Class specific subspace learning for collaborative representation

Collaborative representation based classification (CRC) has been successfully used for visual recognition and showed impressive performance recently. However, it directly uses the training samples from each class as the subspaces to calculate the minimum residual error for a given testing sample. This leads to high residual error and instability, which is critical especially for a small number of training samples in each class. In this paper, we propose a class specific subspace learning algorithm for collaborative representation. By introducing the dual form of subspace learning, it presents an explicit relationship between the basis vectors and the original image features, and thus enhances the interpretability. Lagrange multipliers are then applied to optimize the corresponding objective function, i.e., learning the weights used in constructing the subspaces. Extensive experimental results demonstrate that the proposed algorithm has achieved superior performance in several visual recognition tasks.