Electrical Engineering-Systems Dept.

סמינר מחלקתי

You are invited to attend a lecture by

Dr. Alex Bronstein

Electrical Engineering, Tel Aviv University

on the subject:

Multimodal diffusion geometry

The Laplacian operator and related constructions play a pivotal role in a wide range of machine learning and dimensionality reduction applications, which boil down to finding eigenvectors and eigenvalues of a Laplacian constructed on some high-dimensional manifold. Important examples include spectral clustering, eigenmaps and  diffusion maps, and diffusion metrics measuring the ``connectivity'' of points on a manifold. These applications have been considered mostly in the context of uni-modal data, i.e., a single data space. However, many applications involve observations and measurements of data done using different modalities. 

In this talk, I will show how to construct an extension of diffusion geometry to multiple modalities through joint approximate diagonalization of Laplacian matrices. I will provide several synthetic and real examples of manifold learning, dimensionality reduction, and clustering, demonstrating that the joint diffusion geometry better captures the inherent structure of multi-modal data. I will also show several applications in deformable shape analysis.