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.

提供了一种称为 Multiple Independent Subspace Clusterings 的两阶段方法，其中第一阶段使用独立子空间分析来寻求多个和统计独立的子空间，第二阶段使用图形规范化的半非负矩阵分解来探索集群，实验结果显示其在真实数据集上表现优于其他竞争方法。