Codes and Expansions (CodEx) Seminar

Hrushikesh Mhaskar (Claremont Graduate University)
Local analysis of global data

For a periodic integrable function \(f\), the definition of Fourier coefficients requires the values of \(f\) on the entire period. We refer to such data as “global” data. Even though the sequence of Fourier coefficients determines \(f\) uniquely, they do not reveal by themselves local features such as the locations of discontinuities of \(f\) (whose definition requires the values of \(f\) locally near the point of discontinuity). We will describe our work for extracting such local features from global data. We will discuss some modern applications such as the separation of blind source signals, and machine learning problems, classification and regression in particular.