A Hypergraph-Based Approach to Feature Selection

In many data analysis tasks, one is often confronted with the problem of selecting features from very high dimensional data. The feature selection problem is essentially a combinatorial optimization problem which is computationally expensive. To overcome this problem it is frequently assumed that either features independently influence the class variable or do so only involving pairwise feature interaction. To overcome this problem, we draw on recent work on hyper-graph clustering to extract maximally coherent feature groups from a set of objects using high-order (rather than pairwise) similarities. We propose a three step algorithm that, namely, i) first constructs a graph in which each node corresponds to each feature, and each edge has a weight corresponding to the interaction information among features connected by that edge, ii) perform hypergraph clustering to select a highly coherent set of features, iii) further selects features based on a new measure called the multidimensional interaction information (MII). The advantage of MII is that it incorporates third or higher order feature interactions. This is realized using hypergraph clustering, which separates features into clusters prior to selection, thereby allowing us to limit the search space for higher order interactions. Experimental results demonstrate the effectiveness of our feature selection method on a number of standard data-sets.