Andrea Bertozzi | University of California
Geometric Graph-Based Methods for High Dimensional Data
High dimensional data can be organized on a similarity graph - an undirected graph with edge weights that measure the similarity between data assigned to nodes. We consider problems in semi-supervised and unsupervised machine learning that are formulated as penalized graph cut problems. There are a wide range of problems including Cheeger cuts, modularity optimization on networks, and semi-supervised learning. We show a parallel between these modern problems and classical minimal surface problems in Euclidean space.
This analogy allows us to develop a suite of new algorithms for machine learning that are both very fast and highly accurate. These are analogues of well-known pseudo-spectral methods for partial differential equations.