Building meaningful representations for nonlinear modeling of 1d- and 2d-signals: applications to biomedical signals

Abstract The paper addresses two problems that are frequently encountered when modeling data by linear combinations of nonlinear parameterized functions. The first problem is feature selection, when features are sought as functions that are nonlinear in their parameters (e.g. Gaussians with adjustable centers and widths, wavelets with adjustable translations and dilations, etc.). The second problem is the design of an intelligible representation for 1D- and 2D- signals with peaks and troughs that have a definite meaning for experts. To address the first problem, a generalization of the orthogonal forward regression method is described. To address the second problem, a new family of nonlinear parameterized functions, termed Gaussian mesa functions, is defined. It allows the modeling of signals such that each significant peak or trough is modeled by a single, identifiable function. The resulting representation is sparse in terms of adjustable parameters, thereby lending itself easily to automatic analysis and classification, yet it is readily intelligible for the expert. An application of the methodology to the automatic analysis of electrocardiographic (Holter) recordings is described. Applications to the analysis of neurophysiological signals and EEG signals (early detection of Alzheimer's disease) are outlined.