Hypergraph Spectra for Semi-supervised Feature Selection

In many data analysis tasks, one is often confronted with the problem of selecting features from very high dimensional data. 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. While the labeled data required by supervised feature selection can be scarce, there is usually no shortage of unlabeled data. In this paper, we propose a novel hypergraph based semi-supervised feature selection algorithm to select relevant features using both labeled and unlabeled data. There are two main contributions in this paper. The first is that 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 subspace learning 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. Experimental results demonstrate the effectiveness of our feature selection method on a number of standard face data-sets.