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

arXiv: https://arxiv.org/abs/1806.04420 · HTML: https://mlsanity.com/paper/1806.04420/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2018.

## Built on by (most cited first, 2 of 2)

- [Deinterleaving of Discrete Renewal Process Mixtures with Application to Electronic Support Measures](https://mlsanity.com/paper/2402.09166/) (2024)
- [Statistical description and dimension reduction of continuous time categorical trajectories with multivariate functional principal components](https://mlsanity.com/paper/2502.09986/) (2025)

## Abstract (arXiv)

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.