Mixture Models for the Analysis, Edition, and Synthesis of Continuous Time Series

TL;DR

This chapter reviews mixture model techniques for analyzing, editing, and synthesizing continuous time series, especially motion data, by decomposing signals into basis functions from diverse research fields.

Contribution

It provides a comprehensive overview of mixture models for time series, highlighting various basis functions and their applications across multiple disciplines.

Findings

Effective decomposition of signals into basis functions

Application examples with radial, Bernstein, Fourier bases

Source codes provided for practical understanding

Abstract

This chapter presents an overview of techniques used for the analysis, edition, and synthesis of time series, with a particular emphasis on motion data. The use of mixture models allows the decomposition of time signals as a superposition of basis functions. It provides a compact representation that aims at keeping the essential characteristics of the signals. Various types of basis functions have been proposed, with developments originating from different fields of research, including computer graphics, human motion science, robotics, control, and neuroscience. Examples of applications with radial, Bernstein and Fourier basis functions will be presented, with associated source codes to get familiar with these techniques.