Anchor-based multi-view graph clustering (AMVGC) has received abundant attention owing to its high efficiency and the capability to capture complementary structural information across multiple views. Intuitively, a high-quality anchor graph plays an essential role in the success of AMVGC. However, the existing AMVGC methods only consider single-structure information, i.e., local or global structure, which provides insufficient information for the learning task. To be specific, the over-scattered global structure leads to learned anchors failing to depict the cluster partition well. In contrast, the local structure with an improper similarity measure results in potentially inaccurate anchor assignment, ultimately leading to sub-optimal clustering performance. To tackle the issue, we propose a novel anchor-based multi-view graph clustering framework termed Efficient Multi-View Graph Clustering with Local and Global Structure Preservation (EMVGC-LG). Specifically, a unified framework with a theoretical guarantee is designed to capture local and global information. Besides, EMVGC-LG jointly optimizes anchor construction and graph learning to enhance the clustering quality. In addition, EMVGC-LG inherits the linear complexity of existing AMVGC methods respecting the sample number, which is time-economical and scales well with the data size. Extensive experiments demonstrate the effectiveness and efficiency of our proposed method.

pdf/efficient-multi-view-graph-clustering-with-local-and-global-1xqnbqibc1.pdf

Efficient Multi-View Graph Clustering with Local and Global Structure Preservation

FGC_SS: Fast Graph Clustering Method by Joint Spectral Embedding and Improved Spectral Rotation

Privacy-preserving Multimedia Data Analysis

In graph embedding learning with unsupervised feature selection fields, similarity matrices are usually obtained only from the initial noise-laden samples, and the probable association between various features is often ignored. To tackle the issues described above, this article proposes an effective unsupervised group feature selection approach via non-convex regularized graph embedding and self-representation (NLGMS). NLGMS integrates the similarity matrix and feature selection as a joint system on the basis of graph. It combines self-representation learning into the system to preserve the global structure and learns the nonconvex projection matrix to direct the procedure of feature selection. Specifically, first, NLGMS presents a unified framework for global structure learning, local structure learning, and feature selection process so the data's intrinsic structure is excellently captured and learned adaptively. Second, nonconvex ℓ2,0-norm is enforced upon the projection matrix to perform the process of feature selection, ensuring that the optimal feature subset can be picked precisely. Nonconvex ℓ2,0-norm constraint considers the probable association between various features so that it can deliver optimal performance by considering the feature subset as an integral whole, which other convex regularized constraints often fail to achieve. Finally, the introduction to self-representation learning can facilitate the reconstruction of samples in low-rank subspaces, strengthening the model's robustness. To tackle this challenging nonconvex model, an innovative alternative optimization technique is exploited. In addition, to validate the superiority of NLGMS, exhaustive experiments are performed on one synthetic dataset, six benchmark datasets, and one fish image dataset. The source code is available at: https://github.com/hrbai/NLGMS. 

Precise feature selection via non-convex regularized graph embedding and self-representation for unsupervised learning

Spectral Clustering (SC) is widely used for clustering data on a nonlinear manifold. SC aims to cluster data by considering the preservation of the local neighborhood structure on the manifold data. This paper extends Spectral Clustering to Local and Global Structure Preservation Based Spectral Clustering (LGPSC) that incorporates both global structure and local neighborhood structure simultaneously. For this exten-sion, LGPSC proposes two models to extend local structures preservation to local and global structures preservation: Spectral clustering guided Principal component analysis model and Multilevel model. Finally, we compare the experimental results of the state-of-the-art methods with our two models of LGPSC on various data sets such that the experimental results conﬁrm the effectiveness of our LGPSC models to cluster nonlinear data.

Local and Global Structure Preservation Based Spectral Clustering

\n Spectral clustering is widely applied in real applications, as it utilizes a graph matrix to consider the similarity relationship of subjects. The quality of graph structure is usually important to the robustness of the clustering task. However, existing spectral clustering methods consider either the local structure or the global structure, which can not provide comprehensive information for clustering tasks. Moreover, previous clustering methods only consider the simple similarity relationship, which may not output the optimal clustering performance. To solve these problems, we propose a novel clustering method considering both the local structure and the global structure for conducting nonlinear clustering. Specifically, our proposed method simultaneously considers (i) preserving the local structure and the global structure of subjects to provide comprehensive information for clustering tasks, (ii) exploring the nonlinear similarity relationship to capture the complex and inherent correlation of subjects and (iii) embedding dimensionality reduction techniques and a low-rank constraint in the framework of adaptive graph learning to reduce clustering biases. These constraints are considered in a unified optimization framework to result in one-step clustering. Experimental results on real data sets demonstrate that our method achieved competitive clustering performance in comparison with state-of-the-art clustering methods.

Global and Local Structure Preservation for Nonlinear High-dimensional Spectral Clustering

Spectral clustering is a popular graph-based clustering method which is widely applied to pattern recognition and image segmentation. Traditional spectral clustering usually involves two separate processes: graph learning and graph-based clustering, making such a two-step strategy easily output sub-optimal performance and moreover, noisy data and imbalanced clusters could make existing clustering methods hard to meet practical necessity. To this end, one-step spectral clustering coupled with a balanced constraint is proposed to jointly optimize the robust low-dimensional representation, the spectral rotation and the cluster indicator in a unified learning framework. Specifically, dimensionality reduction is conducted by combining subspace learning and feature selection to obtain a robust low-dimensional representation. Besides, a spectral rotation mechanism is used to produce one-step clustering for reducing clustering biases, and a balanced constraint is utilized to regularize the clustering result to generate clusters with similar sizes. Moreover, an iterative optimization method is put forward to fast solve the proposed objective function. Experimental results on ten benchmark datasets compared to state-of-the-art spectral clustering methods showed that our proposed clustering method could output the balanced clusters and the competitive clustering performance simultaneously.

One-step spectral rotation clustering with balanced constrains

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Global and Local Structure Preservation for Nonlinear High-dimensional Spectral Clustering

One-step spectral rotation clustering with balanced constrains