Matrix regression preserving projections for robust feature extraction

摘要

Dimensionality reduction (DR) technique is a significant tool for feature extraction. In this paper, we propose an innovative two-dimensional (2D) algorithm for DR based on matrix regression model, termed matrix regression preserving projections (MRPP). Unlike many existing 2D algorithms, we construct weight matrix in the high-dimensional space based on nuclear norm (N-norm), which can well preserve the low-rank information of samples. Although MRPP is global in nature, it can also keep locality of data since it uses all training samples to reconstruct data. To make the distance metric more reliable and robust, we also replace F-norm with N-norm to calculate the reconstruction error in the projected space. Besides, L2,1-norm regularization is regularized on transformation matrix so that discrimination information can be learnt in the latent space. MRPP harnesses local and sparse preserving projections, and low rankness of high-dimensional data to build a graph. Therefore, it can learn a robust subspace from the corrupted data, i.e., illumination changes and occlusion. To verify the effectiveness of MRPP, we compare MRPP with a number of the state-of-the-art DR methods. Experiments on benchmark face datasets (Extend Yale B, CMU PIE, FERET, AR and LFW) demonstrate that MRPP outperforms the related state-of-the-arts with prominent results.