Analysis Seminar

DATE2024-05-31 13:30-16:00

PLACE數學系館 3F會議室

SPEAKER吳浩榳(Hau-Tieng Wu)教授(Department of Mathematics Courant Institute of Mathematical Sciences, New York University

TITLEAnalyzing Nonstationary Time Series with Manifold Learning Algorithms

ABSTRACT Compared with snapshot health information, long-term and high-frequency physiological time series provides health information from the other dimension. I will discuss recently developed graph-Laplacian based manifold learning algorithms for such time series. From the clinical aspect, its application to estimating and forecasting airflow signal from thoracic and abdominal respiratory efforts for sleep apnea application will be discussed. From the theoretical aspect, we will discuss some topics toward statistical inference, like L^\infty spectral convergence and local law and rigidity of eigenvalue distribution of graph Laplacian. The current efforts toward including longitudinal data analysis will also be discussed if time permits.