激光与光电子学进展, 2018, 55 (7): 071003, 网络出版: 2018-07-20
基于低秩正则化异构张量分解的子空间聚类算法 下载: 1005次
Low-Rank Regularized Heterogeneous Tensor Decomposition Algorithm for Subspace Clustering
摘要
张量分解是解决高维数据分析问题的有力工具。传统张量Tucker分解模型多采用各项同性假设,即各个因子矩阵具有相同的约束条件(例如正交、非负等),但该种假设不适用于异构张量数据分析。本文提出了一种基于低秩正则化的异构张量分解(LRRHTD)算法,并用于子空间聚类任务。低秩正则化的异构张量分解核心思想是对原始张量寻求一组正交因子矩阵的集合,将高维张量映射到低维的潜在子空间中,同时在最后的因子矩阵上引入低秩约束以获得可用于聚类的全局低秩结构表征。此外,设计了一种基于增广拉格朗日乘子的优化方法对所提算法进行求解。在两个公开数据集上的实验表明,本文提出的方法不仅可以在较少次数的迭代内达到收敛,而且与现有的其他聚类方法相比,取得了较为理想的聚类性能。
Abstract
Tensor decomposition is a powerful computational tool for analyzing multi-dimensional data. The traditional Tucker decomposition models are generally proposed based on the isotropy hypothesis, meaning that the factor matrices are learned in an equivalent way for all modes (such as orthogonal or non-negative constraints), which is not suitable for the heterogeneous tensor data. We propose a low-rank regularized heterogeneous tensor decomposition (LRRHTD) model for subspace clustering. The core idea of LRRHTD is that we seek a set of orthogonal factor matrices for all but the last mode to map the high-dimensional tensor into a low-dimensional latent subspace. In the meantime, we seek the lowest-rank representation of the original tensor by imposing a low-rank constraint on the last mode, in order to reveal the global structure of samples for the purpose of clustering. We also develop an effective optimization algorithm based on augmented Lagrangian multiplier to solve our proposed model. Experiments on two public datasets demonstrate that the proposed method reaches convergence within a small number of iterations and achieves promising clustering results in comparison with state-of-the-art methods.
张静, 付建鹏, 李新慧. 基于低秩正则化异构张量分解的子空间聚类算法[J]. 激光与光电子学进展, 2018, 55(7): 071003. Zhang Jing, Fu Jianpeng, Li Xinhui. Low-Rank Regularized Heterogeneous Tensor Decomposition Algorithm for Subspace Clustering[J]. Laser & Optoelectronics Progress, 2018, 55(7): 071003.