Final thesis for bachelor's degree in mathematical engineering (Politecnico di Milano, A. Y. 2023/24), supervised by prof. M. Beraha.
Authors: Pietro Masini, Maria Chiara Menicucci.
Our main reference is "An invitation to statistics in Wasserstein space" by V. M. Panaretos and Y. Zemel.
In this thesis we tackle the problem of clustering probability measures in the Wasserstein space. After presenting the necessary background in optimal transport and defining the Wasserstein distance, we introduce the problem of clustering and review two major algorithms used in clustering Euclidean data: K-Means and Expectation-Maximization. Then we show how they can be modified for the purpose of clustering probability measures, focusing on proposing a novel algorithm which extends the EM algorithm to the case of measures. We implement such extensions in Python and compare their performances on simulated datasets, ascertaining that EM performs better than K-Means.