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In food science, it is of great interest to get information about thetemporal perception of aliments to create new products, to modify existing onesor more generally to understand the perception mechanisms. Temporal Dominanceof Sensations (TDS) is a technique to measure temporal perception whichconsists in choosing sequentially attributes describing a food product overtasting. This work introduces new statistical models based on finite mixturesof semi-Markov chains in order to describe data collected with the TDSprotocol, allowing different temporal perceptions for a same product within apopulation. The identifiability of the parameters of such mixture models isdiscussed. Sojourn time distributions are fitted with gamma probabilitydistribution and a penalty is added to the log likelihood to ensure convergenceof the EM algorithm to a non degenerate solution. Information criterions areemployed for determining the number of mixture components. Then, the individualqualitative trajectories are clustered with the help of the maximum aposteriori probability (MAP) approach. A simulation study confirms the goodbehavior of the proposed estimation procedure. The methodology is illustratedon an example of consumers perception of a Gouda cheese and assesses theexistence of several behaviors in terms of perception of this product.

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