Tensors or multiarray data are generalizations of matrices. Tensor clustering
has become a very important research topic due to the intrinsically rich
structures in real-world multiarray datasets. Subspace clustering based on
vectorizing multiarray data has been extensively researched. However,
vectorization of tensorial data does not exploit complete structure
information. In this paper, we propose a subspace clustering algorithm without
adopting any vectorization process. Our approach is based on a novel
heterogeneous Tucker decomposition model. In contrast to existing techniques,
we propose a new clustering algorithm that alternates between different modes
of the proposed heterogeneous tensor model. All but the last mode have
closed-form updates. Updating the last mode reduces to optimizing over the
so-called multinomial manifold, for which we investigate second order
Riemannian geometry and propose a trust-region algorithm. Numerical experiments
show that our proposed algorithm compete effectively with state-of-the-art
clustering algorithms that are based on tensor factorization.

本文针对多维数组数据具有丰富结构，而向量化方法难以完整表述结构信息的问题，提出了一种基于新型异构 Tucker 分解模型的子空间聚类算法，并探究了二阶黎曼几何的多项式流形及核心域中的优化问题。数值实验表明，该算法与基于张量因数分解的最新聚类算法竞争效果明显。