Estimating finite mixtures of semi-Markov chains: an application to the segmentation of temporal sensory data

TL;DR

This paper develops statistical models based on finite mixtures of semi-Markov chains to analyze temporal sensory data, enabling the identification of different perception patterns among consumers.

Contribution

It introduces a novel mixture model framework for semi-Markov chains applied to sensory data, with methods for parameter estimation, model selection, and clustering of individual trajectories.

Findings

Successful modeling of sensory perception data with the proposed mixture models

Identification of multiple perception behaviors in Gouda cheese consumers

Validation of the estimation procedure through simulation studies

Abstract

In food science, it is of great interest to get information about the temporal perception of aliments to create new products, to modify existing ones or more generally to understand the perception mechanisms. Temporal Dominance of Sensations (TDS) is a technique to measure temporal perception which consists in choosing sequentially attributes describing a food product over tasting. This work introduces new statistical models based on finite mixtures of semi-Markov chains in order to describe data collected with the TDS protocol, allowing different temporal perceptions for a same product within a population. The identifiability of the parameters of such mixture models is discussed. Sojourn time distributions are fitted with gamma probability distribution and a penalty is added to the log likelihood to ensure convergence of the EM algorithm to a non degenerate solution. Information criterions are employed for determining the number of mixture components. Then, the individual qualitative trajectories are clustered with the help of the maximum a posteriori probability (MAP) approach. A simulation study confirms the good behavior of the proposed estimation procedure. The methodology is illustrated on an example of consumers perception of a Gouda cheese and assesses the existence of several behaviors in terms of perception of this product.