Estimating finite mixtures of semi-Markov chains: an application to the segmentation of temporal sensory data
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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. A penalty is added to the log likelihood to ensure numerical stability and consistency of the EM algorithm used to fit the parameters. The BIC criterion is employed for determining the number of mixture components. Then, the individual qualitative trajectories are clustered by considering the MAP criterion. 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.
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