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A Survey on Incomplete Multi-view Clustering

Jie Wen, Zheng Zhang, Lunke Fei, Bob Zhang, Yong Xu, Zhao Zhang, Jinxing Li

arXiv:2208.08040v1cs.LGcs.MM

TL;DR

Incomplete multi-view clustering lacks a systematic survey despite practical data having missing views and conventional methods assuming complete observations. This paper reviews and categorizes IMC methods, unifies selected frameworks, compares representative approaches experimentally, and identifies open problems. The reported experiments show that IMC methods generally outperform simple single-view, concatenation, and complete-view baselines, although performance varies by dataset and method family.

  • Problem

    Incomplete multi-view clustering addresses data with missing views, but the field lacked a systematic survey of its progress and future directions.

  • Method

    The paper reviews IMC methods, divides them into four categories, unifies representative frameworks, and experimentally compares selected methods.

  • Results

    IMC methods generally outperform single-view and concatenation baselines, while graph and kernel methods show dataset-dependent performance and memory limitations.

  • Takeaways & Limitations

    The survey provides a comparative framework for understanding IMC methods and identifies missing-view recovery rationality as an important unresolved research challenge.

  • Takeaways & Limitations

    Most IMC methods have high computational and memory costs, limiting their applicability to large-scale datasets.

Abstract

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Conventional multi-view clustering seeks to partition data into respective groups based on the assumption that all views are fully observed. However, in practical applications, such as disease diagnosis, multimedia analysis, and recommendation system, it is common to observe that not all views of samples are available in many cases, which leads to the failure of the conventional multi-view clustering methods. Clustering on such incomplete multi-view data is referred to as incomplete multi-view clustering. In view of the promising application prospects, the research of incomplete multi-view clustering has noticeable advances in recent years. However, there is no survey to summarize the current progresses and point out the future research directions. To this end, we review the recent studies of incomplete multi-view clustering. Importantly, we provide some frameworks to unify the corresponding incomplete multi-view clustering methods, and make an in-depth comparative analysis for some representative methods from theoretical and experimental perspectives. Finally, some open problems in the incomplete multi-view clustering field are offered for researchers.

I. INTRODUCTION

Incomplete multi-view clustering addresses data in which some samples lack views, a condition that makes conventional fully observed methods unsuitable. This survey organizes existing IMC research, compares representative methods, and identifies open problems.

  • Multi-view clustering partitions samples using information from multiple views, which may be complementary, consistent, and redundant.
  • Incomplete multi-view data contain samples without all views, commonly arising in practical applications such as diagnosis, multimedia, and recommendation.
  • Removing samples with missing views excludes data points, while filling missing views identically can send them to the same cluster and performs poorly.
  • The survey summarizes state-of-the-art IMC methods, fairly compares representative approaches, and offers unresolved research problems.
  • The paper is organized around preliminary concepts, four IMC method categories, experiments, conclusions, and open problems.

B. Basic background on single-view/multi-view clustering

The paper introduces matrix-factorization and spectral-clustering foundations for multi-view learning, both seeking a consensus representation across views. Their formulations differ in whether they jointly exploit factorized representations or graph information.

  • MF based multi-view clustering: Multi-view matrix factorization assumes views share label distributions and learns a consensus representation together with view-specific representations.
  • Multi-view spectral clustering: Multi-view spectral clustering jointly explores all view graphs to obtain a consensus representation under an orthogonality constraint.
  • MF based multi-view clustering: A co-regularizer can push individual representations toward a consensus representation by minimizing their disagreements.

C. Categorization of the incomplete multi-view data

The survey distinguishes incomplete multi-view data by their missing-view patterns and categorizes methods by how they exploit partial alignment or recover missing information. Special cases use shared information among paired samples, while arbitrary missingness motivates weighted models.

  • Categorization of the incomplete multi-view data: The survey defines three incomplete-data cases: two-view partial data, more-than-two-view paired and single-view data, and arbitrary missing views.
  • Categorization of the incomplete multi-view data: For incomplete data, the central modeling goal is to obtain a common cluster-indicator matrix or consensus representation.
  • Categorization of the incomplete multi-view data: MF-based IMC methods either exploit consistent information among partially aligned views or recover missing views to use fully aligned information.
  • MF based methods for special partial multi-view data: PMVC, IMG, and PMSC use paired-sample alignment constraints to learn a consensus representation shared across views; IMG and PMSC additionally model geometric structure.
  • MF based methods for special partial multi-view data: IMC GRMF extends special-case models to more than two views but requires the feature dimension c ≤ min(m1, . . . , ml) because of an orthogonal basis constraint.

B. MF based methods for incomplete data with arbitrary missing views

Weighted matrix-factorization methods address arbitrary missing views by weighting view-missing information and can be unified into two consensus-representation frameworks. These methods differ in how they obtain consensus representations and face limitations involving hidden information, structure modeling, and parameter selection.

  • Weighted MF methods: Weighted MF methods reduce missing-view influence by imposing weight matrices constructed from view-missing information.Representative methods include MIC, OMVC, DAIMC, OPIMC, and GPMVC.
  • Unified frameworks: Existing weighted MF based IMC methods are unified into WMF IMCF1 and WMF IMCF2 according to their consensus-representation strategies.The paper presents these as two frameworks for organizing the methods.
  • Framework comparison: WMF IMCF1 obtains consensus representations from latent representations derived from all views, whereas WMF IMCF2 directly decomposes multi-view data into a consensus representation and basis matrices.The frameworks use basis matrices, latent representations, weight matrices, boundary constraints, and regularization constraints in different configurations.
  • Limitations: WMF IMCF1 introduces at least one extra tunable hyper-parameter γv, increasing the complexity of optimal parameter selection.Virtual instances used by some weighting choices can also affect consensus-representation learning.
  • Framework comparison: Weighted MF methods impose constraints such as l2,1, l1, or Frobenius norms to avoid trivial solutions, but these constraints do not necessarily improve discriminability.DAIMC and GPMVC additionally attempt to exploit more information from the data.
  • Limitations: PMVCF, WMF IMCF1, and WMF IMCF2 focus on partially aligned available instances, but ignore hidden information in missing views and may inadequately capture intrinsic structure.The paper motivates missing-view restoration and common-representation joint learning as responses to the first issue.

IV. KERNEL LEARNING BASED IMC

Kernel-learning-based incomplete multi-view clustering extends multiple kernel clustering to settings where kernel rows and columns are missing. Existing methods primarily address incompleteness by recovering those missing kernel components through Laplacian/KCCA or multiple-kernel-k-means techniques.

  • Kernel-learning setting: Conventional multiple kernel clustering requires complete input kernels and cannot directly handle absent rows and columns caused by incomplete views.This motivates incomplete multiple kernel clustering methods.
  • Method categories: Existing incomplete multiple kernel clustering methods are divided into Laplacian regularization and KCCA based methods and multiple kernel kmeans based methods.The categorization is based on the main techniques used to address incompleteness.

A. Laplacian regularization and KCCA based IMC

Laplacian regularization and KCCA based methods complete incomplete kernel matrices before learning latent representations with KCCA. Their sequential completion-and-learning design and restricted incomplete cases limit practical suitability.

  • Method pipeline: These methods first complete kernel matrices and then learn latent representations of all views via KCCA.The complete kernel may be pre-constructed from a view without missing instances.
  • Kernel completion: Trivedi et al. recover missing elements of an incomplete kernel by solving a Laplacian-regularized problem based on a complete kernel from another view.The Laplacian matrix is constructed from the complete kernel, and kernel values are computed by a kernel function.
  • Clustering pipeline: MIKC OCK applies KCCA to the complete and recovered kernels, obtains latent representations, and then performs kmeans clustering.The method is named multiple incomplete kernel clustering with one complete kernel.
  • Limitations: CoKL interactively recovers incomplete kernel matrices across views, but it is only suitable for incomplete data with two views.It was proposed to address the complete-view requirement of MIKC OCK.
  • Limitations: These methods can handle only one kind of incomplete case, and separate kernel completion from latent-representation learning without guaranteeing globally optimal kernels and representations.The paper therefore considers the approach unsuitable for practical applications.

B. Multiple kernel kmeans based IMC

Multiple kernel kmeans based methods jointly recover incomplete kernels and learn consensus representations or cluster-index matrices. Later variants add local-structure preservation, sparse kernel reconstruction, or reduced computational cost, while trade-offs remain in structure modeling and efficiency.

  • Joint modeling: Multiple kernel kmeans based IMC methods recover kernel matrices and learn consensus representations or cluster-index matrices simultaneously in a joint framework.This differs from methods that complete kernels and learn representations in separate stages.
  • IMKKC: IMKKC learns a consensus representation P while recovering each view’s kernel matrix from observed-instance sub-kernels and their observed entries.The formulation uses available-instance indexes and pre-constructed sub-kernel matrices.
  • Limitations: IMKKC and CKK-IMC ignore local data structure and insufficiently consider complementary information across views; IMKKC also has relatively high computational complexity.CKK-IMC obtains consensus P with a dissimilarity-based regularization term.
  • Improved methods: LIMKKC introduces neighborhood indication matrices to preserve local data information, while MKKM-IK-MKC adds sparse reconstruction constraints for better recovery of missing kernel rows and columns.Both methods improve on the basic IMKKC model from different perspectives.
  • EE-IMVC: EE-IMVC avoids directly recovering kernel matrices and greatly reduces computational complexity and memory cost compared with other multiple kernel kmeans methods.It nevertheless cannot bring nearest sample pairs closer while pushing other pairs farther apart.

V. GRAPH LEARNING BASED IMC

Graph learning based IMC methods learn either a consensus representation or consensus graph from incomplete views. They differ in whether graph construction, recovery, fusion, and clustering are separated or jointly optimized, with scalability and graph quality remaining important concerns.

  • Overview: Graph learning based IMC obtains a consensus graph or representation from multiple incomplete graphs, with three categories illustrated in Fig. 8.Categories (a) and (c) focus on consensus representations, whereas (b) focuses on the consensus graph.
  • Consensus representation learning: SCIMC alternates latent-representation recovery for missing views and combines view representations by minimizing their disagreement.It uses similarity matrices with missing entries filled by averages of observed-instance column vectors.
  • Consensus graph learning: PIC constructs and completes nearest-neighbor graphs, learns perturbation-oriented fusion coefficients, and fuses the graphs into a consensus graph.Its graph construction, weight calculation, and consensus graph learning are independent, making it sensitive to pre-constructed graph quality.
  • Consensus graph learning: CGL IMC learns a consensus graph through weighted, Laplacian-regularized graph learning and can impose a rank constraint for exactly c graph blocks.Like PIC, it is sensitive to the quality of pre-constructed graphs.
  • Joint graph and representation learning: IMSC AGL jointly optimizes adaptive graph construction and spectral consensus-representation learning, avoiding uncertain guidance used by SCIMC and PIC.Its high computational complexity makes it unsuitable for large-scale datasets.
  • Limitations and directions: Graph learning methods better exploit geometric information than matrix-factorization methods but may be unsuitable for large-scale data because of costly matrix operations.The survey also identifies efficient graph learning and fuller use of global and local information as necessary directions.

VI. DEEP LEARNING BASED IMC

Deep learning based IMC methods combine learned feature representations with incomplete-view clustering components. They can improve representation learning and scale through batch training, but existing methods do not cover all incomplete cases.

  • IMC DSM: IMC DSM integrates DNN feature extraction, partially aligned multi-view clustering, and local graph regularization in one framework.The local graph uses a nearest-neighbor graph pre-constructed from available instances.
  • IMC DSM: IMC DSM explores partially aligned information among available views, while DNNs extract high-level features and local regularization promotes structured representations.The paper identifies its objective as a special case of the unified framework.
  • Other deep methods: PMVC CGAN uses autoencoders for latent representations, GANs for missing-view generation, and a KL-divergence loss suited to clustering.The method is presented for incomplete two-view data.
  • Strengths and limitations: Deep neural networks are reported as beneficial for learning more discriminative representations and improving clustering performance.Batch-based training also allows deep methods to be applied to large-scale datasets.
  • Strengths and limitations: Existing deep-based IMC methods cannot be applied to all kinds of incomplete cases.This is identified as their biggest shortcoming in the survey’s discussion.

VII. EXPERIMENTS

The experiments compare representative incomplete multi-view clustering methods against single-view, concatenation, matrix-factorization, graph-learning, and spectral-clustering baselines.

  • Compared methods: The comparison includes BSV, Concat, MultiNMF, AMGL, MLAN, CCo-MVSC, PMVC, IMG, and additional representative IMC methods.The passage introduces the compared methods at the beginning of the experimental section.

A. Datasets

The survey evaluates IMC methods on five public multi-view datasets spanning visual, near-infrared, gene-expression, image, text, and web-image data. It uses four clustering metrics and constructs incompleteness through dataset-specific random view or instance removal.

  • Datasets: Five public datasets are selected for comparison: BUAA, BDGP, Caltech101, BBCSport, and NUSWIDE.Their dataset information is summarized in the supplementary material.
  • Datasets: BUAA contains visual and near-infrared face views, and the experiments use 90 images from the first 10 classes.The selected subset contains two views of each person.
  • Datasets: BDGP represents samples with texture and three bag-of-words feature views extracted from lateral, dorsal, and ventral images.The dataset is designed for gene-expression research.
  • Datasets: Caltech101 contributes four feature views—Cenhist, Hog, Gist, and LBP—from 9,144 images spanning 102 categories.The categories include a background category and 101 object categories.
  • Datasets: BBCSport uses 116 samples represented by four views across five sports-news categories.The categories are athletics, cricket, football, rugby, and tennis.
  • Datasets: NUSWIDE uses a subset of 30,000 images and 31 classes, with five low-level feature views.The views include color, edge-direction, wavelet-texture, and block-wise color-moment features.
  • Evaluation protocol: Performance is assessed using ACC, NMI, purity, and ARI.These are the four clustering metrics selected for evaluation.
  • Incomplete-data construction: BUAA incompleteness varies paired-sample proportions p ∈ {10, 30, 50}, while the other datasets randomly delete p% of instances from every view.All samples in the latter construction retain at least one view.

C. Experimental results and analysis

Experiments show that IMC methods generally outperform incomplete-data baselines, while method suitability varies substantially across datasets. The analysis also identifies scalability, information imbalance, mixed data types, noise, and missing-view recovery as unresolved challenges.

  • Experimental comparisons: Most multi-view learning-based IMC methods outperform BSV and Concat on the first four datasets.The results attribute this pattern to better exploitation of information in incomplete multi-view data than these baselines.
  • Experimental comparisons: PIC and IMSC AGL generally outperform matrix-factorization-based IMC methods on BUAA, BBCSport, and Caltech101 in ACC, NMI, and purity.On BDGP, these graph-based methods and MKKM-IK-MKC perform worse than other methods; several methods are also unsuitable for NUSWIDE under 64 GB RAM.
  • Experimental comparisons: BDGP contains naturally unavailable instances represented as zero vectors, making high-quality kernels or graphs difficult to obtain with Gaussian kernels or distance-based construction.The analysis links this dataset characteristic to the poor performance of kernel- and graph-based IMC methods.
  • Experimental comparisons: No IMC method maintains consistently good performance across all dataset types, so algorithm selection must be dataset-specific.The paper presents this as a practical implication of the comparative results.
  • Open problems: Most IMC methods remain unsuitable for large-scale datasets because of high computational complexity and memory costs, especially kernel- and graph-based methods.Chunk-by-chunk approaches such as OMVC and OPIMC reduce memory requirements, but their performance is not guaranteed.
  • Open problems: Existing IMC methods generally ignore information imbalance, mixed data types, and noise, while missing-view recovery remains sparse and lacks guaranteed performance.The survey identifies robust modeling, mixed-type handling, and unified recovery–clustering frameworks as research directions; partially view-aligned data and theoretical issues also remain challenging.
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