Multi-View Clustering

Multi-view learning jointly exploits multiple complementary representations of the same data and has become increasingly important in machine learning. However, the Python ecosystem lacks actively maintained, unified tooling for end-to-end multi-view workflows. In this paper, we present polyview, a Python package that provides tools for multi-view embedding, clustering, fusion, and view augmentation, as well as for handling incomplete views, all compatible with scikit-learn. The library offers a unified interface for composing heterogeneous multi-view workflows, including seamless transitions between multi-view and single-view stages. It is built around a core set of classes and utilities that enable composition of different methods and straightforward implementation of new ones. We illustrate the package on five real multi-view datasets and compare its components based on canonical correlation analysis with those of two established libraries. polyview aims to be both a practical toolkit for benchmarking and prototyping multi-view methods and a foundation for future research and development in this area.

Multi-view clustering aims to capture cross-view consistency while exploiting view-specific information. However, shared representations learned to capture cross-view consistency may still retain view-identifying information, potentially compromising the consistency of cross-view clustering structures. To address this issue, we propose ACGRL, an adversarial consistency-guided representation learning framework for multi-view clustering. ACGRL employs a gradient-reversal view discriminator to reduce view identifiability and obtain invariant reference representations. These representations are then frozen to provide fixed references for disentangling view-specific information from cross-view common information in the subsequent learning stage. The fixed reference representations are concatenated with the learned view-specific representations for reconstruction and clustering, with cross-view cluster alignment encouraging consistent clustering assignments. Experiments on four benchmark datasets demonstrate the superior clustering performance of ACGRL compared with representative multi-view clustering methods.

Multi-view clustering (MVC) aims to uncover latent cluster structures by exploiting complementary information from multiple views. Despite substantial progress in clustering performance, fairness remains an important concern when MVC is applied to socially sensitive scenarios. Recent fair multi-view clustering methods have introduced fairness constraints into representation learning or clustering assignments. However, these methods generally treat different views under a largely uniform fairness mechanism, without explicitly distinguishing their varying levels of sensitive dependence during cross-view learning. In practice, different views may encode substantially different levels of sensitive information. Ignoring such cross-view discrepancy can allow highly sensitive-dependent views to influence less sensitive-dependent ones during cross-view learning, potentially degrading both clustering performance and fairness. To address this issue, we propose a novel multi-view fair clustering framework guided by cross-view sensitive information discrepancy. Specifically, we estimate the sensitive dependence of each view and develop a bias-ranked asymmetric alignment mechanism that encourages views with higher sensitive dependence to learn from those with lower sensitive dependence, while cross-view discrepancies are further exploited to adaptively regulate the alignment process. Moreover, fairness regularization is imposed on the consensus soft assignments to further promote group fairness. Extensive experiments on benchmark datasets demonstrate that the proposed method achieves a favorable balance between clustering quality and group fairness.

SNAP-KG is a framework for assigning newly arriving entities to semantic communities in a growing knowledge graph (KG) using only their raw features, with no graph access and no retraining at inference time. It was evaluated on five multi-view benchmarks and a 2.4M-node OGB-WikiKG2 KG. In each of these datasets, at least one graph view is homophilous, meaning that connected nodes usually belong to the same class, and SNAP-KG performs well on all of them. This paper asks what happens outside that setting. We extend the evaluation to three heterophilous graphs (Texas, Wisconsin, Chameleon) and measure the edge homophily of every view. When no homophilous view is available, clustering quality drops sharply for both SNAP-KG and the transductive baselines used in its original evaluation. What decides this is the homophily of the relation, not the number of relations. Multi-view fusion still helps, but only when at least one homophilous relation provides a reliable foundation. The homophily assumption is therefore shared by the whole method family, not specific to SNAP-KG. We argue that heterophilous multi-view clustering is a separate research problem, outside the scope of this work. As future work, we outline how a heterophily-aware teacher could be distilled into SNAP-KG's projector to serve both homophilous and heterophilous KGs.

In recent years, multi-view clustering has attracted widespread research interest. However, due to limitations in data collection devices, data across different views often suffer from misalignment, leading to the partial view alignment problem (PVAP). To mitigate the impact of view asymmetry and irrelevant samples, this paper proposes a framework for partial multi-view clustering via dual alignment and structure enhancement (DAS-PMVC), which leverages view structure consistency and semantic relevance. Specifically, DAS-PMVC includes three parts: \textbf{anchor graph structure alignment}, where sample joint embedding representations with consistent latent space are derived from anchor point relationships for initial view alignment; \textbf{structure-enhanced feature learning}, where the model learns view structure information through pretraining and combines multi-view graph convolutional networks to further extract deep latent features from the aligned graph structure to improve the discriminative power of representations; and \textbf{a dual alignment strategy}, where initial alignment is performed through the anchor graph in the pretraining phase, and contrastive learning loss and the Hungarian algorithm are introduced in the training phase to further optimize the alignment of latent features. Experimental results on various datasets demonstrate that the DAS-PMVC framework outperforms existing state-of-the-art methods in clustering performance, showcasing its effectiveness and superiority.

Tensorial multi-view clustering (TMC) has achieved strong performance due to its ability to capture high-order correlations across multiple views. Most existing t-SVD-based TMC frameworks apply the Fast Fourier Transform (FFT) along the sample mode to impose frequency-domain low-rank constraints. However, we reveal that this widely adopted design critically relies on an implicit ``periodicity assumption'' induced by the sample arrangement. When samples are ordered by class, neighboring indices tend to be semantically similar, creating artificial local continuity along the sample mode and a favorable spectral structure for FFT-based low-rank regularization. Once this ordering is removed by random permutation, existing t-SVD-based TMC methods suffer severe performance degradation. This strong sensitivity to class ordering conflicts with the permutation-invariant nature of clustering and indicates that part of the reported performance may be attributed to a privileged sample arrangement rather than genuine high-order structure modeling. In this paper, we systematically investigate this phenomenon and its underlying algebraic and spectral mechanisms. To address this fundamental flaw, we further propose a graph-spectral low-rank tensor learning framework based on the Graph Fourier Transform (GFT), which replaces the fixed Fourier basis along the sample mode with a data-driven graph spectral basis, thereby capturing the intrinsic manifold structure without relying on a particular sample ordering. Moreover, we develop an anchor-based variant to address large-scale datasets efficiently. Extensive experiments on various benchmarks validate our findings and demonstrate the competitive or superior performance of the proposed methods compared with state-of-the-art TMC approaches.

Prototype-based Incomplete Multi-view Clustering has recently attracted increasing attention by exploiting prototypes as semantic anchors for missing-view imputation. However, existing approaches are still limited in three aspects. First, they typically focus on enforcing cross-view prototype consistency, while ignoring view-specific information embedded in prototypes, thus limiting multi-view expressiveness. Second, most methods rely on instance-level contrastive learning that only aligns paired samples across views, failing to preserve cluster-level relational structures. Third, missing-view imputation is usually performed using global prototypes alone, without considering local geometric neighborhood structures, leading to inaccurate recovery of missing representations. To address these limitations, we propose a novel framework termed Structure-aware PrOtotype disentanglement foR incomplete multi-view clusTering (SPORT), which explicitly disentangles shared and view-specific components of prototypes while preserving cluster-level relational structures. Specifically, we decouple prototypes into orthogonal shared and view-specific components, aligning only shared components to capture consensus semantics while de-correlating view-specific components to preserve complementary information. Meanwhile, a structure-aware contrastive learning mechanism is incorporated to explicitly model cluster-level relationships during cross-view representation learning. Furthermore, a hybrid imputation strategy integrates global prototype matching with local neighborhood matching, enabling joint exploitation of semantic prototypes and manifold structures for missing-view recovery. Extensive experiments on six benchmark datasets show that SPORT achieves superior performance over state-of-the-art methods under various missing rates.

In many realistic scenarios, large volumes of time series data are generated with limited or expensive annotations. This limitation makes supervised learning methods difficult to apply and leads to the use of unsupervised approaches capable of discovering meaningful structures directly from raw data. Clustering therefore plays a crucial role in organizing time series into groups that share similar temporal patterns, enabling exploratory analysis and downstream tasks without requiring manual labeling. However, existing deep clustering methods often struggle to capture long-range temporal dependencies or rely on architectures with high computational cost. This paper introduces FMMVCC, a Mamba-based deep clustering framework for time series that leverages state space sequence modeling to efficiently learn temporal representations with linear complexity. Additionally, it utilizes multi-view self-supervised learning with temporal masking and augmentations. Experimental evaluation in 15 benchmark datasets proves that FMMVCC consistently outperforms state-of-the-art baselines, achieving the best overall performance in 29 of 60 total metric evaluations and the highest average rank in all tested scenarios.

Incomplete Multi-View Clustering addresses the problem of clustering multi-modal data when certain views are missing. Recent end-to-end generative approaches leverage diffusion models to recover missing views via stochastic noise-to-data trajectories. While expressive, such mechanisms are not explicitly designed for clustering, as they initialize from cluster-agnostic noise and rely on stochastic denoising dynamics. In this work, we revisit probability path design in end-to-end generative IMVC. We introduce a flow-matching framework with a linear interpolation path between paired view representations, that replaces diffusion with probability flows between observed and missing views. We provide a formal analysis showing that deterministic ODE flows are inherently better aligned with clustering objectives than diffusion-based stochastic trajectories, especially in terms of transport mechanisms that respect class-conditional data distributions and maintain cluster consistency in finite-step regimes. Building upon this insight, we develop an end-to-end IMVC architecture that integrates straight-path flow-matching view completion with cluster-level and entropy-based alignment to enforce cross-view clustering consistency. Extensive experiments on standard IMVC benchmarks demonstrate that the proposed framework establishes new state-of-the-art performance.

Multimodal feature fusion can effectively capture complex patterns in real-world data by integrating complementary information from different modalities. However, in many applications, such as boiler combustion monitoring, equipment failure, inconsistent sensor sampling frequencies, and network delays often cause missing modalities and temporal asynchrony. These issues lead to incomplete and disorderly multimodal data. To address them, previous studies have proposed several data fusion methods that align cluster centers before fusion. However, these methods have two key limitations. First, they cannot guarantee accurate sample-level alignment of data pairs. Second, they do not address significant discrepancies in data sizes across different classes, which may affect subsequent fusion performance. To address these problems, we propose a dual-learning based penalized multi-align clustering model, named DLPMAC. The dual-learning mechanism enables the model to learn prior knowledge from each modality, including semantic and structural information. This helps preserve semantic consistency and structural similarity across modalities at both local and global levels. In addition, the penalized multi-align module performs multi-to-multi data alignment through a penalty mechanism. It allows one sample to form data pairs with different samples from other modalities, thereby improving data-pair alignment accuracy. The penalty mechanism also prevents data aggregation, avoiding the case where excessive samples are linked to a single sample. Experimental results demonstrate the effectiveness of DLPMAC in addressing data alignment and fusion challenges from both sampling and clustering perspectives.

Time series anomaly detection plays a crucial role in a wide range of real-world applications. Reconstruction-based methods have become the mainstream paradigm, but they suffer from over-generalization and under-generalization problems, which are challenging to balance. To address this, we introduce multi-scale clustering to enhance reconstruction-based methods. At the representation level, we integrate the cluster center representations of normal patterns to constrain the model to target representative normal patterns for reconstruction, preventing dominance of powerful capacity and representation capability. At the anomaly criterion level, we derive anomaly confidence score based on cluster membership probability and combine it with reconstruction error, providing dual criteria for detection. Furthermore, the effectiveness of the cluster center representations and anomaly confidence score depends on the clustering performance. Accordingly, we extract neighborhood-centered representations for multi-view clustering to improve clustering performance. Extensive experiments on multiple real-world datasets from diverse application domains demonstrate the state-of-the-art performance of SCAN.

Real-world multi-view data always suffer from imperfect information problem, where the view-specific observations are absent (i.e., Incomplete Views, IV) and cross-view correspondences are mismatched (i.e., Noisy Correspondences, NC) for certain instances. As a remedy, numerous IV- and NC-oriented multi-view clustering (MvC) methods have been proposed, which however require either reliable correspondences or sufficiently complete instances, thus stopping short of addressing the imperfect information problem. In contrast, we observe that both IV and NC challenges originate from the same issue of imperfect cross-view counterpart information, where the counterpart of an anchor instance in another view might be either unavailable or unreliable. Based on the observation, we propose a novel robust MvC framework, termed Posterior-guided Latent Counterpart Inference (PLCI), which could handle both IV and NC in a unified manner. Specifically, PLCI formulates the desired cross-view counterpart of each anchor instance as a latent variable, and integrates both instance-level reliability and prototype-level semantic transport to infer the posterior distribution of the latent counterpart. Extensive experiments on six widely-used multi-view datasets against 10 state-of-the-art MvC methods demonstrate the effectiveness of PLCI for tackling the imperfect information problem. The code will be released upon acceptance.

Multi-View Clustering (MVC) has gained significant attention for its ability to leverage complementary information across diverse views. However, existing deep MVC methods often struggle with view-distribution entanglement during cross-view fusion, which hampers the quality of the shared latent space and leads to suboptimal Figures. To address this issue, we propose the Generalized Multi-view Auto-Encoder (GMAE), a framework designed to preserve cross-view complementarity through disentangled representation learning. Specifically, GMAE employs dual-path autoencoders to decouple source features into view-specific and view-common embeddings, facilitating the discovery of clearer clustering structures. We further construct cross-view adversarial discriminators to guide view-specific encoders in capturing more discriminative features. By strategically modulating mutual information, GMAE effectively aligns distributions and prevents representation collapse, ensuring the generation of robust, non-trivial embeddings. Comprehensive experiments on 13 benchmark datasets demonstrate that GMAE consistently outperforms state-of-the-art methods in both complete and incomplete MVC tasks. Our code implementation is available at the repository: https://github.com/obananas/GMAE.

Learning low-dimensional representations from multi-view relational data is challenging when underlying geometries differ across views. We propose Bary-GWMDS, a Gromov-Wasserstein-based method that operates directly on distance matrices to learn a consensus embedding preserving shared relational structure. By leveraging intrinsic distances, the approach naturally handles nonlinear distortions across views. We also introduce Mean-GWMDS-C, a clustering-oriented formulation that averages distance matrices and learns reduced-support representations via a consensus Gromov-Wasserstein transport. Experiments on synthetic and real-world datasets show that the proposed framework yields stable and geometrically meaningful embeddings.

In multi-view clustering, the quality of different views may vary substantially, and low-quality or degraded views can impair overall clustering performance. However, existing studies mainly address this issue within the clustering process through view weighting or noise-robust optimization, while paying limited attention to data-level assessment before clustering. In this paper, we study the problem of pre-clustering noisy-view analysis in multi-view data from a clusterability perspective. To this end, we propose a Multi-View Clusterability Score (MVCS), which quantifies the strength of latent cluster-related structures in multi-view data through three complementary components: per-view structural clusterability, joint-space clusterability, and cross-view neighborhood consistency. To the best of our knowledge, this is the first clusterability score specifically designed for multi-view data. We further use it to perform potentially noisy view analysis and noisy-view detection before clustering. Extensive experiments on real-world datasets demonstrate that noisy views can significantly degrade clustering performance, and that, compared with existing clusterability measures designed for single-view data, the proposed method more effectively supports noisy-view analysis and detection.

Incomplete Multi-View Clustering (IMVC) faces the challenge of learning discriminative representations from fragmentary observations while maintaining robustness against missing views. However, prevalent Euclidean-based methods suffer from a geometric mismatch when modeling real-world data with intrinsic hierarchies, leading to semantic blurring where representations drift towards spatially proximal but semantically distinct neighbors. To bridge this gap, we propose HERL, a Hyperbolic Enhanced Representation Learning framework for IMVC. Operating within the Poincaré ball, HERL constructs a structure-aware latent space to enhance representation learning. Specifically, we design a dual-constraint hyperbolic contrastive mechanism optimizing: an angular-based loss to preserve semantic identity via directional alignment, and a distance-based loss to enforce hierarchical compactness. Furthermore, a hyperbolic prototype head is introduced to rectify global structural drift by aligning cross-view hierarchy-aware prototype distributions. Consequently, HERL disentangles fine-grained semantic correlations to sharpen cluster boundaries and imposes geometric constraints to rectify the data recovery process. Extensive experimental results demonstrate that HERL consistently outperforms state-of-the-art approaches.

Deep multi-view clustering has achieved remarkable progress but remains vulnerable to complex noise in real-world applications. Existing noisy robust methods predominantly rely on a simplified binary assumption, treating data as either perfectly clean or completely corrupted. This overlooks the prevalent existence of heterogeneous observation noise, where contamination intensity varies continuously across data. To bridge this gap, we propose a novel framework termed Quality-Aware Robust Multi-View Clustering (QARMVC). Specifically, QARMVC employs an information bottleneck mechanism to extract intrinsic semantics for view reconstruction. Leveraging the insight that noise disrupts semantic integrity and impedes reconstruction, we utilize the resulting reconstruction discrepancy to precisely quantify fine-grained contamination intensity and derive instance-level quality scores. These scores are integrated into a hierarchical learning strategy: at the feature level, a quality-weighted contrastive objective is designed to adaptively suppress the propagation of noise; at the fusion level, a high-quality global consensus is constructed via quality-weighted aggregation, which is subsequently utilized to align and rectify local views via mutual information maximization. Extensive experiments on five benchmark datasets demonstrate that QARMVC consistently outperforms state-of-the-art baselines, particularly in scenarios with heterogeneous noise intensities.