SONAR: Signal De-mixing for Robust Correlation Clustering

Abstract

Clustering is one of the most fundamental challenges in data mining. We identified three core problems which turn finding a natural grouping of a data set into a difficult task: First, clusters may exist in arbitrarily oriented subspaces of various dimensionality (also known as correlation clusters). Secondly, the cluster structure may be hidden by noise and outliers. Finally, the number, size and density of the clusters is usually unknown which makes the parametrization of existing approaches very difficult. In this paper, we address these three problems by combining ideas from information theory and blind signal source separation. Our algorithm is inspired by the idea of an active sonar that reveals hidden objects by sending echo pings with various frequencies and from different directions. Analogously, our algorithm SONAR very efficiently generates primitive pre-clusters and considers exactly these pre-clusters as echo pings. Each echo of a ping is a mixture of the signals of the true clusters. Independent component analysis (ICA) allows us to decompose the mixed signals into statistically independent response patterns. We combine the idea of signal de-mixing with the Minimum Description Length (MDL) principle to allow an outlier-robust and parameter-free detection of the true clusters. Extensive experiments demonstrate the following assets of SONAR: Outlier-robust detection of correlation clusters of various density and subspace orientation, requiring no difficult input parameters, and scalability to large data sets.