Pivot Selection for Median String Problem

The Median String Problem is W[1]-Hard under the Levenshtein distance, thus, approximation heuristics are used. Perturbation-based heuristics have been proved to be very competitive as regards the ratio approximation accuracy/convergence speed. However, the computational burden increase with the size of the set. In this paper, we explore the idea of reducing the size of the problem by selecting a subset of representative elements, i.e. pivots, that are used to compute the approximate median instead of the whole set. We aim to reduce the computation time through a reduction of the problem size while achieving similar approximation accuracy. We explain how we find those pivots and how to compute the median string from them. Results on commonly used test data suggest that our approach can reduce the computational requirements (measured in computed edit distances) by $8$\% with approximation accuracy as good as the state of the art heuristic. This work has been supported in part by CONICYT-PCHA/Doctorado Nacional/$2014-63140074$ through a Ph.D. Scholarship; Universidad Cat\'{o}lica de la Sant\'{i}sima Concepci\'{o}n through the research project DIN-01/2016; European Union's Horizon 2020 under the Marie Sk\l odowska-Curie grant agreement $690941$; Millennium Institute for Foundational Research on Data (IMFD); FONDECYT-CONICYT grant number $1170497$; and for O. Pedreira, Xunta de Galicia/FEDER-UE refs. CSI ED431G/01 and GRC: ED431C 2017/58

New rank methods for reducing the size of the training set using the nearest neighbor rule

Some new rank methods to select the best prototypes from a training set are proposed in this paper in order to establish its size according to an external parameter, while maintaining the classification accuracy. The traditional methods that filter the training set in a classification task like editing or condensing have some rules that apply to the set in order to remove outliers or keep some prototypes that help in the classification. In our approach, new voting methods are proposed to compute the prototype probability and help to classify correctly a new sample. This probability is the key to sorting the training set out, so a relevance factor from 0 to 1 is used to select the best candidates for each class whose accumulated probabilities are less than that parameter. This approach makes it possible to select the number of prototypes necessary to maintain or even increase the classification accuracy. The results obtained in different high dimensional databases show that these methods maintain the final error rate while reducing the size of the training set