNCs based CRC(KNCCRC), and conversely, SRC and CRC can be seen as special cases of KNCSRC and KNCCRC, respectively. Weighted SRC (WSRC) and weighted CRC (WCRC) also can be generalized as KNCs based WSRC (KNCWSRC) and KNCs based WCRC (KNCWSRC), respectively. Competitive classification experiments are carried out on five databases to evaluate the proposed classification scheme. The experimental results show that, in all cases, the proposed KNCSRC and KNCCRC outperform SRC and CRC, respectively.The results also prove that the proposed KNCWCRC outperforms WCRC. In conclusion, collaborative representation with KNCs can further improve collaborative representation based classification.