Detecting clusters in moderate-to-high dimensional data: subspace clustering, pattern-based clustering, and correlation clustering

As a prolific research area in data mining, subspace clustering and related problems induced a vast amount of proposed solutions. However, many publications compare a new proposition – if at all – with one or two competitors or even with a so called “näıve” ad hoc solution but fail to clarify the exact problem definition. As a consequence, even if two solutions are thoroughly compared experimentally, it will often remain unclear whether both solutions tackle the same problem or, if they do, whether they agree in certain tacit assumptions and how such assumptions may influence the outcome of an algorithm. In this tutorial, we try to clarify (i) the different problem definitions related to subspace clustering in general, (ii) the specific difficulties encountered in this field of research, (iii) the varying assumptions, heuristics, and intuitions forming the basis of different approaches, and (iv) how several prominent solutions essentially tackle different problems.