Parameterization of state duration in Hidden semi-Markov Models: an application in electrocardiography

TL;DR

This paper introduces a parametric Hidden semi-Markov Model for time series classification, focusing on efficient state duration representation, and demonstrates its application in electrocardiography for heartbeat classification.

Contribution

It proposes a novel parametric model for state durations in Hidden semi-Markov Models, using maximum likelihood estimation and comparing discrete versus Gamma distribution representations.

Findings

Gamma distribution effectively models state durations with fewer parameters.

Discrete duration distribution requires more data to estimate accurately.

Application on heartbeat data highlights strengths and weaknesses of each approach.

Abstract

This work aims at providing a new model for time series classification based on learning from just one example. We assume that time series can be well characterized as a parametric random process, a sort of Hidden semi-Markov Model representing a sequence of regression models with variable duration. We introduce a parametric stochastic model for time series pattern recognition and provide a maximum-likelihood estimation of its parameters. Particularly, we are interested in examining two different representations for state duration: i) a discrete density distribution requiring an estimate for each possible duration; and ii) a parametric family of continuous density functions, here the Gamma distribution, with just two parameters to estimate. An application on heartbeat classification reveals the main strengths and weaknesses of each alternative.