# Variational Deep Embedding: An Unsupervised and Generative Approach to Clustering

arXiv: https://arxiv.org/abs/1611.05148 · HTML: https://mlsanity.com/paper/1611.05148/

## Key facts

- Cited by 220 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2016.

## Built on by (most cited first, 30 of 220)

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- [A Comprehensive Survey on Deep Clustering: Taxonomy, Challenges, and Future Directions](https://mlsanity.com/paper/2206.07579/) (2022)
- [Identifiability of deep generative models without auxiliary information](https://mlsanity.com/paper/2206.10044/) (2022)
- [Clustering-friendly Representation Learning via Instance Discrimination and Feature Decorrelation](https://mlsanity.com/paper/2106.00131/) (2021)
- [Verifying the Union of Manifolds Hypothesis for Image Data](https://mlsanity.com/paper/2207.02862/) (2022)
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- [Multi-VAE: Learning Disentangled View-common and View-peculiar Visual Representations for Multi-view Clustering](https://mlsanity.com/paper/2106.11232/) (2021)
- [MiCE: Mixture of Contrastive Experts for Unsupervised Image Clustering](https://mlsanity.com/paper/2105.01899/) (2021)
- [You Never Cluster Alone](https://mlsanity.com/paper/2106.01908/) (2021)
- [Causal Representation Learning Made Identifiable by Grouping of Observational Variables](https://mlsanity.com/paper/2310.15709/) (2023)
- [Pseudo-supervised Deep Subspace Clustering](https://mlsanity.com/paper/2104.03531/) (2021)
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- [A Deep Variational Approach to Clustering Survival Data](https://mlsanity.com/paper/2106.05763/) (2021)
- [Clustering by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/2107.11635/) (2021)
- [Congestion-aware Multi-agent Trajectory Prediction for Collision Avoidance](https://mlsanity.com/paper/2103.14231/) (2021)
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- [Deep Bayesian Unsupervised Lifelong Learning](https://mlsanity.com/paper/2106.07035/) (2021)
- [CGC: Contrastive Graph Clustering for Community Detection and Tracking](https://mlsanity.com/paper/2204.08504/) (2022)
- [Interpretable Deep Clustering for Tabular Data](https://mlsanity.com/paper/2306.04785/) (2023)
- [Towards Accurate and Compact Architectures via Neural Architecture Transformer](https://mlsanity.com/paper/2102.10301/) (2021)
- [Manifold Learning by Mixture Models of VAEs for Inverse Problems](https://mlsanity.com/paper/2303.15244/) (2023)
- [SCALE: Online Self-Supervised Lifelong Learning without Prior Knowledge](https://mlsanity.com/paper/2208.11266/) (2022)
- [A Framework for Deep Constrained Clustering](https://mlsanity.com/paper/2101.02792/) (2021)
- [Deep Conditional Gaussian Mixture Model for Constrained Clustering](https://mlsanity.com/paper/2106.06385/) (2021)
- [Strongly Augmented Contrastive Clustering](https://mlsanity.com/paper/2206.00380/) (2022)

## Abstract (arXiv)

Clustering is among the most fundamental tasks in computer vision and machine learning. In this paper, we propose Variational Deep Embedding (VaDE), a novel unsupervised generative clustering approach within the framework of Variational Auto-Encoder (VAE). Specifically, VaDE models the data generative procedure with a Gaussian Mixture Model (GMM) and a deep neural network (DNN): 1) the GMM picks a cluster; 2) from which a latent embedding is generated; 3) then the DNN decodes the latent embedding into observables. Inference in VaDE is done in a variational way: a different DNN is used to encode observables to latent embeddings, so that the evidence lower bound (ELBO) can be optimized using Stochastic Gradient Variational Bayes (SGVB) estimator and the reparameterization trick. Quantitative comparisons with strong baselines are included in this paper, and experimental results show that VaDE significantly outperforms the state-of-the-art clustering methods on 4 benchmarks from various modalities. Moreover, by VaDE's generative nature, we show its capability of generating highly realistic samples for any specified cluster, without using supervised information during training. Lastly, VaDE is a flexible and extensible framework for unsupervised generative clustering, more general mixture models than GMM can be easily plugged in.