Notes

Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami operator on a manifold , and the connections to the heat equation , we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold...

Research notes on DISCRETE DIFFERENTIAL GEOMETRY: AN APPLIED INTRODUCTION.

Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant body of theory that bridges two...

Research notes on CS168: The Modern Algorithmic Toolbox Lectures #11: Spectral Graph Theory, I.

The Hopf fibration is an important object in mathematics and physics. A landmark discovery in topology and a fundamental object in the theory of Lie groups, the Hopf fibration has a wide variety of physical applications including magnetic monopoles, rigid body mechanics, and...