Using Continuum Limits To Understand Data Clustering And Classification

Tuesday, September 15, 2020 - 9:30am - 10:15am
Franca Hoffmann (California Institute of Technology)
Graph Laplacians encode geometric information contained in data, via the eigenfunctions associated with their small eigenvalues. These spectral properties provide powerful tools in data clustering and data classification. When a large number of data points are available one may consider continuum limits of the graph Laplacian, both to give insight and, potentially, as the basis for numerical methods. We summarize recent insights into the properties of a family of weighted elliptic operators arising in the large data limit of different graph Laplacian normalizations, and propose an inverse problem formalism for continuous semi-supervised learning algorithms, making use of these differential operators. This is joint work with Bamdad Hosseini (Caltech), Assad A. Oberai (USC) and Andrew M. Stuart (Caltech).