  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.
