Consensus Graph Weighting via Trace Ratio Criterion for Multi-view Unsupervised Feature Selection

The problem of multi-view unsupervised feature selection receive more attention in recent years. Most of existing works explore the shared information across multi-views. Several embedded algorithms have been developed. All these methods use additional hyper-parameter for regularization, which makes these algorithms are less attractive in practical applications, where it is not easy to select the proper model among potential large candidate parameter spaces. In this paper, we aim at consider a Two-level Weighted Graph Matching for Unsupervised Multi-view Feature Selection. We construct view-specific graphs to capture the local structure of each view. We also compute the feature-level graphs to obtain the local structure of data characterized by single feature. Thus, we learn the optimal unknown graph from both the view-specific graphs and the feature-level graphs. The approximation between the consensus graph and the feature level graphs is achieved by the two-level weighted linear combination measured by the squared loss function. The consensus between the final graph and view-specific graphs are captured by the integrated pairwise alignment among sample pairs. Moreover, these two criteria are integrated into a unified learning procedure under the trace-ratio framework.