In this paper, we investigate the research problem of unsupervised multi-view feature selection. Conventional solutions first simply combine multiple pre-constructed view-specific similarity structures into a collaborative similarity structure, and then perform the subsequent feature selection. These two processes are separate and independent. The collaborative similarity structure remains fixed during feature selection. Further, the simple undirected view combination may adversely reduce the reliability of the ultimate similarity structure for feature selection, as the view-specific similarity structures generally involve noises and outlying entries. To alleviate these problems, we propose an adaptive collaborative similarity learning (ACSL) for multi-view feature selection. We propose to dynamically learn the collaborative similarity structure, and further integrate it with the ultimate feature selection into a unified framework. Moreover, a reasonable rank constraint is devised to adaptively learn an ideal collaborative similarity structure with proper similarity combination weights and desirable neighbor assignment, both of which could positively facilitate the feature selection. An effective solution guaranteed with the proved convergence is derived to iteratively tackle the formulated optimization problem. Experiments demonstrate the superiority of the proposed approach.
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