Single Data, Multiple Clusterings

There has been extensive research in the clustering community on formalizing the definition of the quality of a given data clustering. However, is it possible to measure the quality of a clustering unless human judgment is taken into consideration? The notion of quality is subjective: for example, given the task of clustering a set of movie reviews, some users might want to cluster them according to sentiment, while others might want to cluster them according to genre. If the clustering algorithm is passive (i.e., it does not have the ability to produce multiple clusterings by actively taking user intent into account), it is hard to justify the algorithm to be qualitatively best across different domains. There has been a recent surge of interest in quantifying how clusterable a dataset is [2]. Can we similarly define multi-clusterability? In this paper, we present a (really) simple active clustering architecture that can help understand the multi-clusterability of a dataset.