22.01.2024 15:00 Felix Dietrich (TUM):
Improving Nonlinear Canonical Correlation Analysis through Jointly Smooth FunctionsMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

Identifying similarities and constructing joint latent spaces between heterogeneous, multivariate observation data sets is a challenge. Even in case classical canonical correlation analysis (CCA) is not applicable, nonlinear techniques can often successfully uncover the relationship between the observations. I will discuss our research in this direction: a concept that we call "jointly smooth functions". The construction of these functions is fully data-driven, and relies on spectral methods from manifold learning and a Dirichlet energy-based definition of smoothness. I will illustrate the theoretical results on simple examples, discuss our efficient implementation, and show improvements over existing nonparametric and kernel CCA techniques for real physiological signals in sleep stage identification, the construction of effective parameters in dynamical systems, and positional alignment from different video camera feeds of a race track. Related paper (SIAM Journal on Mathematics of Data Science, Vol. 4, Iss. 1 (2022)): https://doi.org/10.1137/21M141590X