mlsanityData to 7 Oct 2026

Multi-Facet Clustering Variational Autoencoders

arXiv 2106.05241 ↗First posted 9 Jun 2021stat.ML cs.CV cs.LGcited by 28

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Abstract (arXiv)

Work in deep clustering focuses on finding a single partition of data. However, high-dimensional data, such as images, typically feature multiple interesting characteristics one could cluster over. For example, images of objects against a background could be clustered over the shape of the object and separately by the colour of the background. In this paper, we introduce Multi-Facet Clustering Variational Autoencoders (MFCVAE), a novel class of variational autoencoders with a hierarchy of latent variables, each with a Mixture-of-Gaussians prior, that learns multiple clusterings simultaneously, and is trained fully unsupervised and end-to-end. MFCVAE uses a progressively-trained ladder architecture which leads to highly stable performance. We provide novel theoretical results for optimising the ELBO analytically with respect to the categorical variational posterior distribution, correcting earlier influential theoretical work. On image benchmarks, we demonstrate that our approach separates out and clusters over different aspects of the data in a disentangled manner. We also show other advantages of our model: the compositionality of its latent space and that it provides controlled generation of samples.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). Builds on 33 of its 77 references that are in the map. First posted on arXiv 9 Jun 2021.

Builds on

33 of 77 references.

References · 33

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
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  11. 2020NVAE: A Deep Hierarchical Variational Autoencodercited by 635
  12. 2018Disentangling by Factorisingcited by 614
21 more
  1. 2016Ladder Variational Autoencoderscited by 315
  2. 2020Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Imagescited by 261
  3. 2016Towards K-means-friendly Spaces: Simultaneous Deep Learning and Clusteringcited by 237
  4. 2016Variational Deep Embedding: An Unsupervised and Generative Approach to Clusteringcited by 219
  5. 2018Isolating Sources of Disentanglement in Variational Autoencoderscited by 167
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  9. 2017Backpropagation through the Void: Optimizing control variates for black-box gradient estimationcited by 104
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  11. 2020The Hessian Penalty: A Weak Prior for Unsupervised Disentanglementcited by 90
  12. 2018Variational Autoencoders Pursue PCA Directions (by Accident)cited by 84
  13. 2018ClusterGAN : Latent Space Clustering in Generative Adversarial Networkscited by 75
  14. 2019Deep Spectral Clustering using Dual Autoencoder Networkcited by 71
  15. 2018Clustering with Deep Learning: Taxonomy and New Methodscited by 45
  16. 2020Progressive Learning and Disentanglement of Hierarchical Representationscited by 30
  17. 2015Data-dependent Initializations of Convolutional Neural Networkscited by 29
  18. 2017Nonparametric Variational Auto-encoders for Hierarchical Representation Learningcited by 22
  19. 2018Learning Latent Superstructures in Variational Autoencoders for Deep Multidimensional Clusteringcited by 14
  20. 2019Disentangling to Cluster: Gaussian Mixture Variational Ladder Autoencoderscited by 9
  21. 2018Learning Latent Representations in Neural Networks for Clustering through Pseudo Supervision and Graph-based Activity Regularizationcited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 4; 2023: 10; 2024: 6; 2025: 4; 2026: 4.

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  2. 2024On the Origins of Linear Representations in Large Language Modelscited by 76
  3. 2022Identifiability of deep generative models without auxiliary informationcited by 70
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  5. 2023Causal Representation Learning Made Identifiable by Grouping of Observational Variablescited by 30
  6. 2024Learning Interpretable Concepts: Unifying Causal Representation Learning and Foundation Modelscited by 29
  7. 2023Generative learning for nonlinear dynamicscited by 22
  8. 2023Manifold Learning by Mixture Models of VAEs for Inverse Problemscited by 16
  9. 2023A Multi-Resolution Framework for U-Nets with Applications to Hierarchical VAEscited by 9
  10. 2024Identifiable Object-Centric Representation Learning via Probabilistic Slot Attentioncited by 9
  11. 2024The Gaussian Discriminant Variational Autoencoder (GdVAE): A Self-Explainable Model with Counterfactual Explanationscited by 5
  12. 2022Long-horizon video prediction using a dynamic latent hierarchycited by 4
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  1. 2023Learning multi-modal generative models with permutation-invariant encoders and tighter variational objectivescited by 4
  2. 2025Deep Taxonomic Networks for Unsupervised Hierarchical Prototype Discoverycited by 4
  3. 2026PDGMM-VAE: A Variational Autoencoder with Adaptive Per-Dimension Gaussian Mixture Model Priors for Nonlinear ICAcited by 4
  4. 2023A Causal Ordering Prior for Unsupervised Representation Learningcited by 3
  5. 2022Generalized Identifiability Bounds for Mixture Models with Grouped Samplescited by 2
  6. 2023A Prototype-Oriented Clustering for Domain Shift with Source Privacycited by 2
  7. 2024Gaussian Mixture Vector Quantization with Aggregated Categorical Posteriorcited by 2
  8. 2023Causal Dynamic Variational Autoencoder for Counterfactual Regression in Longitudinal Datacited by 1
  9. 2025Estimating Dataset Dimension via Singular Metrics under the Manifold Hypothesis: Application to Inverse Problemscited by 1
  10. 2025Heavy-Tailed Class-Conditional Priors for Long-Tailed Generative Modelingcited by 1
  11. 2022A generative recommender system with GMM prior for cancer drug generation and sensitivity predictioncited by 0
  12. 2024CAVACHON: a hierarchical variational autoencoder to integrate multi-modal single-cell datacited by 0
  13. 2025An Adaptor for Triggering Semi-Supervised Learning to Out-of-Box Serve Deep Image Clusteringcited by 0
  14. 2026Structured Coupling for Flow Matchingcited by 0
  15. 2026PrismQuant: Rate-Distortion-Optimal Vector Quantization for Gaussian-Mixture Sourcescited by 0
  16. 2026Beyond Independence: Learning Correlated Views for Variational Incomplete Multi-View Clusteringcited by 0