Subspace learning for unsupervised feature selection via adaptive structure learning and rank approximation

Abstract Traditional unsupervised feature selection methods usually construct a fixed similarity matrix. This matrix is sensitive to noise and becomes unreliable, which affects the performance of feature selection. The researches have shown that both the global reconstruction information and local structure information are important for feature selection. To solve the above problem effectively and make use of the global and local information of data simultaneously, a novel algorithm is proposed in this paper, called subspace learning for unsupervised feature selection via adaptive structure learning and rank approximation (SLASR). Specifically, SLASR learns the manifold structure adaptively, thus the preserved local geometric structure can be more accurate and more robust to noise. As a result, the learning of the similarity matrix and the low-dimensional embedding is completed in one step, which improves the effect of feature selection. Meanwhile, SLASR adopts the matrix factorization subspace learning framework. By minimizing the reconstruction error of subspace learning residual matrix, the global reconstruction information of data is preserved. Then, to guarantee more accurate manifold structure of the similarity matrix, a rank constraint is used to constrain the Laplacian matrix. Additionally, the l2,1/2 regularization term is used to constrain the projection matrix to select the most sparse and robust features. Experimental results on twelve benchmark datasets show that SLASR is superior to the six comparison algorithms from the literature.