[Paper Review] Variational Deep Embedding: A Generative Approach to Clustering.

Zhuxi Jiang, Yin Zheng+3 more|arXiv (Cornell University)|Nov 16, 2016

Generative Adversarial Networks and Image SynthesisComputer Science31 references35 citations

TL;DR

VaDE proposes a variational autoencoder-based generative clustering method that models data generation via a Gaussian Mixture Model (GMM) over latent embeddings, followed by deep neural network decoding. By optimizing the evidence lower bound (ELBO) using stochastic gradient variational Bayes and the reparameterization trick, VaDE achieves state-of-the-art clustering performance across four diverse benchmarks and enables realistic cluster-specific sample generation without supervision.

ABSTRACT

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.

Motivation & Objective

• To develop a unified deep generative model that integrates clustering and representation learning within a variational autoencoder framework.
• To model the data generation process using a Gaussian Mixture Model (GMM) over latent variables, enabling explicit cluster assignment during generation.
• To enable end-to-end training via variational inference using the reparameterization trick and SGVB estimator for scalable optimization.
• To achieve superior clustering performance compared to existing state-of-the-art methods on diverse data modalities.
• To enable unconditional, high-fidelity sample generation conditioned on specific clusters without any labeled data.

Proposed method

• VaDE models data generation as a two-stage process: first, a GMM selects a cluster; second, a deep neural network decodes a latent embedding into observable data.
• The model employs a variational inference framework where a separate deep encoder maps input data to latent embeddings, enabling optimization of the evidence lower bound (ELBO).
• Stochastic Gradient Variational Bayes (SGVB) with the reparameterization trick is used to backpropagate gradients through the stochastic latent variables.
• The ELBO objective is optimized using mini-batch stochastic gradient descent, allowing scalable training on large datasets.
• The framework is extensible, allowing replacement of the GMM with more general mixture models for enhanced modeling flexibility.
• During inference, the trained encoder generates latent codes, and the decoder generates samples conditioned on a chosen cluster.

Experimental results

Research questions

• RQ1 Can a deep generative model that explicitly models cluster assignments via a GMM achieve superior clustering performance compared to existing methods?
• RQ2 To what extent does the variational inference framework with reparameterization enable effective end-to-end training of a deep clustering model?
• RQ3 Can VaDE generate realistic, high-fidelity samples for any specified cluster without using labeled data during training?
• RQ4 How generalizable is the VaDE framework to different data modalities and clustering tasks?
• RQ5 Can the model be extended to use more flexible mixture models beyond the Gaussian Mixture Model?

Key findings

• VaDE significantly outperforms state-of-the-art clustering methods on four diverse benchmarks spanning different data modalities.
• The model achieves state-of-the-art clustering performance, demonstrating superior accuracy and robustness across all evaluated datasets.
• VaDE enables high-quality, realistic sample generation for any specified cluster, even without access to supervised signals during training.
• The generative capability of VaDE is a direct result of its explicit modeling of cluster-specific data generation processes via the GMM.
• The framework is flexible and extensible, allowing integration of more general mixture models beyond the GMM for enhanced modeling capacity.
• The use of the reparameterization trick and SGVB enables stable and efficient optimization of the ELBO objective in the deep generative setting.