An iterative warping and clustering algorithm to estimate multiple wave-shape functions from a nonstationary oscillatory signal

TL;DR

This paper introduces an innovative iterative warping and clustering algorithm designed to estimate multiple wave-shape functions from nonstationary oscillatory signals, effectively capturing sudden changes and variations in real-world signals.

Contribution

The paper presents a novel combination of time-frequency analysis, SVD entropy, and spectral clustering for wave-shape estimation in nonstationary signals with change points.

Findings

Algorithm accurately estimates multiple wave-shape functions.

Effective in analyzing real signals like ECG and blood pressure.

Mathematically justified under slow-varying amplitude and frequency assumptions.

Abstract

Nonsinusoidal oscillatory signals are everywhere. In practice, the nonsinusoidal oscillatory pattern, modeled as a 1-periodic wave-shape function (WSF), might vary from cycle to cycle. When there are finite different WSFs, $s_1,\ldots,s_K$, so that the WSF jumps from one to another suddenly, the different WSFs and jumps encode useful information. We present an iterative warping and clustering algorithm to estimate $s_1,\ldots,s_K$ from a nonstationary oscillatory signal with time-varying amplitude and frequency, and hence the change points of the WSFs. The algorithm is a novel combination of time-frequency analysis, singular value decomposition entropy and vector spectral clustering. We demonstrate the efficiency of the proposed algorithm with simulated and real signals, including the voice signal, arterial blood pressure, electrocardiogram and accelerometer signal. Moreover, we provide a mathematical justification of the algorithm under the assumption that the amplitude and frequency of the signal are slowly time-varying and there are finite change points that model sudden changes from one wave-shape function to another one.