Localized Graph-based Feature Selection for Clustering
In many data analysis tasks, one is often confronted with very high dimensional data. The feature selection problem is essentially a combinatorial optimization problem which is computationally expensive. On the one hand, to overcome this problem traditional feature selection methods frequently assume either that the features independently influence the class variable or do so only involving pairwise feature interactions. On the other hand, they attempt to select a common feature subset for all the clusters present in the data. However, in doing so they neglect the fact that different features may have different discriminating power for different classes present in data. To tackle the above problems, we propose a localized graph-based feature selection algorithm consisting of three steps, namely, i) based on the label information, we first construct a graph for each class of dataset in which each node corresponds to a feature, and each edge has a weight corresponding to the mutual information (MI) between features connected by that edge, ii) we then perform dominant set clustering for the graphs to select a highly coherent set of features, iii) we further refine the selected features based on a new measure called multidimensional interaction information (MII). The advantage of MII is that it can go beyond pairwise interaction and consider third or higher order feature interactions. Using dominant set clustering, which can extract the most informative features in the leading dominant set as a preprocessing step and in doing so we can limit the search space for higher order interactions. We use a variational EM (VBEM) algorithm to learn a Gaussian mixture model on the selected feature subset for clustering. Experimental results demonstrate the effectiveness of our localized feature selection method on a number of standard data-sets.