Abstract:

We discuss recent developments in the study of data sets embedded in high dimensional space by studying diffusion processes (random walks) on them. Connections with Fourier Analysis (corresponding to large time behavior of such processes), wavelets (multi-scale/time behavior) and kernel smoothing allow to view these developments as a generalization of notions classical in signal processing to graphs and data sets in high-dimensional space. We will discuss applications to dimensionality reduction and machine learning.