Assessing the best edit in perturbation-based iterative refinement algorithms to compute the median string

Abstract

Strings are a natural representation of biological data such as DNA, RNA and protein sequences. The problem of finding a string that summarizes a set of sequences has direct application in relative compression algorithms for genome and proteome analysis, where reference sequences need to be chosen. Median strings have been used as representatives of a set of strings in different domains. However, several formulations of those problems are NP-Complete. Alternatively, heuristic approaches that iteratively refine an initial coarse solution by applying edit operations have been proposed. Recently, we investigated the selection of the optimal edit operations to speed up convergence without spoiling the quality of the approximated median string. We propose a novel algorithm that outperforms state of the art heuristic approximations to the median string in terms of convergence speed by estimating the effect of a perturbation in the minimization of the expressions that define the median strings. We present corpus of comparative experiments to validate these results.

Pivot Selection for Median String Problem

“…We conduct experiments to compare the quality of the approximated median for S obtained using pivots in P respect to the reference algorithm [21] which operates over the whole S. We used the average distance to the median (MAD) as a quality measure and the number of edit distance computed while the algorithms are running as a measure of the speed.…”

“…[1] improved the idea of [2] and achieved more 978-1-7281-5613-2/19/$31.00 ©2019 IEEE solid outcomes, increasing the convergence speed compared with [14] and maintaining the quality of the approximated median. One step further, in [21], the heuristic to select the best edit operation considerate the repercussions of each edition in all strings of the set, improving the ranking of editions. Another approach for the Median String Problem is as a Linear Programming problem, this is the case of [23], which give a lower bound and analyze the cases where the true median cannot be achieved, but do not obtain the median string.…”

“…In this work, we explored how behaves the solution in [21] operating as it is out of the box, i.e. computing the median of S using the whole set, and when is applied to P .…”

“…Algorithm 2 shows our procedure to select pivots. To apply the pivot selection algorithm to the median string problem we propose Algorithm AppMedianStringRepercussion refering to the algorithm proposed in [21]…”

Prototype generation in the string space via approximate median for data reduction in nearest neighbor classification

“…These transformations can be only three possible operations: insertion, deletion, and substitution. Using a similar principle as a basis, the work by Mirabal et al (2019) also considers the different transformations reported by the edit distance and proposes an innovative ranking strategy with which to establish the correct order in which they must be applied. Other research efforts can be found in Kaysar and Khan (2020), in which an approximate version of the median string is computed using Markov chains for DNA motif classification, or in Chakraborty et al (2021), which performs this approximation by resorting to a probabilistic framework based on the so-called Ulam metric.…”