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Robust low-rank representation with adaptive graph regularization from clean data
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DOI：10.1007/s10489-021-02749-w.png)
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Abstract
En 中文
The goal of subspace clustering (SC) methods is to group data samples, which are supposed to be drawn from a union of subspaces, into their underlying subspaces. In the SC problem, the assumption, which is called self-expressive assumption of data samples, has been proven effectively. Low-rank representation (LRR) is a recently proposed famous self-expressive method. However, the LRR method can only capture the global structure among data, and the local structure of data is neglected. Besides, although the real data are often corrupted, the LRR model uses the noisy data instead of the clean data as the dictionary. Then, the learned similarity matrix may be not reliable. To address these problem, in this paper, we propose a novel subspace clustering method called robust low-rank representation with adaptive graph regularization from clean data (RLRR-AGR). In the RLRR-AGR model, a graph regularization term is integrated into the framework of LRR. That is, the graph construction and subsequent optimization are in a unified framework. Then the intrinsic non-linear geometric information in data can be captured. More importantly, the graph can adaptive updated from the clean data instead of the raw data. The clean data are obtained by removing noise in the raw data. Then the clustering performance can be improved. By using the augmented Lagrangian method, an efficient algorithm is also presented to solve the RLRR-AGR model. The experimental results on some data sets show that the proposed RLRR-AGR model outperforms many state-of-the-art clustering approaches.
Keywords:
Low-rank representation
Subspace clustering
Graph regularization
Spectral clustering
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