Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. Traditionally, this involves using dimensionality reduction methods to project data onto interpretable spaces or organizing points into meaningful clusters. In practice, these methods are used sequentially, without guaranteeing that the clustering aligns well with the conducted dimensionality reduction. In this work, we offer a fresh perspective: that of distributions. Leveraging tools from optimal transport, particularly the Gromov-Wasserstein distance, we unify clustering and dimensionality reduction into a single framework called distributional reduction. This allows us to jointly address clustering and dimensionality reduction with a single optimization problem. Through comprehensive experiments, we highlight the versatility and interpretability of our method and show that it outperforms existing approaches across a variety of image and genomics datasets.

These days we hear about machine learning and artificial intelligence (AI) in all aspects of life. We see machines that learn and imitate the human brain in order to automate human processes. There are autonomous cars that learn the road conditions to drive, personal assistants we can converse with and machines that can predict what stock markets will do. In some respects, it can appear as "magic." Behind machine learning there are some fundamental, well-studied and understood techniques.