Self-paced regularized adaptive multi-view unsupervised feature selection

Abstract

Multi-view unsupervised feature selection (MUFS) is an efficient approach for dimensional reduction of heterogeneous data. However, existing MUFS approaches mostly assign the samples the same weight, thus the diversity of samples is not utilized efficiently. Additionally, due to the presence of various regularizations, the resulting MUFS problems are often non-convex, making it difficult to find the optimal solutions. To address this issue, a novel MUFS method named Self-paced Regularized Adaptive Multi-view Unsupervised Feature Selection (SPAMUFS) is proposed. Specifically, the proposed approach firstly trains the MUFS model with simple samples, and gradually learns complex samples by using self-paced regularizer. l2,p-norm (0<p≤1) is employed to measure the learning error and as the sparse regularization to accommodate various sparsity requirements across different datasets. Moreover, hypergraph Laplacian matrices are constructed for each view to better preserve the local manifold structure and encode high-order relationships within the data space. They are adaptively assigned weights to learn the underlying correlated and diverse information among different views. An iterative optimization algorithm is proposed to solve SPAMUFS and the convergence and computational complexity are also analyzed. The effectiveness of SPAMUFS is substantiated by comparing with eight state-of-the-art algorithms on nine public multi-view datasets.