  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.
