Linear Subspace Learning via sparse dimension reduction

Linear Subspace Learning (LSL) has been widely used in many areas of information processing, such as dimensionality reduction, data mining, pattern recognition and computer vision. Recent years have witnessed several excellent extensions of PCA in LSL. One is the recent L1-norm maximization principal component analysis (L1Max-PCA), which aims at learning linear subspace efficiently. L1Max-PCA simply simulates PCA by replacing the covariance with the so-called L1-norm dispersion in the mapped feature space. However, it is difficult to give an intuitive interpretation. In this paper, a novel subspace learning approach based on sparse dimension reduction is proposed, which enforces the sparsity of the mapped data to better recover cluster structures. The optimization problem is solved efficiently via Alternating Direction Method (ADM). Experimental results show that the proposed method is effective in subspace learning.