Self-paced regularized adaptive multi-view unsupervised feature selection

 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. -norm ()  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.