Image classification using kernel collaborative representation with regularized least square

Sparse representation based classification (SRC) has received much attention in computer vision and pattern recognition. SRC codes a testing sample by sparse linear combination of all the training samples and classifies the testing sample into the class with the minimum representation error. Recently, Zhang analyzes the working mechanism of SRC and points out that it is the collaborative representation but not the L1-norm sparsity that makes SRC powerful. Based on the analysis, they propose a very simple and much more efficient classification scheme, called collaborative representation based classification with regularized least square (CRC-RLS). CRC-RLS is a linear method in nature. Here we propose a kernel collaborative representation based classification with regularized least square (Kernel CRC-RLS, KCRC-RLS) by implicitly mapping the sample into high-dimensional space via kernel tricks. Our approach is highly motivated by the kernel methods which can capture the nonlinear similarity among samples and have been successfully applied in pattern recognition and machine learning. The experimental results on the CENPAMI handwritten digital database, ETH80 database, FERET face database, ORL database, AR face database, demonstrate that Kernel CRC-RLS is effective in classification, leading to promising performance.