Incomplete Data Meets Uncoupled Case: A Challenging Task of Multiview Clustering.

Incomplete multi-view clustering has gained considerable attention in recent years due to the prevalence of incomplete multi-view data in real-world applications. However, existing methods often struggle to effectively deal with large-scale datasets, particularly those with a significant number of missing instances. To address these issues, we propose a novel method called Hubness-Enabled Clustering and Recovery for Large-Scale Incomplete Multi-View Data (HENRI). HENRI utilizes the consensus hubs of all views to identify informative anchors to handle large-scale incomplete datasets. Furthermore, it incorporates a novel sample-level fusion strategy that effectively integrates information from all views, leading to remarkable outcomes in both cluster formation and missing data reconstruction. HENRI demonstrates exceptional capability in capturing the underlying structures of the data and recovering missing information, even when faced with a significant number of instances with incomplete data in partial views. To validate its effectiveness, we conducted experiments on 6 complete datasets and 31 incomplete datasets, comparing against 11 baseline methods. The results are impressive, demonstrating the superior performance of HENRI over the state-of-the-art methods.

With the development of data collection technologies, a significant volume of multiview data has appeared, and their clustering has become topical. Most methods of multiview clustering assume that all views are fully observable. However, in many cases this is not the case. Several tensor methods have been proposed to deal with incomplete multiview data. However, the traditional tensor norm is computationally expensive, and such methods generally cannot handle undersampling and imbalances of various views. A new method for clustering incomplete multiview data is proposed. A new tensor norm is defined to reconstruct the connectivity graph, and the graphs are regularized to a consistent low-dimensional representation of patterns. The weights are then iteratively updated for each view. Compared to the existing ones, the proposed method not only determines the consistency between views but also obtains a low-dimensional representation of the samples using the resulting projection matrix. An efficient optimization algorithm based on the method of indefinite Lagrange multipliers is developed for the solution. The experimental results on four data sets demonstrate the effectiveness of the method.

Incomplete multi-view data presents a significant challenge for multi-view clustering (MVC). Existing incomplete MVC solutions commonly rely on data imputation to convert incomplete data into complete data. However, this paradigm suffers from the risk of error accumulation when clustering unreliable imputed data, causing suboptimal clustering performance. Moreover, using imputation to fulfill missing data is inefficient, while inferring data categories based solely on the existing views is extremely challenging. To this end, we propose an Imputation-free Incomplete MVC (I2MVC) via pseudo-supervised knowledge distillation. Specifically, I2MVC decomposes the incomplete MVC problem into two tasks: an MVC task for complete data and a pseudo-supervised classification task for fully incomplete data. A self-supervised simple contrastive Teacher network is trained for clustering complete data, and its knowledge is distilled into a lightweight pseudo-supervised Student network. The Student network, unrestricted by view completeness, further guides the clustering of fully incomplete data. Finally, the clustering results from both tasks are merged to generate the final clustering outcome. Experimental results on benchmark datasets demonstrate the effectiveness of I2MVC.

In this article, we address the challenging problem of unpaired multiview clustering (UMC), which aims to achieve effective joint clustering using unpaired samples observed across multiple views. Traditional incomplete multiview clustering (IMC) methods typically rely on paired samples to capture complementary information between views. However, such strategies become impractical in the UMC due to the absence of paired samples. Although some researchers have attempted to address this issue by preserving consistent cluster structures across views, effectively mining such consistency remains challenging when the cluster structures with low confidence. Therefore, we propose a novel method, multilevel reliable guidance for UMC (MRG-UMC), which integrates multilevel clustering and reliable view guidance to learn consistent and confident cluster structures from three perspectives. Specifically, inner view multilevel clustering exploits high-confidence sample pairs across different levels to reduce the impact of boundary samples, resulting in more confident cluster structures. Synthesized-view alignment leverages a synthesized view to mitigate cross-view discrepancies and promote consistency. Cross-view guidance employs a reliable view guidance strategy to enhance the clustering confidence of poorly clustered views. These three modules are jointly optimized across multiple levels to achieve consistent and confident cluster structures. Furthermore, theoretical analyses verify the effectiveness of MRG-UMC in enhancing clustering confidence. Extensive experimental results show that MRG-UMC outperforms state-of-the-art UMC methods, achieving an average NMI improvement of 12.95% on multiview datasets. The source code is available at https://anonymous.4open.science/r/MRG-UMC-5E20.

Multi-view clustering via pairwise sparse subspace representation

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.

With the widespread existence of multi-view data, many multi-view clustering methods have emerged. The purpose of multi-view clustering is to classify data into multiple clusters based on different views. Existing multi-view clustering methods usually do not sufficiently mine the complementary information of data, which makes the effective information of multi-view data cannot be fully utilized. By considering the diversity of different views, we propose a new multi-view subspace clustering method. Specifically, we first extend single-view self-expression learning to the multi-view domain. Then, based on manifold learning, the public information of multi-view data is obtained. In addition, diversity among the data was measured using the Hilbert-Schmidt Independence Criteria (HSIC). Experimental results on four datasets show that our model has good clustering performance on different evaluation indicators.

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> .

In recent years, multi-view clustering (MVC) has become a promising approach for analyzing heterogeneous multi-source data. However, during the collection of multi-view data, factors such as environmental interference or sensor failure often lead to the loss of view sample data, resulting in incomplete multi-view clustering (IMVC). Graph contrastive IMVC has demonstrated promising performance as an effective solution, which typically utilizes in-graph instances as positive pairs and out-of-graph instances as negative pairs. However, the construction of positive and negative pairs in this paradigm inevitably leads to graph noise Correspondence (GNC). To this end, we propose a new IMVC framework, namely robust graph contrastive learning (RGCL). Specifically, RGCL first completes the missing data by using a multi-view consistency transfer relationship graph. Then, to mitigate the impact of false negative pairs from graph contrastive, we propose noise-robust graph contrastive learning to mine intra-view consistency accurately. Finally, we present cross-view graph-level alignment to fully exploit the complementary information across different views. Experimental results on the six multi-view datasets demonstrate that our RGCL exhibits superiority and effectiveness compared with 9 state-of-the-art IMVC methods. The source code is available at https://github.com/DYZ163/RGCL.git.

Despite the promising progress having been made, the two challenges of multi-view clustering (MVC) are still waiting for better solutions: i) Most existing methods are either not qualified or require additional steps for incomplete multi-view clustering and ii) noise or outliers might significantly degrade the overall clustering performance. In this paper, we propose a novel unified framework for incomplete and complete MVC named multi-view probabilistic clustering (MPC). MPC equivalently transforms multi-view pairwise posterior matching probability into composition of each view's individual distribution, which tolerates data missing and might extend to any number of views. Then graph-context-aware refinement with path propagation and co-neighbor propagation is used to refine pairwise probability, which alleviates the impact of noise and outliers. Finally, MPC also equivalently transforms probabilistic clustering's objective to avoid complete pairwise computation and adjusts clustering assignments by maximizing joint probability iteratively. Extensive experiments on multiple benchmarks for incomplete and complete MVC show that MPC significantly outperforms previous state-of-the-art methods in both effectiveness and efficiency.

Incomplete multi-view clustering via kernelized graph learning

Scalable incomplete multi-view clustering via tensor Schatten p-norm and tensorized bipartite graph

Deep multi-view subspace clustering has achieved promising performance compared with other multi-view clustering. However, existing deep multi-view subspace clustering only considers the global structure for all views, and they ignore the local geometric structure among each view. In addition, they cannot learn discriminative feature on different clusters of different views, i.e., inter-cluster difference. To solve these problems, in this paper, we propose a novel Deep Multi-view Subspace Clustering with Unified and Discriminative Learning (DMSC-UDL). DMSC-UDL combines global and local structures with self-expression layer. The global and local structures help each other forward and achieve small distance between samples of the same cluster. To make samples in different clusters of different views farther, DMSC-UDL uses a discriminative constraint between different views. In this way, DMSC-UDL makes the same cluster's samples have large weights, while different clusters’ samples have small weights. Thus, it can learn a better shared connection matrix for multi-view clustering. Extensive experimental results reveal that the proposed multi-view clustering method is superior to several state-of-the-art multi-view clustering methods in terms of performance.

Multi-view intact space clustering

We propose a novel multi-view clustering method by learning auto-regression problems under structural constraints and treating the regression coefficients as new feature representations for the cluster partition. In particular, we take the data intrinsic correlation structure into account. Correlated data under one view tend to be also related under another view and are likely to fall into the same group. Therefore we pair the data matrix from one view and the regression coefficient from a different view together to meet a trace Lasso constraint, which adaptively adjusts the sparsity of regression coefficients in order to promote consistent data correlations across views. Then a joint low-rank constraint is further imposed to encourage similar regression coefficients for the same samples under distinct views. Finally, we develop an effective algorithm to optimize the objective function. And experimental results demonstrate that our method is useful and fairly competitive compared with other state-of-the-art multi-view clustering methods.