Supervised Feature Selection via Multi-Center and Local Structure Learning

Feature selection has achieved unprecedented success in obtaining sparse discriminative features. However, the existing methods almost use the
$\ell _{2,p}$
-norm constraint on transformation matrix to obtain sparse features, which introduces extra parameters and cannot obtain the features directly. In addition, existing algorithms only focused on the global structure and ignored the local structure, leading to poor performance when solving data with non-Gaussian distributions which a single center point cannot describe precisely. Based on above considerations, we propose a supervised feature selection via multi-center and local structure learning. We further introduce trace ratio criterion into our model in favor of improving the discriminant of features selected. In order to address the overlap problem, we use multiple center points to match the distribution of data and construct a
$k$
-Nearest Neighbor graph to explore the local structure of the data. In addition, we also propose an efficient method to optimize the transformation matrix with the
$\ell _{2,0}$
-norm constraint and can directly obtain the sparse features. We evaluate our method on Toy datasets and several real-world datasets, show improvement over state-of-the-art feature selection methods, and demonstrate the effectiveness of our model in dealing with non-Gaussian distributed data problems.