Robust Unsupervised Feature Selection by Nonnegative Sparse Subspace Learning

Sparse subspace learning has been demonstrated to be effective in data mining and machine learning. In this paper, we cast the unsupervised feature selection scenario as a matrix factorization problem from the view of sparse subspace learning. By minimizing the reconstruction residual, the learned feature weight matrix with the l(2,1)-norm and the non-negative constraints not only removes the irrelevant features, but also captures the underlying low dimensional structure of the data points. Meanwhile in order to enhance the model's robustness, we attempt to solve our problem by l(1)-norm error function which is resistant to outliers and sparse noise. An efficient iterative algorithm is introduced to optimize this non-convex and non-smooth objective function and the proof of its convergence is given. Particularly, differ from conventional non-negative updating rules, we design a novel multiplicative update rule to iteratively solve the feature weight matrix, and we validate its non-negativity. Comparative experiments on various original datasets with and without malicious pollution demonstrate performance superiority of our model.