CMI: An Information-Theoretic Contrast Measure for Enhancing Subspace Cluster and Outlier Detection

In many real world applications data is collected in multi-dimensional spaces, with the knowledge hidden in subspaces (i.e., subsets of the dimensions). It is an open research issue to select meaningful subspaces without any prior knowledge about such hidden patterns. Standard approaches, such as pairwise correlation measures, or statistical approaches based on entropy, do not solve this problem; due to their restrictive pairwise analysis and loss of information in discretization they are bound to miss subspaces with potential clusters and outliers. In this paper, we focus on finding subspaces with strong mutual dependency in the selected dimension set. Chosen subspaces should provide a high discrepancy between clusters and outliers and enhance detection of these patterns. To measure this, we propose a novel contrast score that quantifies mutual correlations in subspaces by considering their cumulative distributions— without having to discretize the data. In our experiments, we show that these high contrast subspaces provide enhanced quality in cluster and outlier detection for both synthetic and real world data.