Subjectively Interesting Alternative Clusters

We deploy a recently proposed framework for mining subjectively interesting patterns from data [3] to the problem of clustering, where patterns are clusters in the data. This framework outlines how subjective interestingness of patterns (here, clusters) can be quantified using sound information theoretic concepts. We demonstrate how it motivates a new objective function quantifying the interestingness of (a set of) clusters, automatically accounting for a user’s prior beliefs and for redundancies between the clusters. Directly searching for the optimal set of clusters defined in this way is hard. However, the optimization problem can be solved to a provably good approximation if clusters are generated iteratively, paralleling the iterative data mining setting discussed in [3]. In this iterative scheme, each subsequent cluster is maximally interesting given the previously generated ones, automatically trading off interestingness with non-redundancy. Thus, this implementation of the clustering approach can be regarded as a method for alternative clustering. Although generating each cluster in an iterative fashion is computationally hard as well, we develop an approximation technique similar to spectral clustering algorithms. We end with a few visual demonstrations of the alternative clustering approach to artificial datasets.