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Conventional clustering methods based on pairwise affinity usually sufferfrom the concentration effect while processing huge dimensional features yetlow sample sizes data, resulting in inaccuracy to encode the sample proximityand suboptimal performance in clustering. To address this issue, we propose aunified tensor clustering method (UTC) that characterizes sample proximityusing multiple samples' affinity, thereby supplementing rich spatial sampledistributions to boost clustering. Specifically, we find that the triadictensor affinity can be constructed via the Khari-Rao product of two affinitymatrices. Furthermore, our early work shows that the fourth-order tensoraffinity is defined by the Kronecker product. Therefore, we utilizearithmetical products, Khatri-Rao and Kronecker products, to mathematicallyintegrate different orders of affinity into a unified tensor clusteringframework. Thus, the UTC jointly learns a joint low-dimensional embedding tocombine various orders. Finally, a numerical scheme is designed to solve theproblem. Experiments on synthetic datasets and real-world datasets demonstratethat 1) the usage of high-order tensor affinity could provide a supplementarycharacterization of sample proximity to the popular affinity matrix; 2) theproposed method of UTC is affirmed to enhance clustering by exploitingdifferent order affinities when processing high-dimensional data.

Uniform tensor clustering by jointly exploring sample affinities of various orders