Generalized Independent Subspace Clustering

Data can encapsulate different object groupings in subspaces of arbitrary dimension and orientation. Finding such subspaces and the groupings within them is the goal of generalized subspace clustering. In this work we present a generalized subspace clustering technique capable of finding multiple non-redundant clusterings in arbitrarily-oriented subspaces. We use Independent Subspace Analysis (ISA) to find the subspace collection that minimizes the statistical dependency (redundancy) between clusterings. We then cluster in the arbitrarily-oriented subspaces identified by ISA. Our algorithm ISAAC (Independent Subspace Analysis and Clustering) uses the Minimum Description Length principle to automatically choose parameters that are otherwise difficult to set. We comprehensively demonstrate the effectiveness of our approach on synthetic and real-world data.