Nicolas Chopin , ENSAE, Institut Polytechnique de Paris, France
Function systems are widely used in mathematics to adress various questions like approximation, compressing and denoising of functions. Famous examples are the Fourier basis and wavelets which are known to be a powerful tool. There exist wavelets for various domains like R, R^d, the sphere and even more general spaces.
In this talk we consider the case when we do not know the domain (we only assume the domain to be some Euclidean submanifold), but have only access to a finite number of randomly chosen points. We propose a method to construct a system of functions (vectors) that behave similar to wavelets. This approach is based on the graph representation of the given data points. We have a look at some properties of this function system and how it can be applied to some statistical problems.
Zoom link on request