Multi-view Spectral Clustering Research Articles

Large-scale multi-view spectral clustering based on two-stage well-distributed anchor selection

Spectral clustering has attracted much attention because of its good clustering effect, but its high computational cost makes it difficult to apply to large-scale multi-view clustering. In response to this issue, a simple and efficient large-scale multi-view spectral clustering algorithm is proposed, which is based on a Two-stage Well-distributed Anchor Selection strategy (TWAS). Firstly, the data set is divided into several disjoint sample blocks to get the global well-distributed anchor candidate. Then, the algorithm proceeds to select anchor points within each local candidate anchor set. This two-stage anchor selection strategy facilitates the identification of anchors with significant representativeness at a reduced computational expense, thereby adeptly capturing the intrinsic data structure. Secondly, the present study devises an adaptive near-neighbor graph learning approach to construct an anchor-based intra-view similarity matrix. Finally, the multiple views are fused to obtain a consistent inter-view similarity matrix, and the clustering results are obtained. Extensive experiments demonstrate the effectiveness, efficiency, and stability of the TWAS algorithm.

Flexible and Parameter-Free Graph Learning for Multi-View Spectral Clustering

Flexible and Parameter-Free Graph Learning for Multi-View Spectral Clustering

Robust Tensor Learning for Multi-View Spectral Clustering

Tensor-based multi-view spectral clustering methods are promising in practical clustering applications. However, most of the existing methods adopt the ℓ2,1 norm to depict the sparsity of the error matrix, and they usually ignore the global structure embedded in each single view, compromising the clustering performance. Here, we design a robust tensor learning method for multi-view spectral clustering (RTL-MSC), which employs the weighted tensor nuclear norm to regularize the essential tensor for exploiting the high-order correlations underlying multiple views and adopts the nuclear norm to constrain each frontal slice of the essential tensor as the block diagonal matrix. Simultaneously, a novel column-wise sparse norm, namely, ℓ2,p, is defined in RTL-MSC to measure the error tensor, making it sparser than the one derived by the ℓ2,1 norm. We design an effective optimization algorithm to solve the proposed model. Experiments on three widely used datasets demonstrate the superiority of our method.

Sparse multi-view image clustering with complete similarity information

Multi-view image clustering aims to efficiently divide the collection of images by studying the characteristics of different views. Many studies performed Laplacian dimensionality reduction on the original image to avoid noise interference in constructing the similarity matrix. However, they ignored the problem that local similarity information and isolated image information are lost due to dimensionality reduction. These problems will result in the similarity matrix being insufficient to accurately describe the similarity between images, which in turn affects the clustering accuracy. Therefore, we propose a sparse multi-view spectral clustering model with complete similarity information between images (SMSC-CSI). The model combines the original image space and the low-dimensional spectral embedding space based on the adaptive neighbors method to learn the initial similarity matrices of each view jointly. On the one hand, the original space can retain all the similarity information between images so that the initial similarity matrix can accurately describe the similarity between images, which is conducive to accurate clustering. On the other hand, the low-dimensional space can avoid noise interference and retain the main structure of high-dimensional data, improving the robustness of the initial similarity matrix. Meanwhile, to ensure consistency among the views, the model minimizes the difference between the initial similarity matrix and the central fusion matrix by alternately updating to obtain the optimal weights and central fusion matrix for each view. Finally, we can obtain ideal clustering results directly with low model complexity and without post-processing steps such as K-means by adding non-negative Laplace rank constraints and ℓ0-norm constraints to the model objective function. Experimental results on different real image datasets show that SMSC-CSI can outperform some traditional clustering models and recent models on multi-view image clustering.

Consistent graph learning for multi-view spectral clustering

Given the heterogeneous information of multiple views and the possible noise embedded in multi-view data, it is difficult to directly learn a consistent representation from multiple graphs to depict the intrinsic structure of all views. We propose a consistent graph learning method by exploiting both the high-order correlations underlying multiple views and the global structure of each single view. First, we calculate a transition probability matrix from each view. Second, a tensor is constructed by stacking each transition matrix as its frontal slice and then decomposed into the latent and error tensors. For the latent tensor, after rotated, a weighted tensor nuclear norm is used to encourage the rotate tensor to fully exploit the high-order correlations underlying multiple views. Furthermore, each frontal slice of the latent tensor is regularized by the nuclear norm to capture the global structure of each single view, and is restricted by probability constraints. Besides, we adopt the Frobenius-norm-based regularization to directly learn a common affinity matrix from the latent tensor. The established model is readily optimized by the alternating Lagrangian method. Extensive experiments on six real world datasets demonstrate that our method outperforms state-of-the-art methods.

One-step incremental multi-view spectral clustering based on graph linkage learning

Most traditional multi-view spectral clustering algorithms involve two separate steps: solving the spectral embedding matrix and clustering, which may introduce errors during the clustering process. Moreover, in practical applications, the number of available views may increase over time, and the approach of re-fusing all views in each computation would result in elevated computational costs. In this paper, we propose a novel model: One-step Incremental Multi-view Spectral Clustering based on Graph Linkage learning (OIMvSC). OIMvSC only needs to store the consensus spectral embedding matrix and the consensus label matrix of all previous views and combines them with the spectral embedding matrix of the newly available view to solve the fused consensus spectral embedding matrix and consensus label matrix. To further enhance clustering performance, OIMvSC introduces graph linkage learning, which reduces erroneous connections between clusters while preserving correct connections within clusters. A convergent iterative algorithm for solving OIMvSC is proposed. Experimental results demonstrate that OIMvSC exhibits excellent clustering performance.

Tensor schatten-p norm guided incomplete multi-view self-representation clustering

Incomplete multi-view clustering (IMC), which aims to handle incomplete data with missing views, has recently received more attention. According to the investigation of the existing IMC methods, they have at least one of the four limitations. First, some methods do not recover the missing view-specific information. Second, some approaches rely on fixed similarity graphs of incomplete views. Third, some methods need a separate spectral clustering step to produce the final cluster indicator. Last, most works utilize tensor nuclear norm to characterize the low-rank property of multi-view representation. These four limitations degrade the clustering performance. Hence, this paper proposes a tensor schatten-p norm guided incomplete multi-view self-representation clustering (TIMSRC) method to handle these four limitations simultaneously. TIMSRC models the missing instances as a data matrix for each view. And it integrates the missing samples inferring and complete self-representation graph learning into a unified framework. TIMSRC adopts a multi-view spectral clustering with adaptive weights to mine the semantic information while considering the contributions of multiple self-representing graphs. TIMSRC exploits the tensor schatten-p norm to enhance the low-rank property of a three-order tensor constructed with multiple self-representation graphs. We present an optimization algorithm to solve the objective function. The experiments demonstrate that TIMSRC outperforms the state-of-the-art IMC approaches.

Preprocessed Spectral Clustering with Higher Connectivity for Robustness in Real-World Applications

This paper introduces a novel model for spectral clustering to solve the problem of poor connectivity among points within the same cluster as this can negatively impact the performance of spectral clustering. The proposed method leverages both sparsity and connectivity properties within each cluster to find a consensus similarity matrix. More precisely, the proposed approach considers paths of varying lengths in the graph, computing a similarity matrix for each path, and generating a cluster for each path. By combining these clusters using multi-view spectral clustering, the method produces clusters of good quality and robustness when there are outliers and noise. The extracted multiple independent views from different paths in the graph are integrated into a consensus graph. The performance of the proposed method is evaluated on various benchmark datasets and compared to state-of-the-art techniques.

Tensor-based multi-view spectral clustering via shared latent space

Multi-view Spectral Clustering (MvSC) partitions data into clusters according to multiple views for higher performance. However, most existing works overlook model interpretability and involve iterative and alternating updates on parameters with expensive computations, where out-of-sample predictions are also commonly prohibitive. In this paper, we construct a novel weighted conjugate feature duality for formulating the MvSC problem cast as a weighted principal components analysis. In this new method, a common latent space is derived with shared dual variables, which achieves the couplings by learning projections from different views into the latent space. To boost higher-order correlations, the tensor-based modeling is introduced. Our method leads to a closed-form solution in the dual through a single eigendecomposition thanks to the primal–dual representation, leading to easy algorithmic setups in practice. Our novel conjugate duality and the conceived shared latent space greatly boost the efficiency in model representation and computation: element-wise operations of kernels are involved in the dual instead of the explicit tensor computation in the primal and the size of our eigendecomposition is independent of the number of views. Besides, we can effectively incorporate the visualization of the clusters in a single latent space, which is particularly useful with many data views. For predicting unseen data under generic applications, our method can be flexibly applied with out-of-sample extensions, which can also be utilized for further efficiency in large-scale cases with fixed-size kernel schemes. Numerical experiments verify our superiority in accuracy, efficiency, and diverse data explorations.

Generalized latent multi-view clustering with tensorized bipartite graph

Tensor-based multi-view spectral clustering algorithms use tensors to model the structure of multi-dimensional data to take advantage of the complementary information and high-order correlations embedded in the graph, thus achieving impressive clustering performance. However, these algorithms use linear models to obtain consensus, which prevents the learned consensus from adequately representing the nonlinear structure of complex data. In order to address this issue, we propose a method called Generalized Latent Multi-View Clustering with Tensorized Bipartite Graph (GLMC-TBG). Specifically, in this paper we introduce neural networks to learn highly nonlinear mappings that encode nonlinear structures in graphs into latent representations. In addition, multiple views share the same latent consensus through nonlinear interactions. In this way, a more comprehensive common representation from multiple views can be achieved. An Augmented Lagrangian Multiplier with Alternating Direction Minimization (ALM-ADM) framework is designed to optimize the model. Experiments on seven real-world data sets verify that the proposed algorithm is superior to state-of-the-art algorithms.

Anchor graph-based multiview spectral clustering

Significant advances in graph-oriented clustering methods can be attributed to their effectiveness in leveraging relationships and complex structures within multiview data. However, several limitations persist in most existing graph-based multiview clustering approaches. First, quadratic or cubic complexity is required for graph construction or eigendecomposition of the Laplacian matrix in many existing methods. Second, certain methods overlook the differences between views and employ an identical indicator matrix, which can lead to over-learning in practical scenarios. Third, existing methods often neglect spatial structure and complementary information, focusing primarily on calculating error feature-by-feature using different norms. In order to tackle these drawbacks, we propose a new multiview spectral clustering model called Anchor Graph-based Multiview Spectral Clustering(AG-MSC). AG-MSC incorporates an adaptive weighting mechanism that assigns weights to each view, enhancing the robustness of the algorithm. Using a tensor Schatten p-norm constraint minimizes the discrepancy between indicator matrices obtained from different views, thereby preserving high-order information and spatial structure. To improve computational efficiency, we replace the full adjacency matrices of the corresponding views with anchor graphs. AG-MSC offers a distinct advantage over conventional spectral clustering by directly obtaining all sample categories without additional post-processing steps. We have validated the efficiency of our method through extensive experimental evaluations.

Self-Supervised Deep Multiview Spectral Clustering.

Multiview spectral clustering has received considerable attention in the past decades and still has great potential due to its unsupervised integration manner. It is well known that pairwise constraints boost the clustering process to a great extent. Nevertheless, the constraints are usually marked by human beings. To ameliorate the performance of multiview spectral clustering and alleviate the consumption of human resources, we propose self-supervised multiview spectral clustering with a small number of automatically retrieved pairwise constraints. First, the fused multiple autoencoders are used to extract the latent consistent feature of multiple views. Second, the pairwise constraints are achieved based on the commonality among multiple views. Then, the pairwise constraints are propagated through the neural network with historical memory. Finally, the propagated constraints are used to optimize the fused affinity matrix of spectral clustering. Our experiments on four benchmark datasets show the effectiveness of our proposed approach.

Recognizing and detecting COVID-19 in chest X-ray images using constrained multi-view spectral clustering

AbstractMachine learning, particularly classification algorithms, has been widely employed for diagnosing COVID-19 cases. However, these methods typically rely on labeled datasets and analyze a single data view. With the vast amount of patient data available without labels, this paper addresses the novel challenge of unsupervised COVID-19 diagnosis. The goal is to harness the abundant data without labels effectively. In recent times, multi-view clustering has garnered considerable attention in the research community. Spectral clustering, known for its robust theoretical framework, is a key focus. However, traditional spectral clustering methods generate only nonlinear data projections, necessitating additional clustering steps. The quality of these post-processing steps can be influenced by various factors, such as initialization procedures and outliers. This paper introduces an enhanced version of the recent “Multiview Spectral Clustering via integrating Nonnegative Embedding and Spectral Embedding” method. While retaining the benefits of the original technique, the proposed model integrates two essential constraints: (1) a constraint for ensuring the consistent smoothness of the nonnegative embedding across all views and (2) an orthogonality constraint imposed on the columns of the nonnegative embedding matrix. The effectiveness of this approach is demonstrated using COVIDx datasets. Additionally, the method is evaluated on other image datasets to validate its suitability for this study.

A Similarity Matrix Low-Rank Approximation and Inconsistency Separation Fusion Approach for Multiview Clustering

In recent years, multi-view clustering algorithms have achieved promising performance by exploiting the com-plementarity and consistency of different views. However, many multi-view spectral clustering methods only focus on the con-sistent information of views, and the time cost of feature decomposition is expensive. Moreover, these methods also require post-processing (e.g., k-means) to obtain the final clustering results. To overcome these limitations simultaneously, we propose a novel multi-view clustering algorithm. Firstly, the method removes the inconsistent information of the views through cross-view measurement to maintain consistent information. These inconsistencies may be caused by noise, corruptions, or view-specific properties and will affect the quality of the similarity matrix. Then, we learn a consensus embedding matrix with non-negative constraints by performing a low-rank decomposition of the consistency information. In this way, we can replace the eigendecomposition of the n × n Laplacian matrix in spectral clustering with the singular value decomposition of a n × c low-rank matrix to reduce the computational burden, where c ≪ n. Furthermore, due to the non-negative constraint, we can directly obtain the clustering results. Also, to consider the diversity of views, adaptive weighting is applied to different view data. Compared to state-of-the-art multi-view clustering methods on five benchmark multi-view datasets, we demonstrate the superiority and effectiveness of our approach. We release the source code at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/hulu88/FAMvC</uri> .

Tensorized Discrete Multi-View Spectral Clustering

Discrete spectral clustering directly obtains the discrete labels of data, but existing clustering methods assume that the real-valued indicator matrices of different views are identical, which is unreasonable in practical applications. Moreover, they do not effectively exploit the spatial structure and complementary information embedded in views. To overcome this disadvantage, we propose a tensorized discrete multi-view spectral clustering model that integrates spectral embedding and spectral rotation into a unified framework. Specifically, we leverage the weighted tensor nuclear-norm regularizer on the third-order tensor, which consists of the real-valued indicator matrices of views, to exploit the complementary information embedded in the indicator matrices of different views. Furthermore, we present an adaptively weighted scheme that takes into account the relationship between views for clustering. Finally, discrete labels are obtained by spectral rotation. Experiments show the effectiveness of our proposed method.

Multi-view spectral clustering based on constrained Laplacian rank

Multi-view spectral clustering based on constrained Laplacian rank

Multiview Spectral Clustering Based on Consensus Neighbor Strategy.

Multiview spectral clustering, renowned for its spatial learning capability, has garnered significant attention in the data mining field. However, existing methods assume that the optimal consensus adjacency matrix is confined within the space spanned by each view's adjacency matrix. This constraint restricts the feasible domain of the algorithm and hinders the exploration of the optimal consensus adjacency matrix. To address this limitation, we propose a novel and convex strategy, termed the consensus neighbor strategy, for learning the optimal consensus adjacency matrix. This approach constructs the optimal consensus adjacency matrix by capturing the consensus local structure of each sample across all views, thereby expanding the search space and facilitating the discovery of the optimal consensus adjacency matrix. Furthermore, we introduce the concept of a correlation measuring matrix to prevent trivial solution. We develop an efficient iterative algorithm to solve the resulting optimization problem, benefitting from the convex nature of our model, which ensures convergence to a global optimum. Experimental results on 16 multiview datasets demonstrate that our proposed algorithm surpasses state-of-the-art methods in terms of its robust consensus representation learning capability. The code of this article is uploaded to https://github.com/PhdJiayiTang/Consensus-Neighbor-Strategy.git.

Adaptive graph fusion learning for multi-view spectral clustering

Multi-view data suffer from issues related to low quality and heterogeneity, which leads to instability issues in existing learning models for clustering. To overcome the limitations of traditional clustering methods, we propose a novel multi-view spectral clustering based on a contrastive feedback strategy. The proposed method constructs kernelized graphs to obtain higher-order feature representations, mapping primary sample data from different views into an isomorphic feature space and masking differences in type and structure between multiple views. In the meantime, the proposed method leverages a contrastive feedback optimization strategy based on mutual information to iteratively optimize the kernelized graphs of all views and their dynamically fused graph. This method effectively exploits the consistency and complementary information between multi-view, further improving the clustering accuracy. Experiments on multiple datasets demonstrate that the proposed method achieves satisfactory results in terms of clustering, validating the feasibility and effectiveness of the contrastive feedback strategy.

Hypergraph Learning-Based Semi-Supervised Multi-View Spectral Clustering

Graph-based semi-supervised multi-view clustering has demonstrated promising performance and gained significant attention due to its capability to handle sample spaces with arbitrary shapes. Nevertheless, the ordinary graph employed by most existing semi-supervised multi-view clustering methods only captures the pairwise relationships between samples, and cannot fully explore the higher-order information and complex structure among multiple sample points. Additionally, most existing methods do not make full use of the complementary information and spatial structure contained in multi-view data, which is crucial to clustering results. We propose a novel hypergraph learning-based semi-supervised multi-view spectral clustering approach to overcome these limitations. Specifically, the proposed method fully considers the relationship between multiple sample points and utilizes hypergraph-induced hyper-Laplacian matrices to preserve the high-order geometrical structure in data. Based on the principle of complementarity and consistency between views, this method simultaneously learns indicator matrices of all views and harnesses the tensor Schatten p-norm to extract both complementary information and low-rank spatial structure within these views. Furthermore, we introduce an auto-weighted strategy to address the discrepancy between singular values, enhancing the robustness and stability of the algorithm. Detailed experimental results on various datasets demonstrate that our approach surpasses existing state-of-the-art semi-supervised multi-view clustering methods.

A novel graph-based multi-view spectral clustering: application to X-ray image analysis for COVID-19 recognition

A novel graph-based multi-view spectral clustering: application to X-ray image analysis for COVID-19 recognition