Distribution learning focuses on learning the probability density function from a set of data samples. In contrast, clustering aims to group similar objects together in an unsupervised manner. Usually, these two tasks are considered unrelated. However, the relationship between the two may be indirectly correlated, with Gaussian Mixture Models (GMM) acting as a bridge. In this paper, we focus on exploring the correlation between distribution learning and clustering, with the motivation to fill the gap between these two fields, utilizing an autoencoder (AE) to encode images into a high-dimensional latent space. Then, Monte-Carlo Marginalization (MCMarg) and Kullback-Leibler (KL) divergence loss are used to fit the Gaussian components of the GMM and learn the data distribution. Finally, image clustering is achieved through each Gaussian component of GMM. Yet, the "curse of dimensionality" poses severe challenges for most clustering algorithms. Compared with the classic Expectation-Maximization (EM) Algorithm, experimental results show that MCMarg and KL divergence can greatly alleviate the difficulty. Based on the experimental results, we believe distribution learning can exploit the potential of GMM in image clustering within high-dimensional space.

翻译：分布学习旨在从一组数据样本中学习概率密度函数，而聚类则是在无监督方式下将相似对象归为一组。通常这两项任务被认为互不相关，但高斯混合模型（GMM）可能作为桥梁间接关联两者。本文聚焦于探索分布学习与聚类之间的相关性，旨在填补这两个领域间的空白。我们利用自编码器（AE）将图像编码至高维潜在空间，随后采用蒙特卡洛边缘化（MCMarg）和KL散度损失拟合GMM的高斯分量以学习数据分布，最终通过GMM的每个高斯分量实现图像聚类。然而，“维度灾难”对多数聚类算法构成严峻挑战。实验结果表明，与经典期望最大化（EM）算法相比，MCMarg和KL散度能极大缓解这一难题。基于实验结果，我们认为分布学习能挖掘GMM在高维空间中图像聚类的潜力。