低秩分块矩阵的核近似

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Title:

Kernel approximation of a low-rank block matrix

作者:

王中元, 刘惊雷

烟台大学 计算机与控制工程学院, 山东 烟台 264005

Author(s):

WANG Zhongyuan, LIU Jinglei

School of Computer and Control Engineering, Yantai University, Yantai 264005, China

关键词:

低秩近似; 块对角矩阵; 稀疏矩阵; 核近似; 矩阵分解; 交替向量乘子法; 子空间聚类; 图像识别

Keywords:

low-rank approximation; block diagonal matrix; sparse matrix; kernel approximation; matrix factorization; alternating direction method of multipliers (ADMM); subspace clustering; image identification

分类号:

TP181

DOI:

10.11992/tis.201904058

摘要:

为了探讨结构受限下的矩阵分解问题，通过最小化块外对角线来增强类与类之间数据表示的不相关性，从而实现分块约束，即数据来源于不同的聚类结构，是一种局部结构的约束；同时通过增强样本的自表达属性并缩小样本之间的差距来增强类内数据表示的相关性，从而实现低秩约束，即数据行出现冗余，是一种全局结构的约束。随后设计了一个低秩分块矩阵的核近似算法，通过交替方向乘子法迭代求解。最后将该方法分别在人脸识别和字符识别上进行测试。实验结果表明，所提出的低秩分块矩阵分解算法在收敛速度和近似精度上都具有一定的优势。

Abstract:

In order to explore the matrix decomposition problem under structural constraints, irrelevance of data representation between classes was enhanced in this paper by minimizing the diagonal outside the block, thus realizing the block constraint, i.e., the data is derived from different cluster structures. It is a local structure constraint. At the same time, by enhancing the self-expressing property of the sample and narrowing the gap between samples, the correlation of the data representation in the class was enhanced, thereby realizing the low-rank constraint, i.e., the redundancy of the data row was a constraint of the global structure, thereby realizing the low-rank constraint. A kernel approximation algorithm for low-rank block matrix was then designed and solved iteratively by alternating the direction method of multipliers (ADMM). Finally, the method was tested on face recognition and character recognition. Experimental results showed that the proposed low-rank block matrix decomposition algorithm has certain advantages in solving speed and approximate accuracy.