Enhanced Multi-View Low-Rank Graph Optimization for Dimensionality Reduction

Abstract

In the last decade, graph embedding-based dimensionality reduction for multi-view data has been extensively studied. However, constructing a high-quality graph for dimensionality reduction is still a significant challenge. Herein, we propose a new algorithm, named multi-view low-rank graph optimization for dimensionality reduction (MvLRGO), which integrates graph optimization with dimensionality reduction into one objective function in order to simultaneously determine the optimal subspace and graph. The subspace learning of each view is conducted independently by the general graph embedding framework. For graph construction, we exploit low-rank representation (LRR) to obtain reconstruction relationships as the affinity weight of the graph. Subsequently, the learned graph of each view is further optimized throughout the learning process to obtain the ideal assignment of relations. Moreover, to integrate information from multiple views, MvLRGO regularizes each of the view-specific optimal graphs such that they align with one another. Benefiting from this term, MvLRGO can achieve flexible multi-view communication without constraining the subspaces of all views to be the same. Various experimental results obtained with different datasets show that the proposed method outperforms many state-of-the-art multi-view and single-view dimensionality reduction algorithms.