Multi-view clustering (MVC) leverages complementary information across heterogeneous views to improve unsupervised partitioning. Nevertheless, the majority of existing MVC methods critically assume that samples are fully aligned across views, an assumption frequently violated in practice when multi-view data are collected from independent sources without any correspondence. This gives rise to Completely Unaligned multi-view Clustering (CUC), where cross-view sample correspondences are entirely unknown, fundamentally impeding effective multi-view fusion. Prior CUC-oriented methods typically infer inter-view relations from distance/similarity matrices; however, severe cross-view heterogeneity often induces over-smoothing in such matrices, leading to unreliable matching signals and degraded clustering performance. To address these issues, we propose Cross-view Graph Matching for Completely Unaligned multi-view Clustering (CGM-CUC), a unified framework that couples structure-aware representation learning with progressive cross-view alignment. Specifically, CGM-CUC introduces a bipartite graph-based sample re-encoding mechanism to enhance discriminative structural cues, and an iterative cross-view matching network that progressively refines permutation matrices to recover latent correspondences. Moreover, we develop an alignment-guided optimization strategy that mitigates the over-smoothing effect in similarity estimation, thereby stabilizing the matching process and improving downstream clustering. Extensive experiments on multiple benchmark datasets demonstrate that CGM-CUC consistently achieves superior performance over state-of-the-art baselines, with particularly notable gains under fully unaligned view settings.

Multi-view clustering aims to leverage complementary information from multiple data sources to improve clustering quality. Traditional graph-based Non-k multi-view clustering methods enable automatic cluster number determination but suffer from severe scalability issues due to their reliance on constructing large sample-level affinity graphs with quadratic complexity. To address this limitation, we propose a novel scalable Non-k Multi-View Clustering framework via Inter-Anchor Graph learning (MVC-IAG). Our method first extracts a small set of representative anchors via k-means on concatenated multi-view features, then learns a unified inter-anchor graph by integrating multi-view structural information and feature similarity priors. Our framework performs Non-k cluster discovery directly on this compact, learned inter-anchor graph, thereby enabling automatic cluster number determination, and subsequently propagates the results to all samples. Extensive experiments on multiple large scale datasets demonstrate that MVC-IAG significantly reduces computational cost while achieving competitive or superior clustering performance compared to state-of-the-art Non-k multi view clustering approaches.

Anchor-based multi-view graph clustering has recently gained popularity as an effective approach for clustering data with multiple views. However, existing methods have limitations in terms of handling inconsistent information and noise across views, resulting in an unreliable consensus representation. Additionally, post-processing is needed to obtain final results after anchor graph construction, which negatively affects clustering performance. In this paper, we propose a Robust and Consistent Anchor Graph Learning method (RCAGL) for multi-view clustering to address these challenges. RCAGL constructs a consistent anchor graph that captures inter-view commonality and filters out view-specific noise by learning a consistent part and a view-specific part simultaneously. A k-connectivity constraint is imposed on the consistent anchor graph, leading to a clear graph structure and direct generation of cluster labels without additional post-processing. Experimental results on several benchmark datasets demonstrate the superiority of RCAGL in terms of clustering accuracy, scalability to large-scale data, and robustness to view-specific noise, outperforming advanced multi-view clustering methods. Our code is publicly available at https://github.com/Tracesource/RCAGL.

Multi-Domain Recommendation (MDR) achieves the desirable recommendation performance by effectively utilizing the transfer information across different domains. Despite the great success, most existing MDR methods adopt a single structure to transfer complex domain-shared knowledge. However, the beneficial transferring information should vary across different domains. When there is knowledge conflict between domains or a domain is of poor quality, unselectively leveraging information from all domains will lead to a serious Negative Transfer Problem (NTP). Therefore, how to effectively model the complex transfer relationships between domains to avoid NTP is still a direction worth exploring. To address these issues, we propose a simple and dynamic Similar Domain Selection Principle (SDSP) for multi-domain recommendation in this paper. SDSP presents the initial exploration of selecting suitable domain knowledge for each domain to alleviate NTP. Specifically, we propose a novel prototype-based domain distance measure to effectively model the complexity relationship between domains. Thereafter, the proposed SDSP can dynamically find similar domains for each domain based on the supervised signals of the domain metrics and the unsupervised distance measure from the learned domain prototype. We emphasize that SDSP is a lightweight method that can be incorporated with existing MDR methods for better performance while not introducing excessive time overheads. To the best of our knowledge, it is the first solution that can explicitly measure domain-level gaps and dynamically select appropriate domains in the MDR field. Extensive experiments on three datasets demonstrate the effectiveness of our proposed method.

Multi-view graph clustering (MVGC) explores pairwise correlations of entire instances and comprehensively aggregates diverse source information with optimal graph structure. One major issue of practical MVGC is the high time and space complexities prohibiting being applied on large-scale applications. As a promising solution of addressing large-scale problems, anchor-based strategy identifies small portion and key landmarks to serve as replacements for the entire dataset. Despite of its efficiency, anchors chosen across views may be semantically unaligned contrasting to naturally-aligned full sample setting, which may lead to the latter inappropriate graph fusion. Limited attention has been focused on the mentioned Multi-View Anchor-Unaligned Problem (MV-AUP) in the existing literature. In this paper, we first revisit existing multi-view anchor graph clustering frameworks and present the MV-AUP phenomenon. Then, we propose a novelMulti-viewCorrespondingAnchorGraphAlignmentFusion framework (MV-CAGAF), which elegantly solves MV-AUP with structural representation matching in multi-dimensional spaces. Further, we theoretically prove our proposed structural matching approach can be regarded as minimizing the EMD distance of the two relative anchor distributions. Based on this, we design the innovative multi-view anchor graph fusion paradigm with correspondence alignment, which inherits the linear sample complexity for scalable cross-view clustering. Our proposed MV-CAGAF achieves significant improvements with the help of the novel fusion framework on comprehensive benchmark datasets. Most importantly, the experimental results on both of the simulated and real-world datasets significantly prove the importance of cross-view alignment for large-scale multi-view clustering.

Anchor-based multi-view graph clustering has recently gained popularity as an effective approach for clustering data with multiple views. However, existing methods have limitations in terms of handling inconsistent information and noise across views, resulting in an unreliable consensus representation. Additionally, post-processing is needed to obtain final results after anchor graph construction, which negatively affects clustering performance. In this paper, we propose a Robust and Consistent Anchor Graph Learning method (RCAGL) for multi-view clustering to address these challenges. RCAGL constructs a consistent anchor graph that captures inter-view commonality and filters out view-specific noise by learning a consistent part and a view-specific part simultaneously. A$k$-connectivity constraint is imposed on the consistent anchor graph, leading to a clear graph structure and direct generation of cluster labels without additional post-processing. Experimental results on several benchmark datasets demonstrate the superiority of RCAGL in terms of clustering accuracy, scalability to large-scale data, and robustness to view-specific noise, outperforming advanced multi-view clustering methods. Our code is publicly available athttps://github.com/Tracesource/RCAGL.

Reasoning on temporal knowledge graphs (TKGR), aiming to infer missing events along the timeline, has been widely studied to alleviate incompleteness issues in TKG, which is composed of a series of KG snapshots at different timestamps. Two types of information, i.e., intra-snapshot structural information and inter-snapshot temporal interactions, mainly contribute to the learned representations for reasoning in previous models. However, these models fail to leverage (1) semantic correlations between relationships for the former information and (2) the periodic temporal patterns along the timeline for the latter one. Thus, such insufficient mining manners hinder expressive ability, leading to sub-optimal performances. To address these limitations, we propose a novel reasoning model, termed RPC, which sufficiently mines the information underlying the Relational correlations and Periodic patterns via two novel Correspondence units, i.e., relational correspondence unit (RCU) and periodic correspondence unit (PCU). Concretely, relational graph convolutional network (RGCN) and RCU are used to encode the intra-snapshot graph structural information for entities and relations, respectively. Besides, the gated recurrent units (GRU) and PCU are designed for sequential and periodic inter-snapshot temporal interactions, separately. Moreover, the model-agnostic time vectors are generated by time2vector encoders to guide the time-dependent decoder for fact scoring. Extensive experiments on six benchmark datasets show that RPC outperforms the state-of-the-art TKGR models, and also demonstrate the effectiveness of two novel strategies in our model.

Multi-view learning becomes increasingly attractive and promising because multimodal or multi-view data are commonly encountered in real-world applications. In this study, we develop a novel multi-view Takagi–Sugeno–Kang (TSK) fuzzy system framework to handle classification problems for such data. We propose an anchor and graph subspace clustering strategy to discover and represent the actual latent data distribution for each view separately. In this way, the discriminate anchors (landmarks) are learned to capture the main structure of the multi-view data. This strategy also provides a computationally efficient clustering algorithm with respect to the number of instances. These resulting anchors are formed as the prototypes of information granules (IGs) for fuzzy modeling. Then we construct an information-granule-based multi-view TSK fuzzy classification model inherited from the natural interpretability of fuzzy rule-based systems. Concretely, the relationship between the multi-view input and label output spaces is depicted by IGs-oriented fuzzy rules. The experimental studies involve various commonly used benchmark datasets, which indicate that our proposed method achieves comparable or better performance compared to the state-of-the-art algorithms.

Unsupervised bipartite graph learning has been a hotpot in multi-view clustering, to tackle the restricted scalability issue of traditional full graph clustering in large-scale applications. However, the existing bipartite graph clustering paradigm pays little attention to the adverse impact of noisy features on learning process. To further facilitate this part of research, apart from simply reweighting features to depress the noisy ones, we take the first step towards analyzing the induced adverse impact via theoretical and experimental investigations. One crucial finding in this paper is that the existence of noisy features will incur “anchor shift” phenomenon, which deviates the potential representations of anchors and then degrades performance. To this end, we propose a coupled noisy feature filter mechanism with automatically finding feature importance to remedy the anchor shift issue in this paper. Apart from leveraging features, we theoretically analyze the bounds of proposed feature-adaptive bipartite graph's fuzzy membership. Specifically, distinguishing features' discrimination will increase the fuzzy membership to achieve soft partitions against the potential inaccurate absolute relationship. With the afore-mentioned merits, our proposed multi-view bipartite graph clustering with coupled noisy feature filter model (MVBGC-NFF) provides novel and interesting insights on the feature level of anchor shift. The effectiveness and efficiency of MVBGC-NFF are demonstrated on synthetic and real-world datasets with improving clustering performance, increasing fuzzy membership, and filtering noisy features. The code is available onhttps://github.com/liliangnudt/MVBGC-NFF.

Multi-view spectral clustering can effectively reveal the intrinsic cluster structure among data by performing clustering on the learned optimal embedding across views. Though demonstrating promising performance in various applications, most of existing methods usually linearly combine a group of pre-specified first-order Laplacian matrices to construct the optimal Laplacian matrix, which may result in limited representation capability and insufficient information exploitation. Also, storing and implementing complex operations on the{$n\times n}$Laplacian matrices incurs intensive storage and computation complexity. To address these issues, this paper first proposes a multi-view spectral clustering algorithm that learns a high-order optimal neighborhood Laplacian matrix, and then extends it to the late fusion version for accurate and efficient multi-view clustering. Specifically, our proposed algorithm generates the optimal Laplacian matrix by searching the neighborhood of the linear combination of both the first-order and high-order base Laplacian matrices simultaneously. By this way, the representative capacity of the learned optimal Laplacian matrix is enhanced, which is helpful to better utilize the hidden high-order connection information among data, leading to improved clustering performance. We design an efficient algorithm with proved convergence to solve the resultant optimization problem. Extensive experimental results on nine datasets demonstrate the superiority of the proposed algorithm

Multiple kernel clustering (MKC) algorithm aims to group data into different categories by optimally integrating information from a group of pre-specified kernels. Though demonstrating superiorities in various applications, we observe that existing MKC algorithms usuallydo not sufficiently consider the local density around individual data samplesandexcessively limit the representation capacity of the learned optimal kernel, leading to unsatisfying performance. In this paper, we propose an algorithm, called optimal neighborhood MKC with adaptive local kernels (ON-ALK), to address the two issues. In specific, we construct adaptive local kernels to sufficiently consider the local density around individual data samples, where different numbers of neighbors are discriminatingly selected on each sample. Further, the proposed ON-ALK algorithm boosts the representation of the learned optimal kernel via relaxing it into the neighborhood area of weighted combination of the pre-specified kernels. To solve the resultant optimization problem, a three-step iterative algorithm is designed and theoretically proven to be convergent. After that, we also study the generalization bound of the proposed algorithm. Extensive experiments have been conducted to evaluate the clustering performance. As indicated, the algorithm significantly outperforms state-of-the-art methods in recent literatures on six challenging benchmark datasets, verifying its advantages and effectiveness.

Deep autoencoder-based methods are the majority of deep anomaly detection. An autoencoder learning on training data is assumed to produce higher reconstruction error for the anomalous samples than the normal samples and thus can distinguish anomalies from normal data. However, this assumption does not always hold in practice, especially in unsupervised anomaly detection, where the training data is anomaly contaminated. We observe that the autoencoder generalizes so well on the training data that it can reconstruct both the normal data and the anomalous data well, leading to poor anomaly detection performance. Besides, we find that anomaly detection performance is not stable when using reconstruction error as anomaly score, which is unacceptable in the unsupervised scenario. Because there are no labels to guide on selecting a proper model. To mitigate these drawbacks for autoencoder-based anomaly detection methods, we propose an Improved AutoEncoder for unsupervised Anomaly Detection (IAEAD). Specifically, we manipulate feature space to make normal data points closer using anomaly detection-based loss as guidance. Different from previous methods, by integrating the anomaly detection-based loss and autoencoder's reconstruction loss, IAEAD can jointly optimize for anomaly detection tasks and learn representations that preserve the local data structure to avoid feature distortion. Experiments on five image data sets empirically validate the effectiveness and stability of our method.

Multiview clustering (MVC) collects complementary and abundant information, which draws much attention in machine learning and data mining community. Existing MVC methods usually hold the assumption that all the views are complete. However, multiple source data are often incomplete in real-world applications, and so on sensor failure or unfinished collection process, which gives rise to incomplete multiview clustering (IMVC). Although enormous efforts have been devoted in IMVC, there still are some urgent issues that need to be solved: (i) The locality among multiple views has not been utilized in the existing mechanism; (ii) Existing methods inappropriately force all the views to share consensus representation while ignoring specific structures. In this paper, we propose a novel method termed partial MVC with locality graph regularization to address these issues. First, followed the traditional IMVC approaches, we construct weighted semi-nonnegative matrix factorization models to handle incomplete multiview data. Then, upon the consensus representation matrix, the locality graph is constructed for regularizing the shared feature matrix. Moreover, we add the coefficient regression term to constraint the various base matrices among views. We incorporate the three aforementioned processes into a unified framework, whereas they can negotiate with each other serving for learning tasks. An effective iterative algorithm is proposed to solve the resultant optimization problem with theoretically guaranteed convergence. The comprehensive experiment results on several benchmarks demonstrate the effectiveness of the proposed method.

Multiple kernel clustering (MKC) methods aim at integrating an optimal partition from a set of precalculated kernel matrices. Though achieving success in various applications, we observe that existing MKC methods: (i) lack of representation flexibility; and (ii) do not considerably preserve the locality structure in partition space. These issues may adversely affect the learning procedure of MKC, leading to unsatisfying clustering performance. In this paper, we propose a late fusion MKC method with local graph refinement to address the aforementioned issues. Different from existing MKC mechanisms, our method unifies the traditional weighted multiple kernel k-means, kernel partition, and graph construction into a single optimization procedure. The local graph is utilized to preserve the locality information in partition space and therefore all of the counterparts can be boosted for mutual clustering improvements. By this way, our approach enhances the local graph structure in partition space and enjoys more flexible kernel representations, leading to significant clustering improvements. Moreover, a three-step alternate algorithm is developed to solve the resultant optimization problem with proved convergence. Extensive experiments are conducted on several multiple kernel benchmark datasets to compare the proposed algorithm with the state-of-the-art ones, and the results well demonstrate its effectiveness and superiority.