Simultaneous Global and Local Graph Structure Preserving for Multiple Kernel Clustering

Ren, Zhenwen; Sun, Quansen

doi:10.1109/tnnls.2020.2991366

Cited by 107 publications

(42 citation statements)

References 45 publications

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“…Theorem

boldL

is the Laplacian matrix of symmetry similarity matrix

boldS

and the

i, j

th element of

boldQ

is denoted as

Q_{i j} = ∥ v_{i} - v_{j} ∥_{2}^{2}

, where

v_{i}

is the

i

th row of matrix

boldV

. Then we can obtain the equivalent representation 33

Tr (V^{⊤} boldL boldV) = Tr (boldS boldQ) .

…”

Section: Optimizationmentioning

confidence: 99%

Partial multiview clustering with locality graph regularization

Lian

Wang

et al. 2021

Int J Intell Syst

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Multiview clustering (MVC) collects complementary and abundant information, which draws much attention in machine learning and data mining community. Existing MVC methods usually hold the assumption that all the views are complete. However, multiple source data are often incomplete in real‐world applications, and so on sensor failure or unfinished collection process, which gives rise to incomplete multiview clustering (IMVC). Although enormous efforts have been devoted in IMVC, there still are some urgent issues that need to be solved: (i) The locality among multiple views has not been utilized in the existing mechanism; (ii) Existing methods inappropriately force all the views to share consensus representation while ignoring specific structures. In this paper, we propose a novel method termed partial MVC with locality graph regularization to address these issues. First, followed the traditional IMVC approaches, we construct weighted semi‐nonnegative matrix factorization models to handle incomplete multiview data. Then, upon the consensus representation matrix, the locality graph is constructed for regularizing the shared feature matrix. Moreover, we add the coefficient regression term to constraint the various base matrices among views. We incorporate the three aforementioned processes into a unified framework, whereas they can negotiate with each other serving for learning tasks. An effective iterative algorithm is proposed to solve the resultant optimization problem with theoretically guaranteed convergence. The comprehensive experiment results on several benchmarks demonstrate the effectiveness of the proposed method.

show abstract

“…Theorem

boldL

is the Laplacian matrix of symmetry similarity matrix

boldS

and the

i, j

th element of

boldQ

is denoted as

Q_{i j} = ∥ v_{i} - v_{j} ∥_{2}^{2}

, where

v_{i}

is the

i

th row of matrix

boldV

. Then we can obtain the equivalent representation 33

Tr (V^{⊤} boldL boldV) = Tr (boldS boldQ) .

…”

Section: Optimizationmentioning

confidence: 99%

Partial multiview clustering with locality graph regularization

Lian

Wang

et al. 2021

Int J Intell Syst

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show abstract

“…In practice, since the weights of edges in a network can diverge over a very wide range, we use the normalized adjacency matrix (i.e., the one-step transition probability matrix) Λ as the formal first-order proximity matrix, where each normalized entry Λ i,j is the first-order proximity of node pair (v i , v j ), which also represents the transition probability of one-step random walk from v i to v j . It is necessary to consider the structural characteristics of the network from local and global perspectives, which has been proved by many researches, such as feature selection (Liu et al, 2014), semi-supervised classification (Kang et al, 2020b(Kang et al, , 2021, clustering (Ren & Sun, 2020;Kang et al, 2020a), etc. The defined first-order proximity can measure the adjacent structures in both local and global aspects:…”

Section: Definitions and Preliminariesmentioning

confidence: 99%

RWNE: A Scalable Random-Walk based Network Embedding Framework with Personalized Higher-order Proximity Preserved

Li¹,

Ji²,

Peng

et al. 2021

jair

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Higher-order proximity preserved network embedding has attracted increasing attention. In particular, due to the superior scalability, random-walk-based network embedding has also been well developed, which could efficiently explore higher-order neighborhoods via multi-hop random walks. However, despite the success of current random-walk-based methods, most of them are usually not expressive enough to preserve the personalized higher-order proximity and lack a straightforward objective to theoretically articulate what and how network proximity is preserved. In this paper, to address the above issues, we present a general scalable random-walk-based network embedding framework, in which random walk is explicitly incorporated into a sound objective designed theoretically to preserve arbitrary higher-order proximity. Further, we introduce the random walk with restart process into the framework to naturally and effectively achieve personalized-weighted preservation of proximities of different orders. We conduct extensive experiments on several real-world networks and demonstrate that our proposed method consistently and substantially outperforms the state-of-the-art network embedding methods.

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“…Also it is worth to mention that many new methods in multiple kernel graph-based clustering (MKGC) and multiple kernel learning (MKL) for graphbased spectral clustering has emerged in recent years. For example, Ren et al [37] proposed a new MKGC method to learn a consensus affinity graph directly and Ren et al [38] proposed a novel MKL method, namely structure-preserving multiple kernel clustering (SPMKC).…”

Section: Related Workmentioning

confidence: 99%

Robust Multiview Subspace Clustering of Images via Tighter Rank Approximation

et al. 2021

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In this paper, we focus on the multi-view subspace clustering problem under the framework of third order tensor. Recently, tensor nuclear norm (TNN) has been widely used in the multi-view subspace clustering problem. It is known that TNN is a convex surrogate of the tensor rank. However, TNN is linearly proportional to the sum of the singular values. Thus solving the TNN minimization problem will overpenalize the large singular values and lead to a sub-optimal solution. To address this issue, in this paper, a novel tighter tensor log-determinant (TLD) regularizer is proposed to better approximate the tensor rank. Although the proposed method is non-convex, a closed-form solution has been deduced via solving the Euler-Lagrange equation. A corresponding algorithm associated with augmented Lagrangian multipliers is established and the constructed convergent sequence to the Karush-Kuhn-Tucker (KKT) critical point solution is mathematically validated in detail. Extensive experiments indicate that the proposed model achieves significant improvements compared to the state-of-the-art convex subspace clustering models.

show abstract

Simultaneous Global and Local Graph Structure Preserving for Multiple Kernel Clustering

Cited by 107 publications

References 45 publications

Partial multiview clustering with locality graph regularization

Partial multiview clustering with locality graph regularization

RWNE: A Scalable Random-Walk based Network Embedding Framework with Personalized Higher-order Proximity Preserved

Robust Multiview Subspace Clustering of Images via Tighter Rank Approximation

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