Improving generalization of double low-rank representation using Schatten-p norm

• Published in: Pattern recognition Vol. 138; p. 109352
• Main Authors: Zhao, Jiaoyan, Liang, Yongsheng, Yi, Shuangyan, Shen, Qiangqiang, Cao, Xiaofeng
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2023
• Subjects: Feature extraction; Low-rank representation; Schatten-p norm; Subspace clustering; Subspace clustering; Feature extraction; Low-rank representation; Schatten-p norm
• ISSN: 0031-3203; 1873-5142
• DOI: 10.1016/j.patcog.2023.109352

•We develop a novel DLRR method on large-scale or high-dimension data that can be used in feature extraction and subspace clustering.•We employ the Schatten-p norm to constrain low-rank matrices and the Schatten-p norm with a smaller p value, which is closer to the real low-rank data structure of the data, improving the effectiveness of the projection matrix for feature extraction and the similarity graph for clustering tasks.•Considering the sample and feature space, we remove the null space of the data, significantly reducing the computational complexity when dealing with large-scale or high-dimensional data. Low-rank representation reveals a highly-informative entailment of sparse matrices, where double low-rank representation (DLRR) presents an effective solution by adopting nuclear norm. However, it is a special constraint of Schatten-p norm with p=1 which equally treats all singular values, deviating from the optimal low-rank representation that considers p=0. Thus, this paper improves the DLRR generalization of DLRR by relaxing p=1 into 0<p≤1 to tighten the low-rank constraint of the Schatten-p norm. With such a relaxation, low-rank optimization is then accelerated, resulting in a lower bound on the calculation complexity. Experiments on unsupervised feature extraction and subspace clustering demonstrate that our low-rank optimization taking 0<p≤1 achieves a superior performance against state-of-the-art methods.