DATE2020-03-19 16:10-17:00


SPEAKER陳志偉 助理教授(中山大學應用數學系

TITLEGeometric Problems in Data Analysis

ABSTRACT Modern differential geometry is a tool designed to find global invariants by doing local computation and overall integration. Our aim is to apply geometric techniques to extract local information of high dimensional data points and reconstruct the global shape in a lower dimensional space as faithful as possible. Indeed, there were lots of embedding maps, including PCA, MDS, LLE, Laplacian eigenmap, to do such dimensionality reduction, but most of them lack theoretical justifications and error estimates. Rigorous geometric analysis would help explaining and improving the performance of these embedding maps.