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In this paper we consider the problem of segmenting $n$ aligned randomsequences of equal length $m$, into a finite number of independent blocks. Wepropose to use a penalized maximum likelihood criterion to infer simultaneouslythe number of points of independence as well as the position of each one ofthese points. We show how to compute the estimator efficiently by means of adynamic programming algorithm with time complexity $O(m^2n)$. We also proposeanother algorithm, called hierarchical algorithm, that provides anapproximation to the estimator when the sample size increases and runs in time$O(mn)$. Our main theoretical result is the proof of almost sure consistency ofthe estimator and the convergence of the hierarchical algorithm when the samplesize $n$ grows to infinity. We illustrate the convergence of these algorithmsthrough some simulation examples and we apply the method to a real proteinsequence alignment of Ebola Virus.

A model selection approach for multiple sequence segmentation and dimensionality reduction