Recursive Diffeomorphism-Based Regression for Shape Functions

Code

• github.com/HaizhaoYang/DeCom
  OfficialIn papernone★ 16

Abstract

This paper proposes a recursive diffeomorphism based regression method for one-dimensional generalized mode decomposition problem that aims at extracting generalized modes _k(t)s_k(2 N_k_k(t)) from their superposition _k=1^K _k(t)s_k(2 N_k_k(t)). First, a one-dimensional synchrosqueezed transform is applied to estimate instantaneous information, e.g., _k(t) and N_k_k(t). Second, a novel approach based on diffeomorphisms and nonparametric regression is proposed to estimate wave shape functions s_k(t). These two methods lead to a framework for the generalized mode decomposition problem under a weak well-separation condition. Numerical examples of synthetic and real data are provided to demonstrate the fruitful applications of these methods.

Tasks

Reproductions