ABSTRACT
This chapter briefly introduces the heat diffusion theory, including heat equation and heat kernel. Heat diffusion models the physical phenomenon of heat transfer and distribution on a surface over time. It is related to partial differential equation (PDE), Brownian motion, and Fourier transform. When applied to different types of data, it has a wide range of applications in multiscale analysis, spectral analysis, probability theory, statistical learning, data mining, financial mathematics, social network, etc. Particularly in computer graphics, it naturally connects key subjects in stochastic differential geometry curvature, spectrum, Brownian motion, and topology.
