Low-rank graph optimization for multi-view dimensionality reduction

Qian, Youcheng; Yin, Xueyan; Kong, Jun; Jian-zhong, Wang; Gao, Wei

doi:10.1371/journal.pone.0225987

Cited by 5 publications

(4 citation statements)

References 57 publications

(45 reference statements)

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“…When

λ_{3}

is large enough, the term

\sum_{i = 1}^{k} θ_{i}

will equal to 0 and the constraint

rank (L) = n - k

will be satisfied. According to Ky Fan's Theorem [19],

\sum_{i = 1}^{k} θ_{i}

is equal to minimizing

Tr (F^{T} L F)

subject to

F^{T} F = I

. Then Equation () can be rewritten as:

\begin{matrix} left \min {(‖‖ Z_{0} - W)}_{F}^{2} + λ_{1} \sum_{i = 1}^{v} ({‖P_{i}‖}_{*} + {‖Z_{i}‖}_{1}) \\ left + λ_{2} \sum_{i = 1}^{v} tr (Z_{i}^{T} Z_{0}) + λ_{2} \sum_{i = 1}^{v} \sum_{i \neq j} tr (Z_{i}^{T} Z_{j}) \\ left + λ_{3} Tr (F^{T} L F) + \sum_{i = i}^{v} {(‖‖, E_{i})}_{2, 1} \\ left s.t. X_{i} = X_{i} P_{i} + E_{i}, P_{i} = Z_{i} + Z_{0}, F^{T} F = I, \\ left W_{i j} \geq 0, \sum_{...} \end{matrix}

…”

Section: The Proposed Approachmentioning

confidence: 99%

“…When 𝜆 3 is large enough, the term ∑ k i=1 𝜃 i will equal to 0 and the constraint rank(L) = n − k will be satisfied. According to Ky Fan's Theorem [19],…”

Section: Optimizationmentioning

confidence: 99%

“…Multi‐Spectral Low‐Rank Structured Dictionary Learning (MLSDL) [18] applied low‐rank structural incoherence term to reduce the discrepancy between different views. Low‐Rank Graph Optimization for Multi‐View Dimensionality Reduction (LRGO‐MVDR) [19] used an adaptive non‐negative weight vector to capture the complementary structure in different face images. Common Subspace based Low‐Rank and Joint Sparse Representation (CSLRJSR) [20] found common face representation fusing discriminative features in different views through a joint low‐rank and sparse methods.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multi‐view intrinsic low‐rank representation for robust face recognition and clustering

Wang

Abhadiomhen

Liu

et al. 2021

IET Image Processing

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In the last years, subspace-based multi-view face recognition has attracted increasing attention and many related methods have been proposed. However, the most existing methods ignore the specific local structure of different views. This drawback can cause these methods' discriminating ability to degrade when many noisy samples exist in data. To tackle this problem, a multi-view low-rank representation method is proposed, which exploits both intrinsic relationships and specific local structures of different views simultaneously. It is achieved by hierarchical Bayesian methods that constrain the low-rank representation of each view so that it matches a linear combination of an intrinsic representation matrix and a specific representation matrix to obtain common and specific characteristics of different views. The intrinsic representation matrix holds the consensus information between views, and the specific representation matrices indicate the diversity among views. Furthermore, the model injects a clustering structure into the low-rank representation. This approach allows for adaptive adjustment of the clustering structure while pursuing the optimization of the low-rank representation. Hence, the model can well capture both the relationship between data and the clustering structure explicitly. Extensive experiments on several datasets demonstrated the effectiveness of the proposed method compared to similar state-of-the-art methods in classification and clustering. How to cite this article: Wang, Z.-y., et al.: Multi-view intrinsic low-rank representation for robust face recognition and clustering. IET Image Process. 1-12 (2021).

show abstract

“…When

λ_{3}

is large enough, the term

\sum_{i = 1}^{k} θ_{i}

will equal to 0 and the constraint

rank (L) = n - k

will be satisfied. According to Ky Fan's Theorem [19],

\sum_{i = 1}^{k} θ_{i}

is equal to minimizing

Tr (F^{T} L F)

subject to

F^{T} F = I

. Then Equation () can be rewritten as:

\begin{matrix} left \min {(‖‖ Z_{0} - W)}_{F}^{2} + λ_{1} \sum_{i = 1}^{v} ({‖P_{i}‖}_{*} + {‖Z_{i}‖}_{1}) \\ left + λ_{2} \sum_{i = 1}^{v} tr (Z_{i}^{T} Z_{0}) + λ_{2} \sum_{i = 1}^{v} \sum_{i \neq j} tr (Z_{i}^{T} Z_{j}) \\ left + λ_{3} Tr (F^{T} L F) + \sum_{i = i}^{v} {(‖‖, E_{i})}_{2, 1} \\ left s.t. X_{i} = X_{i} P_{i} + E_{i}, P_{i} = Z_{i} + Z_{0}, F^{T} F = I, \\ left W_{i j} \geq 0, \sum_{...} \end{matrix}

…”

Section: The Proposed Approachmentioning

confidence: 99%

“…When 𝜆 3 is large enough, the term ∑ k i=1 𝜃 i will equal to 0 and the constraint rank(L) = n − k will be satisfied. According to Ky Fan's Theorem [19],…”

Section: Optimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multi‐view intrinsic low‐rank representation for robust face recognition and clustering

Wang

Abhadiomhen

Liu

et al. 2021

IET Image Processing

View full text Add to dashboard Cite

show abstract

“…[26]. Compared with single-view clustering, multi-view clustering [27][28][29][30][31][32] has received extensive attention due to its better clustering performance. So far, a variety of multi-view clustering methods have been proposed.…”

Section: Introductionmentioning

confidence: 99%

Reweighted multi-view clustering with tissue-like P system

Chen

Liu

2023

PLoS ONE

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Multi-view clustering has received substantial research because of its ability to discover heterogeneous information in the data. The weight distribution of each view of data has always been difficult problem in multi-view clustering. In order to solve this problem and improve computational efficiency at the same time, in this paper, Reweighted multi-view clustering with tissue-like P system (RMVCP) algorithm is proposed. RMVCP performs a two-step operation on data. Firstly, each similarity matrix is constructed by self-representation method, and each view is fused to obtain a unified similarity matrix and the updated similarity matrix of each view. Subsequently, the updated similarity matrix of each view obtained in the first step is taken as the input, and then the view fusion operation is carried out to obtain the final similarity matrix. At the same time, Constrained Laplacian Rank (CLR) is applied to the final matrix, so that the clustering result is directly obtained without additional clustering steps. In addition, in order to improve the computational efficiency of the RMVCP algorithm, the algorithm is embedded in the framework of the tissue-like P system, and the computational efficiency can be improved through the computational parallelism of the tissue-like P system. Finally, experiments verify that the effectiveness of the RMVCP algorithm is better than existing state-of-the-art algorithms.

show abstract

Multi-view low rank sparse representation method for three-way clustering

Khan

et al. 2021

Int. J. Mach. Learn. & Cyber.

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Low-rank graph optimization for multi-view dimensionality reduction

Cited by 5 publications

References 57 publications

Multi‐view intrinsic low‐rank representation for robust face recognition and clustering

Multi‐view intrinsic low‐rank representation for robust face recognition and clustering

Reweighted multi-view clustering with tissue-like P system

Multi-view low rank sparse representation method for three-way clustering

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