Clustering categorical sequences is a problem that arises in many fields. There is a few techniques available in this framework but none of them take into account the possible temporal character of transitions from one state to another. A mixture of Markov models is proposed, where transition probabilities are represented as functions of time. The corresponding expectation–maximization algorithm is discussed along with related computational challenges. The effectiveness of the proposed procedure is illustrated on the set of simulation studies, in which it outperforms four alternative approaches. The method is applied to major life event sequences from the British Household Panel Survey. As reflected by Bayesian Information Criterion, the proposed model demonstrates substantially better performance than its competitors. The analysis of obtained results and related transition probability plots reveals two groups of individuals: people with a conventional development of life course and those encountering some challenges.

中文翻译：

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基于时间的分类序列的基于模型的聚类及其在主要生命事件模式分析中的应用

对分类序列进行聚类是许多领域中出现的问题。在此框架中有几种可用的技术，但是它们都没有考虑到从一种状态到另一种状态的过渡的可能时间特性。提出了混合的马尔可夫模型，其中转移概率表示为时间的函数。讨论了相应的期望最大化算法以及相关的计算挑战。一组模拟研究表明了所提出程序的有效性，其效果优于四种替代方法。该方法适用于英国家庭面板调查中的主要生命事件序列。正如贝叶斯信息准则所反映的那样，所提出的模型显示出比其竞争对手更好的性能。