Discriminating Tensor Spectral Clustering for High-Dimension-Low-Sample-Size Data.

Abstract

Tensor spectral clustering (TSC) is a recently proposed approach to robustly group data into underlying clusters. Unlike the traditional spectral clustering (SC), which merely uses pairwise similarities of data in an affinity matrix, TSC aims at exploring their multiwise similarities in an affinity tensor to achieve better performance. However, the performance of TSC highly relies on the design of multiwise similarities, and it remains unclear especially for high-dimension-low-sample-size (HDLSS) data. To this end, this article has proposed a discriminating TSC (DTSC) for HDLSS data. Specifically, DTSC uses the proposed discriminating affinity tensor that encodes the pair-to-pair similarities, which are particularly constructed by the anchor-based distance. HDLSS asymptotic analysis shows that the proposed affinity tensor can explicitly differentiate samples from different clusters when the feature dimension is large. This theoretical property allows DTSC to improve the clustering performance on HDLSS data. Experimental results on synthetic and benchmark datasets demonstrate the effectiveness and robustness of the proposed method in comparison to several baseline methods.