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Graph-based dimensionality reduction methods have attracted substantial attention due to their successful applications in many tasks, including classification and clustering. However, most classical graph-based dimensionality reduction approaches are only applied to data from one view. Hence, combining information from different data views has attracted considerable attention in the literature. Although various multi-view graph-based dimensionality reduction algorithms have been proposed, the graph construction strategies utilized in them do not adequately take noise and different importance of multiple views into account, which may degrade their performance. In this paper, we propose a novel algorithm, namely, Low-Rank Graph Optimization for Multi-View Dimensionality Reduction (LRGO-MVDR), that overcomes these limitations. First, we construct a low-rank shared matrix and a sparse error matrix from the graph that corresponds to each view for capturing potential noise. Second, an adaptive nonnegative weight vector is learned to explore complementarity among views. Moreover, an effective optimization procedure based on the Alternating Direction Method of Multipliers scheme is utilized. Extensive experiments are carried out to evaluate the effectiveness of the proposed algorithm. The experimental results demonstrate that the proposed LRGO-MVDR algorithm outperforms related methods.

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