Nuclear reconstructive feature extraction

In this paper, we propose a novel feature extraction method for pattern classification problem. We propose to map the original data to subspaces for feature extraction and hope the mapped data can reconstruct the original data. The motive is to avoid of losing of information of the original data in the process of subspace mapping. We assume that if the original data can be reconstructed from the subspace, the critical information can be preserved. Moreover, we also observed that the reconstruction error is a low-rank matrix if the reconstruction is performed well. We propose to measure the reconstruction error matrix rank by the nuclear norm and minimize it to learn the optimal subspace transformation matrix. Meanwhile, the classification is also used to regularize the learning to improve the discriminate ability of the subspace representations. Experiments over several benchmark data sets show the advantage of the proposed method over the existing subspace learning methods.