Learnable low-rank latent dictionary for subspace clustering

Xu, Yesong; Chen, Shuo; Li, Jun; Luo, Lei; Yang, Jian

doi:10.1016/j.patcog.2021.108142

Cited by 22 publications

(6 citation statements)

References 24 publications

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“…It is obvious that the above equation ( 10) is the Lyapunov matrix equation, and adopting Bartels-Stewart algorithm can ensure that it has a closed-form solution [7].…”

Section: Optimization Algorithmmentioning

confidence: 99%

“…The proposed robust subspace clustering approach FCSC is compared with the subspace clustering methods including SSC [2], LSR [5], LRR [3], Correlation Adaptive Subspace Segmentation(CASS) [10], Latent Low Rank Representation (LatLRR) [11], Block Diagonal Representation (BDR) [12], Implicit Block Diagonal Low Rank Representation (IBDLR) [13]. In our experiments, four benchmark datasets are utilized to evaluate our proposed FCSC.They are COIL-20 dataset, Extended-YaleB dataset, USPS dataset, and Robust-NUST dataset [7], [14]. Furthermore, the clustering ACCuracy (ACC) and Normalized Mutual Information (NMI) are employed, which are frequently used in experiments on subspace clustering [7].…”

Section: Preliminarymentioning

confidence: 99%

“…However, previous works generally utilize raw data directly [6] and focus on selecting an appropriate regularization to characterize the coefficient matrix [4], but they ignore the influence of noise in the real world [7]. For example, face images are frequently obscured by masks or sunglasses, as well as are affected by various lighting conditions, which makes face images have more complex noise.…”

Section: Introductionmentioning

confidence: 99%

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Towards Robust Subspace Clustering via Joint Feature Extraction and Cauchy Loss Function

Xu,

2024

J. Phys.: Conf. Ser.

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The purpose of the subspace clustering approach is to discover the similarity between samples by learning a self-representation matrix, and it has been widely employed in machine learning and pattern recognition. Most existing subspace clustering techniques discover subspace structures from raw data and simply adopt L2 loss to characterize the reconstruction error. To break through these limitations, a novel robust model named Feature extraction and Cauchy loss function-based Subspace Clustering (FCSC) is proposed. FCSC performs low dimensional and low-rank feature extraction at the same time, as well as processing large noise in the data to generate a more ideal similarity matrix. Furthermore, we provide an efficient iterative strategy to solve the resultant problem. Extensive experiments on benchmark datasets confirm its superiority in the robustness of some advanced subspace clustering algorithms.

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“…It is obvious that the above equation ( 10) is the Lyapunov matrix equation, and adopting Bartels-Stewart algorithm can ensure that it has a closed-form solution [7].…”

Section: Optimization Algorithmmentioning

confidence: 99%

Section: Preliminarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Towards Robust Subspace Clustering via Joint Feature Extraction and Cauchy Loss Function

Xu,

2024

J. Phys.: Conf. Ser.

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“…The self-expressive-based subspace clustering method has shown its superior performance in machine learning and computer vision (Lu et al 2018;Li et al 2020a;Chen et al 2021c), but there are two non-negligible drawbacks. One is that it may fail to discover subspace structure sufficiently when the original data is directly utilized to acquire the similarity matrix (Liu and Yan 2011;Xu et al 2021). The other is that the self-expressive strategy is hard to describe the linear relationship between samples for real-world data accurately, it makes the learned similarity matrix may be inaccurate.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Evaluation Measures: To evaluate the performance of different subspace clustering methods, we employ two popular metrics to evaluate clustering performance, each of which favors different properties of clustering, including Accuracy (ACC) and Normalized Mutual Information (NMI), the detailed definitions of ACC and NMI can be seen in (Xu et al 2021). The above two metrics both lie in the range of [0, 1], and the higher value indicates better clustering performance.…”

Section: Experimental Settingsmentioning

confidence: 99%

Linearity-Aware Subspace Clustering

Chen

et al. 2022

AAAI

Self Cite

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Obtaining a good similarity matrix is extremely important in subspace clustering. Current state-of-the-art methods learn the similarity matrix through self-expressive strategy. However, these methods directly adopt original samples as a set of basis to represent itself linearly. It is difficult to accurately describe the linear relation between samples in the real-world applications, and thus is hard to find an ideal similarity matrix. To better represent the linear relation of samples, we present a subspace clustering model, Linearity-Aware Subspace Clustering (LASC), which can consciously learn the similarity matrix by employing a linearity-aware metric. This is a new subspace clustering method that combines metric learning and subspace clustering into a joint learning framework. In our model, we first utilize the self-expressive strategy to obtain an initial subspace structure and discover a low-dimensional representation of the original data. Subsequently, we use the proposed metric to learn an intrinsic similarity matrix with linearity-aware on the obtained subspace. Based on such a learned similarity matrix, the inter-cluster distance becomes larger than the intra-cluster distances, and thus successfully obtaining a good subspace cluster result. In addition, to enrich the similarity matrix with more consistent knowledge, we adopt a collaborative learning strategy for self-expressive subspace learning and linearity-aware subspace learning. Moreover, we provide detailed mathematical analysis to show that the metric can properly characterize the linear correlation between samples.

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