A probabilistic approach to melodic similarity

Melodic similarity is an important research topic in music information retrieval. The representation of symbolic music by means of trees has proven to be suitable in melodic similarity computation, because they are able to code rhythm in their structure leaving only pitch representations as a degree of freedom for coding. In order to compare trees, different edit distances have been previously used. In this paper, stochastic k-testable tree-models, formerly used in other domains like structured document compression or natural language processing, have been used for computing a similarity measure between melody trees as a probability and their performance has been compared to a classical tree edit distance.This work is supported by the Spanish Ministry projects: DPI2006-15542-C04, TIN2006-14932-C02, both partially supported by EU ERDF, the Consolider Ingenio 2010 research programme (project MIPRCV, CSD2007-00018) and the Pascal Network of Excellence

Grammatical inference of directed acyclic graph languages with polynomial time complexity

[EN] In this paper we study the learning of graph languages. We extend the well-known classes of k-testability and k-testability in the strict sense languages to directed graph languages. We propose a grammatical inference algorithm to learn the class of directed acyclic k- testable in the strict sense graph languages. The algorithm runs in polynomial time and identifies this class of languages from positive data. We study its efficiency under several criteria, and perform a comprehensive experimentation with four datasets to show the validity of the method. Many fields, from pattern recognition to data compression, can take advantage of these results.Gallego, A.; López Rodríguez, D.; Calera-Rubio, J. (2018). Grammatical inference of directed acyclic graph languages with polynomial time complexity. Journal of Computer and System Sciences. 95:19-34. https://doi.org/10.1016/j.jcss.2017.12.002S19349

Recognizable tree series with discounting

We consider weighted tree automata with discounting over commutative semirings. For their behaviors we establish a Kleene theorem and an MSO-logic characterization. We introduce also weighted Muller tree automata with discounting over the max-plus and the min-plus semirings, and we show their expressive equivalence with two fragments of weighted MSO-sentences

Sublinear Computation Paradigm

This open access book gives an overview of cutting-edge work on a new paradigm called the “sublinear computation paradigm,” which was proposed in the large multiyear academic research project “Foundations of Innovative Algorithms for Big Data.” That project ran from October 2014 to March 2020, in Japan. To handle the unprecedented explosion of big data sets in research, industry, and other areas of society, there is an urgent need to develop novel methods and approaches for big data analysis. To meet this need, innovative changes in algorithm theory for big data are being pursued. For example, polynomial-time algorithms have thus far been regarded as “fast,” but if a quadratic-time algorithm is applied to a petabyte-scale or larger big data set, problems are encountered in terms of computational resources or running time. To deal with this critical computational and algorithmic bottleneck, linear, sublinear, and constant time algorithms are required. The sublinear computation paradigm is proposed here in order to support innovation in the big data era. A foundation of innovative algorithms has been created by developing computational procedures, data structures, and modelling techniques for big data. The project is organized into three teams that focus on sublinear algorithms, sublinear data structures, and sublinear modelling. The work has provided high-level academic research results of strong computational and algorithmic interest, which are presented in this book. The book consists of five parts: Part I, which consists of a single chapter on the concept of the sublinear computation paradigm; Parts II, III, and IV review results on sublinear algorithms, sublinear data structures, and sublinear modelling, respectively; Part V presents application results. The information presented here will inspire the researchers who work in the field of modern algorithms