Robust subspace clustering via symmetry constrained latent low rank representation with converted nuclear norm

Fang, Xian; Tie, Zhixin; Song, Feiyang; Yang, Jialiang

doi:10.1016/j.neucom.2019.02.055

Cited by 14 publications

(6 citation statements)

References 38 publications

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“…To verify the efficiency and effectiveness of the proposed LLRRSC method, we compare it with the following some state‐of‐the‐art unsupervised feature selection approaches: Joints embedding learning with sparse regression (JELSR) [5], Robust LatLRR (ROBLRR) [28], Regularized self‐representation (RSR) [17], Unsupervised feature selection with structured graph optimization (SOGFS) [19], Low‐rank representation with a symmetric constraint (LRRSC) [29], Symmetry constrained latent low‐rank representation with converted nuclear norm (SLLRRC) [30], Generalized uncorrelated regression with adaptive graph for unsupervised feature selection (URAFS) [18], Latent representation learning and manifold regularization (LRLMR) [50], Hypergraph regularized latent representation learning (AHRLRL) [31], Dual space latent representation learning (DSLRL) [32].…”

Section: Methodsmentioning

confidence: 99%

“…Proof. We only need to prove that the objective function in (11) decreases monotonically under the updating rules ( 16), ( 18), ( 22), ( 27) and (30), respectively.…”

Section: Complexity and Convergencementioning

confidence: 99%

“…Chen et al [29] incorporated the symmetric constraint into LRR for robust subspace clustering (LRRSC), where the symmetry constraint of the representation matrix in LRR guarantees the weight consistency for every pair of data points. To simultaneously learn a lowrank and sparse coefficient matrix, Fang et al [30] presented latent low-rank representation with symmetric constraint based on the converted nuclear norm for robust subspace clustering (SLLRRC), where the nuclear norm enhances the sparsity of the coefficient matrix. Ding et al [31] integrated adaptively learning of hypergraph with latent representation learning for unsupervised feature selection to capture the local manifold geometrical structure of original data in a high-order way.…”

Section: Introductionmentioning

confidence: 99%

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Latent low‐rank representation sparse regression model with symmetric constraint for unsupervised feature selection

Guo

Chen

2023

IET Image Processing

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Unsupervised feature selection is a dimensionality reduction method and has been widely used as an important and indispensable preprocessing step in many tasks. However, realworld data are not only high-dimensional, but also have intrinsic correlations between data points, which are not fully utilized in feature selection. Furthermore, real-world data usually inevitably contain noise or outliers. In order to select features from data more effectively, a sparse regression model based on latent low-rank representation with the symmetric constraint for unsupervised feature selection is proposed. With the coefficient matrix of non-negative symmetric low-rank representation, an affinity matrix characterized by the correlation relationship between data points is adaptively obtained, which reveals the intrinsic geometric relationship, global structure, and discrimination of data points. A latent representation of all data points obtained from this affinity matrix is employed as a pseudolabel, and feature selection is carried out by sparse linear regression. This method performs feature selection in the learned latent space instead of the original data space. An alternating iteration algorithm is designed to solve the proposed model, and its effectiveness and efficiency are verified on several benchmark data sets.

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Section: Methodsmentioning

confidence: 99%

“…Proof. We only need to prove that the objective function in (11) decreases monotonically under the updating rules ( 16), ( 18), ( 22), ( 27) and (30), respectively.…”

Section: Complexity and Convergencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Latent low‐rank representation sparse regression model with symmetric constraint for unsupervised feature selection

Guo

Chen

2023

IET Image Processing

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“…As for constrained subspace clustering, more efforts pay attention to the constrained (semi-supervised) LRR [42], [43], [44] than constrained SSC [21]. Fang et al [42] proposed a robust semi-supervised subspace clustering method based on non-negative LRR (NNLRR).…”

Section: B Constrained Subspace Clusteringmentioning

confidence: 99%

“…CLRR incorporates supervision information as hard constraints for enhancing the discriminating power of optimal low-rank representation of data. Fang et al [44] proposed a symmetry constrained latent low rank representation with converted nuclear norm (SLLRRC) algorithm for robust subspace clustering. SLL-RRC both enhances the sparsity of the coefficient matrix and guarantees weight consistency for each pair of data samples when seeking the low rank representation.…”

Section: B Constrained Subspace Clusteringmentioning

confidence: 99%

Active Block Diagonal Subspace Clustering

Xie

Wang

2021

IEEE Access

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Subspace clustering aims to find clusters in the low-dimensional subspaces for high-dimensional data. Subspace clustering with Block Diagonal Representation (BDR) maintains the number of connected components of the graph by Laplacian rank constraint, and the learned affinity matrix shows a block diagonal structure, which will achieve a good segmentation for the dataset by spectral clustering. However, the subspaces of real data may overlap and the learned affinity matrix may be imprecise. In this work, we propose an Active learning framework for BDR(ABDR) to acquire and incorporate prior knowledge to improve the subspace clustering performance. An active selection strategy is designed to acquire labels of the informative data points from both the skeleton of clusters and the boundaries of clusters, and then the labeled data are converted into pairwise constraints, which are incorporated into BDR. The optimization of the new objective function is given and the convergence of ABDR is discussed. Experimental results on three images datasets (MNIST, and one UCI dataset(ISOLET) demonstrate the effectiveness of ABDR on complex clustering tasks and show that ABDR is superior to multiple state-of-the-art active clustering and learning techniques.

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Subspace Clustering with Block Diagonal Sparse Representation

Fang

Zhang²,

et al. 2021

Neural Process Lett

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Structured representation is of remarkable significance in subspace clustering. However, most of the existing subspace clustering algorithms resort to single-structured representation, which may fail to fully capture the essential characteristics of data. To address this issue, a novel multi-structured representation subspace clustering algorithm called block diagonal sparse representation (BDSR) is proposed in this paper. It takes both sparse and block diagonal structured representations into account to obtain the desired affinity matrix. The unified framework is established by integrating the block diagonal prior into the original sparse subspace clustering framework and the resulting optimization problem is iteratively solved by the inexact augmented Lagrange multipliers (IALM). Extensive experiments on both synthetic and real-world datasets well demonstrate the effectiveness and efficiency of the proposed algorithm against the state-of-the-art algorithms.

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Robust subspace clustering via symmetry constrained latent low rank representation with converted nuclear norm

Cited by 14 publications

References 38 publications

Latent low‐rank representation sparse regression model with symmetric constraint for unsupervised feature selection

Latent low‐rank representation sparse regression model with symmetric constraint for unsupervised feature selection

Active Block Diagonal Subspace Clustering

Subspace Clustering with Block Diagonal Sparse Representation

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