Supervised neighborhood regularized collaborative representation for face recognition

How to represent a test sample is very crucial for linear representation based classification. The famous sparse representation focuses on employing linear combination of small samples to represent the query sample. However, the local structure and label information of data are neglected. Recently, locality-constrained collaborative representation (LCCR) has been proposed and integrates a kind of locality-constrained term into the collaborative representation scheme. For each test sample, LCCR mainly considers its neighbors to deal with noise and LCCR is robust to various corruptions. However, the nearby samples may not belong to the same class. To deal with this situation, in this paper, we not only utilize the positive effect of neighbors, but also consider the side effect of neighbors. A novel supervised neighborhood regularized collaborative representation (SNRCR) is proposed, which employs the local structure of data and the label information of neighbors to improve the discriminative capability of the coding vector. The objective function of SNRCR obtains the global optimal solution. Many experiments are conducted over six face data sets and the results show that SNRCR outperforms other algorithms in most case, especially when the size of training data is relatively small. We also analyze the differences between SNRCR and LCCR.