Self-taught Multi-view Spectral Clustering

Multi-view spectral clustering by simultaneous consensus graph learning and discretization

Recent researches on multiview learning have received widespread attention due to the increasing generalization of multiview data. As an effective probabilistic model, random walk has also shown encouraging performance in various fields. To further exploit the potential of utilizing random walk schemes to address multiview learning problems, this article proposes a simple yet efficient multigraph random walk scheme for both multiview clustering and semisupervised classification tasks. The proposed model integrates random walk with multiview learning, and recursively learns a globally stable probability distribution matrix from multiple views, on the basis of which the label indicator is obtained in the scene of clustering or semisupervised classification. Furthermore, an adaptive weight vector is learned to incorporate the diversity and complementarity of multiview data. Besides, the relationships between the proposed scheme and spectral clustering, neighborhood embedding and manifold embedding are analyzed theoretically. Finally, comprehensive comparative experiments are conducted with several state-of-the-art multiview clustering and semisupervised classification methods on eight real-world datasets. The experimental results demonstrate the superiority of the proposed method in terms of both clustering and classification performance.

Information in multiple views is typically symmetrical and distinctive. Multi-view clustering generally attempts to address two key issues: (1) how to mine/leverage additional useful information between different views for current view clustering, and (2) how to combine multiple clustering results from multiple views by using compatible and complementary information hidden in multiple views. In order to achieve this, we propose a multi-view clustering method, namely the multi-view utility-based clustering method (MUC), from the novel perspective of utility-based mutual supervision between different views. The proposed method, MUC, has notable merits: (1) It moves multi-view clustering from the level of feature and/or sample side to partition side information. That is, in order to handle the first issue, MUC considers how to use utility-based partition-level side information from all the other views for current view clustering. Such partition-level side information is consistent with human thinking; it is high-caliber and instructional for clustering. (2) The utility-based partition-level side information provided by other views complements current view information in a mutually supervised way. Then, we conduct multi-view clustering via a mutual supervision mode to circumvent the second issue. As a result, using an alternating optimization strategy, the objective function of MUC can be solved in a K-means-like way. Moreover, we leverage multi-view weight learning based on maximum entropy to integrate multi-view clustering results and further improve performance. The extensive experimental results on various multi-view datasets indicate that the proposed method is better than—or at least comparable to—the existing commonly used single- and multi-view clustering methods, in terms of both clustering performance and running speed.

Advances in single-cell biotechnologies have generated the single-cell RNA sequencing (scRNA-seq) of gene expression profiles at cell levels, providing an opportunity to study cellular distribution. Although significant efforts developed in their analysis, many problems remain in studying cell types distribution because of the heterogeneity, high dimensionality, and noise of scRNA-seq. In this study, a multi-view clustering with graph learning algorithm (MCGL) for scRNA-seq data is proposed, which consists of multi-view learning, graph learning, and cell type clustering. In order to avoid a single feature space of scRNA-seq being inadequate to comprehensively characterize the functions of cells, MCGL constructs the multiple feature spaces and utilizes multi-view learning to comprehensively characterize scRNA-seq data from different perspectives. MCGL adaptively learns the similarity graphs of cells that overcome the dependence on fixed similarity, transforming scRNA-seq analysis into the analysis of multi-view clustering. MCGL decomposes the networks of cells into view-specific and common networks in multi-view learning, which better characterizes the topological relationship of cells. MCGL simultaneously utilizes multiple types of cell-cell networks and fully exploits the connection relationship between cells through the complementarity between networks to improve clustering performance. The graph learning, graph factorization, and cell-type clustering processes are accomplished simultaneously under one optimization framework. The performance of the MCGL algorithm is validated with ten scRNA-seq datasets from different scales, and experimental results imply that the proposed algorithm significantly outperforms fourteen state-of-the-art scRNA-seq algorithms.

Deep multi-view representation learning focuses on training a unified low-dimensional representation for data with multiple sources or modalities. With the rapidly growing attention of graph neural networks, more and more researchers have introduced various graph models into multi-view learning. Although considerable achievements have been made, most existing methods usually propagate information in a single view and fuse multiple information only from the perspective of attributes or relationships. To solve the aforementioned problems, we propose an efficient model termed Dual Fusion-Propagation Graph Neural Network (DFP-GNN) and apply it to deep multi-view clustering tasks. The proposed method is designed with three submodules and has the following merits: a) The proposed view-specific and cross-view propagation modules can capture the consistency and complementarity information among multiple views; b) The designed fusion module performs multi-view information fusion with the attributes of nodes and the relationships among them simultaneously. Experiments on popular databases show that DFP-GNN achieves significant results compared with several state-of-the-art algorithms.

Multi-view clustering utilizes information from diverse views to improve the performance of clustering. For most existing multi-view spectral clustering methods, information of different views is integrated by pursuing a consensus similarity matrix for clustering. However, view-specific structures, which contain the complementary information of multi-view data, may be lost during the clustering process. Actually, in multi-view spectral clustering, similarity matrices of multiple views would have the same clustering structures or properties rather than be numerically uniform. To overcome the aforementioned problem, a novel essential multi-view graph learning (EMGL) method for clustering is proposed in this paper. Different from most existing multi-view spectral clustering, an orthogonal matrix factorization is imposed on multi-view similarity matrices for making them have the same nuclear norm, which indicates the same clustering structures of different views. Furthermore, we also propose an alternating direction method of multipliers (ADMM) based optimization algorithm to address the objective function of our method. Extensive experiments on several datasets demonstrate the superior performance of our proposed method.

Multiview clustering (MVC) is a popular research topic in the fields of data mining and pattern recognition, which focuses on fully exploring and employing the correlations between views to jointly discover a consistent cluster structure across data. Typically, weighted MVC is a common clustering method aimed at learning the importance or weights of each view and applying them to explore the complementary information between views. However, current weighted MVCs primarily focus on the quality of each view while overlooking the crucial role of pseudo-label-based self-supervision in weight learning. In addition, most weighted MVCs only use a weighting mechanism to utilize complementary features without sufficiently considering the consistency relationship between the clustering results of individual views and the final clustering result. Aiming to solve the above problems, this article proposes a structure-enhanced self-supervised weighted information bottleneck (S2WIB) method for MVC. Specifically, the S2WIB method establishes a view-weight learning mechanism that leverages both the view-contained information and the self-supervised information to learn view weights, and then integrates the weighted information from different views. Meanwhile, based on the information bottleneck (IB) theory, it explores view correlations from two perspectives, namely complementary information and consistent view cluster structure information, thereby fully exploiting the potential information contained in multiview data. Experiments on various multiview text datasets, multifeature image datasets, multiangle video datasets, multimodal text-image datasets, as well as large-scale datasets and biological multiomics datasets, demonstrate that the S2WIB method performs effectively and exhibits superiority across various fields.

Co-segmentation of 3D shapes in the same category is an intensive topic in computer graphics. In this paper, we present an unsupervised method to segment a set of meshes into corresponding parts in a consistent manner. Given the over-segmented patches as input, the co-segmentation result is generated by grouping them. In contrast to the previous method, we formulate the problem as a multi-view spectral clustering task by co-training a set of affinity matrices derived from different shape descriptors. For each shape descriptor, the affinity matrix is constructed via combining low-rankness and sparse representation. The integration of multiple features makes our method tolerate the large geometry and topology variations among the 3D meshes in a set. Moreover, the low-rank and sparse representation can capture not only the global structure but also the local relationship, which demonstrate robust to outliers. The experimental results show that our approach successfully segments each category in the benchmark dataset into corresponding parts and generates more reliable results compared with the state-of-the-art.

Multi-view clustering is an effective method to process massive unlabeled multi-view data. Since data of different views may be collected and held by different parties, it becomes impractical to train a multi-view clustering model in a centralized way, for the sake of privacy. However, federated multi-view clustering is challenging because multi-view learning has to consider the complementary and consistent information between each view distributed across different clients. For another, efficiency is highly expected in federated scenarios. Therefore, we propose a novel federated multi-view clustering method with tensor factorization (TensorFMVC), which is built based on K-means and hence is more efficient. Besides, TensorFMVC avoids initializing centroids to address the performance degradation of K-means due to its sensitivity to centroid initialization. A three-order tensor stacked by cluster assignment matrices is introduced to exploit the complementary information and spatial structure of different views. Furthermore, we divide the optimization into several subproblems and develop a federated optimization approach to support cooperative model training. Extensive experiments on several datasets demonstrate that our proposed method exhibits superior performance in federated multi-view clustering.

Machine 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.

Multi-view clustering aims to discover common patterns from multi-source data, whose generality is remarkable. Compared with traditional methods, deep learning methods are data-driven and have a larger search space for solutions, which may find a better solution to the problem. In addition, more considerations can be introduced by loss functions, so deep models are highly reusable. However, compared with deep learning methods, traditional methods have better interpretability, whose optimization is relatively stable. In this paper, we propose a multi-view spectral clustering model, combining the advantages of traditional methods and deep learning methods. Specifically, we start with the objective function of traditional spectral clustering, perform multi-view extension, and then obtain the traditional optimization process. By partially parameterizing this process, we further design corresponding differentiable modules, and finally construct a complete network structure. The model is interpretable and extensible to a certain extent. Experiments show that the model performs better than other multi-view clustering algorithms, and its semi-supervised classification extension also has excellent performance compared to other algorithms. Further experiments also show the stability and fewer iterations of the model training.

Multiview learning with twin parametric margin SVM

Multi-view spectral clustering, which exploits the complementary information among graphs of diverse views to obtain superior clustering results, has attracted intensive attention recently. However, most existing multi-view spectral clustering methods obtain the clustering partitions in a two-step scheme, i.e., spectral embedding and subsequent k-means. This two-step scheme inevitably seeks sub-optimal clustering results due to the information loss during the two-steps processes. Besides, existing multi-view spectral clustering methods do not jointly utilize the information of graphs and embedding matrices, which also degrades final clustering results. To solve these issues, we propose a unified one-step multi-view spectral clustering method, which integrates the spectral embedding and <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$k$</tex></formula> -means into a unified framework to obtain discrete clustering labels with a one-step strategy. Under the observation that the inner product of the embedding matrix is a low-rank approximation of the graph, we combine graphs and embedding matrices of different views to obtain a unified graph. Then, we directly capture the discrete clustering indicator matrix from the unified graph. Furthermore, we design an effective optimization algorithm to solve the resultant problem. Finally, a set of experiments on various datasets are conducted to verify the effectiveness of the proposed method. The demo code of this work is publicly available at https://github.com/guanyuezhen/UOMvSC.

Scientific mapping has now become an important subject in the scientometrics field. Journal clustering can provide insights into both the internal relations among journals and the evolution trend of studies. In this paper, we apply the affinity propagation (AP) algorithm to do scientific journal clustering. The AP algorithm identifies clusters by detecting their representative points through message passing within the data points. Compared with other clustering algorithms, it can provide representatives for each cluster and does not need to pre-specify the number of clusters. Because the input of the AP algorithm is the similarity matrix among data points, it can be applied to various forms of data sets with different similarity metrics. In this paper, we extract the similarity matrices from the journal data sets in both cross citation view and text view and use the AP algorithm to cluster the journals. Through empirical analysis, we conclude that these two clustering results by the two single views are highly complementary. Therefore, we further combine text information with cross citation information by using the simple average scheme and apply the AP algorithm to conduct multi-view clustering. The multi-view clustering strategy aims at obtaining refined clusters by integrating information from multiple views. With text view and citation view integrated, experiments on the Web of Science journal data set verify that the AP algorithm obtains better clustering results as expected.

In recent years, multiview clustering algorithms have achieved promising performance by exploiting the complementarity and consistency of different views. However, many multiview spectral clustering methods only focus on the consistent information of views, and the time cost of feature decomposition is expensive. Moreover, these methods also require postprocessing (e.g., k-means) to obtain the final clustering results. To overcome these limitations simultaneously, we propose a novel multiview clustering algorithm. First, 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 nonnegative constraints by performing a low-rank decomposition of the consistency information. In this way, we can replace the eigendecomposition of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm {\times }$</tex-math></inline-formula> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> Laplacian matrix in spectral clustering with the singular value decomposition of a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm {\times }$</tex-math></inline-formula> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> low-rank matrix to reduce the computational burden, where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bm {\ll }$</tex-math></inline-formula> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> . Furthermore, due to the nonnegative 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 multiview clustering methods on five benchmark multiview 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> .