A hierarchical weighted low-rank representation for image clustering and classification

The low-rank representation (LRR) method has recently gained enormous popularity due to its robust approach in solving the subspace segmentation problem, particularly those concerning corrupted data. In this paper, the recursive sample scaling low-rank representation (RSS-LRR) method is proposed. The advantage of RSS-LRR over traditional LRR is that a cosine scaling factor is further introduced, which imposes a penalty on each sample to minimize noise and outlier influence better. Specifically, the cosine scaling factor is a similarity measure learned to extract each sample’s relationship with the low-rank representation’s principal components in the feature space. In order words, the smaller the angle between an individual data sample and the low-rank representation’s principal components, the more likely it is that the data sample is clean. Thus, the proposed method can then effectively obtain a good low-rank representation influenced mainly by clean data. Several experiments are performed with varying levels of corruption on ORL, CMU PIE, COIL20, COIL100, and LFW in order to evaluate RSS-LRR’s effectiveness over state-of-the-art low-rank methods. The experimental results show that RSS-LRR consistently performs better than the compared methods in image clustering and classification tasks.

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Graph Regularized Weighted Low-Rank Representation for Image Clustering

2018 37th Chinese Control Conference (CCC) ◽

10.23919/chicc.2018.8483648 ◽

2018 ◽

Cited By ~ 2

Author(s):

Lei Cheng ◽

Min Yang

Keyword(s):

Low Rank ◽

Image Clustering ◽

Low Rank Representation

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Low-rank sparse subspace clustering with a clean dictionary

Journal of Algorithms & Computational Technology ◽

10.1177/1748302621999620 ◽

2021 ◽

Vol 15 ◽

pp. 174830262199962

Author(s):

Cong-Zhe You ◽

Zhen-Qiu Shu ◽

Hong-Hui Fan

Keyword(s):

Optimization Problem ◽

Clustering Algorithms ◽

Subspace Clustering ◽

Low Rank ◽

Data Matrix ◽

Image Clustering ◽

Convex Optimization Problem ◽

Data Points ◽

Low Rank Representation ◽

Sparse Subspace Clustering

Low-Rank Representation (LRR) and Sparse Subspace Clustering (SSC) are considered as the hot topics of subspace clustering algorithms. SSC induces the sparsity through minimizing the l1-norm of the data matrix while LRR promotes a low-rank structure through minimizing the nuclear norm. In this paper, considering the problem of fitting a union of subspace to a collection of data points drawn from one more subspaces and corrupted by noise, we pose this problem as a non-convex optimization problem, where the goal is to decompose the corrupted data matrix as the sum of a clean and self-expressive dictionary plus a matrix of noise. We propose a new algorithm, named Low-Rank and Sparse Subspace Clustering with a Clean dictionary (LRS2C2), by combining SSC and LRR, as the representation is often both sparse and low-rank. The effectiveness of the proposed algorithm is demonstrated through experiments on motion segmentation and image clustering.

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Cross-Domain Object Representation via Robust Low-Rank Correlation Analysis

ACM Transactions on Multimedia Computing Communications and Applications ◽

10.1145/3458825 ◽

2021 ◽

Vol 17 (4) ◽

pp. 1-20

Author(s):

Xiangjun Shen ◽

Jinghui Zhou ◽

Zhongchen Ma ◽

Bingkun Bao ◽

Zhengjun Zha

Keyword(s):

Correlation Analysis ◽

Object Representation ◽

Rank Correlation ◽

Data Representation ◽

Low Rank ◽

Superior Performance ◽

Image Clustering ◽

Cross Domain ◽

Clustering And Classification ◽

Correlated Components

Cross-domain data has become very popular recently since various viewpoints and different sensors tend to facilitate better data representation. In this article, we propose a novel cross-domain object representation algorithm (RLRCA) which not only explores the complexity of multiple relationships of variables by canonical correlation analysis (CCA) but also uses a low rank model to decrease the effect of noisy data. To the best of our knowledge, this is the first try to smoothly integrate CCA and a low-rank model to uncover correlated components across different domains and to suppress the effect of noisy or corrupted data. In order to improve the flexibility of the algorithm to address various cross-domain object representation problems, two instantiation methods of RLRCA are proposed from feature and sample space, respectively. In this way, a better cross-domain object representation can be achieved through effectively learning the intrinsic CCA features and taking full advantage of cross-domain object alignment information while pursuing low rank representations. Extensive experimental results on CMU PIE, Office-Caltech, Pascal VOC 2007, and NUS-WIDE-Object datasets, demonstrate that our designed models have superior performance over several state-of-the-art cross-domain low rank methods in image clustering and classification tasks with various corruption levels.

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Local consistent low rank representation for image clustering

2016 Chinese Control and Decision Conference (CCDC) ◽

10.1109/ccdc.2016.7531662 ◽

2016 ◽

Cited By ~ 2

Author(s):

Yuqing Shi ◽

Shiqiang Du ◽

Weilan Wang

Keyword(s):

Low Rank ◽

Image Clustering ◽

Low Rank Representation

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Low-rank sparse subspace clustering with a clean dictionary

Journal of Algorithms & Computational Technology ◽

10.1177/1748302620983690 ◽

2021 ◽

Vol 15 ◽

pp. 174830262098369

Author(s):

Cong-Zhe You ◽

Zhen-Qiu Shu ◽

Hong-Hui Fan

Keyword(s):

Optimization Problem ◽

Clustering Algorithms ◽

Subspace Clustering ◽

Low Rank ◽

Data Matrix ◽

Image Clustering ◽

Convex Optimization Problem ◽

Data Points ◽

Low Rank Representation ◽

Sparse Subspace Clustering

Low-Rank Representation (LRR) and Sparse Subspace Clustering (SSC) are considered as the hot topics of subspace clustering algorithms. SSC induces the sparsity through minimizing the [Formula: see text]-norm of the data matrix while LRR promotes a low-rank structure through minimizing the nuclear norm. In this paper, considering the problem of fitting a union of subspace to a collection of data points drawn from one more subspaces and corrupted by noise, we pose this problem as a non-convex optimization problem, where the goal is to decompose the corrupted data matrix as the sum of a clean and self-expressive dictionary plus a matrix of noise. We propose a new algorithm, named Low-Rank and Sparse Subspace Clustering with a Clean dictionary (LRS2C2), by combining SSC and LRR, as the representation is often both sparse and low-rank. The effectiveness of the proposed algorithm is demonstrated through experiments on motion segmentation and image clustering.

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