Multi-view Spectral Clustering Research Articles

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.

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 modelling 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.

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.

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.

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.

Flexible and Parameter-free Graph Learning for Multi-view Spectral Clustering

Flexible and Parameter-free Graph Learning for Multi-view Spectral Clustering

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

Multi-view clustering with Laplacian rank constraint based on symmetric and nonnegative low-rank representation

Multi-view spectral clustering has attracted more and more attention due to its promising advantages in data clustering, and many related methods have been proposed, among which the method based on low-rank representation have become increasingly popular. However, the similarity matrices learned by the existing methods inevitably contain some negative entries and are generally nonsymmetric. In order to guarantee weight consistency for each pair of data points and highly correlated data points to be together, we propose a new multi-view spectral clustering model based on the symmetric and nonnegative low-rank representation. This model can learn the view-specific consistent similarity matrix and also capture the local structure and discriminative information among data by imposing symmetric and nonnegative constraints on the representation matrix. By employing the compatible and complementary information from multi-view data points, it can also learn the consensus similarity matrix for all views and perform the spectral clustering simultaneously. By the augmented Lagrangian multiplier method, an alternating iterative optimization algorithm is designed for solving this model and its computational complexity and convergence is analyzed. Comprehensive experiments on multiple multi-view data sets also verify the effectiveness and superiority of the proposed approach.

Multi-view clustering via efficient representation learning with anchors

Multi-view spectral clustering has gained considerable attention due to its potential to enhance clustering performance. Although many methods have shown promising results, they often suffer from high time complexity and are not suitable for large-scale datasets. On the other hand, anchor-based methods are well-known for their efficiency. These methods typically learn the similarity relationship between instances and anchors and then convert it into the similarity relationship between instances, involving a considerable number of calculations. To address this issue, we propose a novel method called Multi-view clustering via Efficient Representation LearnIng with aNchors (MERLIN) in this paper. Instead of learning the instance–instance relationship, MERLIN approaches the clustering problem from the perspective of representation learning. Specifically, MERLIN selects the same anchors for different views and utilizes these anchors to learn a consensus representation that integrates information from all views. Additionally, MERLIN adaptively learns weights for different views to fully exploit the complementary information among multiple views. In comparison with seven state-of-the-art baseline methods across five datasets, MERLIN demonstrates both efficiency and effectiveness in handling multi-view datasets and is suitable for handling large-scale datasets.

Deep multi-view spectral clustering via ensemble

Graph-based methods have achieved great success in multi-view clustering. However, existing graph-based models generally utilize shallow and linear embedding functions to obtain the common spectral embedding for clustering assignments. In addition, the fusion similarity graphs from multiple views are generally obtained by a simple weighted-sum rule. To this end, we propose a novel deep multi-view spectral clustering via ensemble model (DMCE), which applies ensemble clustering to fuse the similarity graphs from different views. On this basis, we employ the graph auto-encoder to learn the common spectral embedding, which can be regarded as the indicator matrix directly. Moreover, a unified optimization framework is designed to update the variables in the proposed DMCE, which consists of graph reconstruction loss, orthogonal loss, and graph contrastive learning loss. Extensive experiments on six real-world benchmark datasets have demonstrated the effectiveness of our model compared with the state-of-the-art multi-view clustering methods.

Balance guided incomplete multi-view spectral clustering

There is a large volume of incomplete multi-view data in the real-world. How to partition these incomplete multi-view data is an urgent realistic problem since almost all of the conventional multi-view clustering methods are inapplicable to cases with missing views. In this paper, a novel graph learning-based incomplete multi-view clustering (IMVC) method is proposed to address this issue. Different from existing works, our method aims at learning a common consensus graph from all incomplete views and obtaining a clustering indicator matrix in a unified framework. To achieve a stable clustering result, a relaxed spectral clustering model is introduced to obtain a probability consensus representation with all positive elements that reflect the data clustering result. Considering the different contributions of views to the clustering task, a weighted multi-view learning mechanism is introduced to automatically balance the effects of different views in model optimization. In this way, the intrinsic information of the incomplete multi-view data can be fully exploited. The experiments on several incomplete multi-view datasets show that our method outperforms the compared state-of-the-art clustering methods, which demonstrates the effectiveness of our method for IMVC.

Low-rank discrete multi-view spectral clustering

Spectral clustering has attracted intensive attention in multimedia applications due to its good performance on arbitrary shaped clusters and well-defined mathematical framework. However, most existing multi-view spectral clustering methods still have the following demerits: (1) They ignore useful complementary information embedded in indicator matrices of different views. (2) The conventional post-processing methods based on the relax and discrete strategy inevitably result in the sub-optimal discrete solution. To tackle the aforementioned drawbacks, we propose a low-rank discrete multi-view spectral clustering model. Drawing inspiration from the fact that the difference between indicator matrices of different views provides useful complementary information for clustering, our model exploits the complementary information embedded in indicator matrices with tensor Schatten p-norm constraint. Further, we integrate low-rank tensor learning and discrete label recovering into a uniform framework, which avoids the uncertainty of the relaxed and discrete strategy. Extensive experiments on benchmark datasets have demonstrated the effectiveness and superiority of the proposed method.