Comparing subspace clusterings

We present the first framework for comparing subspace clusterings. We propose several distance measures for subspace clusterings, including generalizations of well-known distance measures for ordinary clusterings. We describe a set of important properties for any measure for comparing subspace clusterings and give a systematic comparison of our proposed measures in terms of these properties. We validate the usefulness of our subspace clustering distance measures by comparing clusterings produced by the algorithms FastDOC, HARP, PROCLUS, ORCLUS, and SSPC. We show that our distance measures can be also used to compare partial clusterings, overlapping clusterings, and patterns in binary data matrices.