Uniform Tensor Clustering by Jointly Exploring Sample Affinities of Various Orders

Traditional clustering methods rely on pairwise affinity to divide samples into different subgroups. However, high-dimensional small-sample (HDLSS) data are affected by the concentration effects, rendering traditional pairwise metrics unable to accurately describe relationships between samples, leading to suboptimal clustering results. This article advances the proposition of employing high-order affinities to characterize multiple sample relationships as a strategic means to circumnavigate the concentration effects. We establish a nexus between different order affinities by constructing specialized decomposable high-order affinities, thereby formulating a uniform mathematical framework. Building upon this insight, a novel clustering method named uniform tensor clustering (UTC) is proposed, which learns a consensus low-dimensional embedding for clustering by the synergistic exploitation of multiple-order affinities. Extensive experiments on synthetic and real-world datasets demonstrate two findings: 1) high-order affinities are better suited for characterizing sample relationships in complex data and 2) reasonable use of different order affinities can enhance clustering effectiveness, especially in handling high-dimensional data.