Multi-View Projection Learning via Adaptive Graph Embedding for Dimensionality Reduction

In order to explore complex structures and relationships hidden in data, plenty of graph-based dimensionality reduction methods have been widely investigated and extended to the multi-view learning field. For multi-view dimensionality reduction, the key point is extracting the complementary and compatible multi-view information to analyze the complex underlying structure of the samples, which is still a challenging task. We propose a novel multi-view dimensionality reduction algorithm that integrates underlying structure learning and dimensionality reduction for each view into one framework. Because the prespecified graph derived from original noisy high-dimensional data is usually low-quality, the subspace constructed based on such a graph is also low-quality. To obtain the optimal graph for dimensionality reduction, we propose a framework that learns the affinity based on the low-dimensional representation of all views and performs the dimensionality reduction based on it jointly. Although original data is noisy, the local structure information of them is also valuable. Therefore, in the graph learning process, we also introduce the information of predefined graphs based on each view feature into the optimal graph. Moreover, assigning the weight to each view based on its importance is essential in multi-view learning, the proposed GoMPL automatically allocates an appropriate weight to each view in the graph learning process. The obtained optimal graph is then adopted to learn the projection matrix for each individual view by graph embedding. We provide an effective alternate update method for learning the optimal graph and optimal subspace jointly for each view. We conduct many experiments on various benchmark datasets to evaluate the effectiveness of the proposed method.