Hypergraph spectra for unsupervised feature selection

Abstract

Most existing feature selection methods focus on ranking individual features based on a utility criterion, and select the optimal feature set in a greedy manner. However, the feature combinations found in this way do not give optimal classification performance, since they neglect the correlations among features. In an attempt to overcome this problem, we develop a novel unsupervised feature selection technique by using hypergraph spectral embedding, where the projection matrix is constrained to be a selection matrix designed to select the optimal feature subset. Specifically, by incorporating multidimensional interaction information (MII) for higher order similarities measure, we establish a novel hypergraph framework which is used for characterizing the multiple relationships within a set of samples. Thus, the structural information latent in the data can be more effectively modeled. Secondly, we derive a hypergraph embedding view of feature selection which casting the feature discriminant analysis into a regression framework that considers the correlations among features. As a result, we can evaluate joint feature combinations, rather than being confined to consider them individually, and are thus able to handle feature redundancy. Experimental results demonstrate the effectiveness of our feature selection method on a number of standard datasets. © 2012 Springer-Verlag Berlin Heidelberg.