Unsupervised Feature Selection via Adaptive Graph Learning and Constraint

The performance of graph-based feature selection methods relies heavily on the quality of the construction of the similarity matrix. However, most of the graphs on these methods are initially fixed, where few of them are constrained. Once the graph is determined, it will remain constant in the whole optimization process. In other words, in case that the graph constructed on the raw data is not appropriate, it will drag down the entire algorithm. Aiming to tackle this defect, a novel unsupervised feature selection via adaptive graph learning and constraint (EGCFS) is proposed to select the uncorrelated yet discriminative features by exploiting the embedded graph learning and constraint. The adaptive graph learning method incorporates the structure of the similarity matrix into the optimization process, which not only learns the graph structure adaptively but also obtains the closed-form solution of the graph coefficient. Special graph constraint is embedded with the feature selection process to connect nearer data points with larger probability. The idea of maximizing between-class scatter matrix and the adaptive graph structure is integrated into a uniform framework to obtain excellent structural performance. Moreover, the proposed embedded graph constraint not only performs with manifold structure but also validates the link between graph-based approach and k -means from a unique perspective. Experiments on several benchmark data sets verify the effectiveness and superiority of the proposed method.