  Multiple clustering aims at discovering diverse ways of organizing data into
clusters. Despite the progress made, it's still a challenge for users to
analyze and understand the distinctive structure of each output clustering. To
ease this process, we consider diverse clusterings embedded in different
subspaces, and analyze the embedding subspaces to shed light into the structure
of each clustering. To this end, we provide a two-stage approach called MISC
(Multiple Independent Subspace Clusterings). In the first stage, MISC uses
independent subspace analysis to seek multiple and statistical independent
(i.e. non-redundant) subspaces, and determines the number of subspaces via the
minimum description length principle. In the second stage, to account for the
intrinsic geometric structure of samples embedded in each subspace, MISC
performs graph regularized semi-nonnegative matrix factorization to explore
clusters. It additionally integrates the kernel trick into matrix factorization
to handle non-linearly separable clusters. Experimental results on synthetic
datasets show that MISC can find different interesting clusterings from the
sought independent subspaces, and it also outperforms other related and
competitive approaches on real-world datasets.
