Abstract: In this talk, I will discuss how incorporating geometric information into classical learning algorithms can improve their performance. The main focus will be on optimal mass transport (OMT), which has evolved as a major method to analyze distributional data. In particular, I will show how embeddings can be used to build OMT-based classifiers, both in supervised and unsupervised learning settings. The proposed framework significantly reduces the computational effort and the required training data.
Using OMT and other geometric data analysis tools, I will demonstrate applications in cancer research, focusing on the analysis of gene expression data and on protein dynamics.