Optimal matching

Optimal matching is a sequence analysis method used in social science, to assess the dissimilarity of ordered arrays of tokens that usually represent a time-ordered sequence of socio-economic states two individuals have experienced. Once such distances have been calculated for a set of observations (e.g. individuals in a cohort) classical tools (such as cluster analysis) can be used. The method was tailored to social sciences from a technique originally introduced to study molecular biology (protein or genetic) sequences (see sequence alignment). Optimal matching uses the Needleman-Wunsch algorithm.

Let ${\displaystyle S=(s_{1},s_{2},s_{3},\ldots s_{T})}$ be a sequence of states ${\displaystyle s_{i}}$ belonging to a finite set of possible states. Let us denote ${\displaystyle {\mathbf {S} }}$ the sequence space, i.e. the set of all possible sequences of states.

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