Functional Supervised Classification With Wavelets
Year: 2008
Type: article
Abstract: \n Let X be a random variable taking values in a Hilbert space and let Y be a random label with values in {0, 1}. Given a collection of classification rules and a learning sample of independent copies of the pair (X, Y ), it is shown how to select optimally and consistently a classifier. As a general strategy, the learning sample observations are first expanded on a wavelet basis and the overall infinite dimension is reduced to a finite one via a suitable data-dependent thresholding. Then, a finite-dimensional classification rule is performed on the non-zero coefficients. Both the dimension and the classifier are automatically selected by data-splitting and empirical risk minimization. Applications of this technique to a signal discrimination problem involving speech recordings and simulated data are presented.\n
Source: HAL
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2306171568