Computing a T-transitive lower approximation or opening of a proximity relation

Fuzzy Sets and Systems. IMPACT FACTOR: 1,181. Fuzzy Sets and Systems. IMPACT FACTOR: 1,181. Since transitivity is quite often violated even by decision makers that accept transitivity in their preferences as a condition for consistency, a standard approach to deal with intransitive preference elicitations is the search for a close enough transitive preference relation, assuming that such a violation is mainly due to decision maker estimation errors. In some way, the more number of elicitations, the more probable inconsistency is. This is mostly the case within a fuzzy framework, even when the number of alternatives or object to be classified is relatively small. In this paper we propose a fast method to compute a T-indistinguishability from a reflexive and symmetric fuzzy relation, being T any left-continuous t-norm. The computed approximation we propose will take O(n3) time complexity, where n is the number of elements under consideration, and is expected to produce a T-transitive opening. To the authors¿ knowledge, there are no other proposed algorithm that computes T-transitive lower approximations or openings while preserving the reflexivity and symmetry properties

An algorithm to compute the transitive closure, a transitive approximation and a transitive opening of a fuzzy proximity

A method to compute the transitive closure, a transitive opening and a transitive approximation of a reflexive and symmetric fuzzy relation is given. Other previous methods in literature compute just the transitive closure, some transitive approximations or some transitive openings. The proposed algorithm computes the three different similarities that approximate a proximity for the computational cost of computing just one. The shape of the binary partition tree for the three output similarities are the same.Peer ReviewedPostprint (published version

Advances in Big Data Analytics: Algorithmic Stability and Data Cleansing

Analysis of what has come to be called “big data” presents a number of challenges as data continues to grow in size, complexity and heterogeneity. To help addresses these challenges, we study a pair of foundational issues in algorithmic stability (robustness and tuning), with application to clustering in high-throughput computational biology, and an issue in data cleansing (outlier detection), with application to pre-processing in streaming meteorological measurement. These issues highlight major ongoing research aspects of modern big data analytics. First, a new metric, robustness, is proposed in the setting of biological data clustering to measure an algorithm’s tendency to maintain output coherence over a range of parameter settings. It is well known that different algorithms tend to produce different clusters, and that the choice of algorithm is often driven by factors such as data size and type, similarity measure(s) employed, and the sort of clusters desired. Even within the context of a single algorithm, clusters often vary drastically depending on parameter settings. Empirical comparisons performed over a variety of algorithms and settings show highly differential performance on transcriptomic data and demonstrate that many popular methods actually perform poorly. Second, tuning strategies are studied for maximizing biological fidelity when using the well-known paraclique algorithm. Three initialization strategies are compared, using ontological enrichment as a proxy for cluster quality. Although extant paraclique codes begin by simply employing the first maximum clique found, results indicate that by generating all maximum cliques and then choosing one of highest average edge weight, one can produce a small but statistically significant expected improvement in overall cluster quality. Third, a novel outlier detection method is described that helps cleanse data by combining Pearson correlation coefficients, K-means clustering, and Singular Spectrum Analysis in a coherent framework that detects instrument failures and extreme weather events in Atmospheric Radiation Measurement sensor data. The framework is tested and found to produce more accurate results than do traditional approaches that rely on a hand-annotated database

Trading the stock market : hybrid financial analyses and evolutionary computation

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Informática, Departamento de Arquitectura de Computadores y Automática, leída el 02-07-2014Esta tesis presenta la implementación de un innovador sistema de comercio automatizado que utiliza tres importantes análisis para determinar lugares y momentos de inversión. Para ello, este trabajo profundiza en sistemas automáticos de comercio y estudia series temporales de precios históricos pertenecientes a empresas que cotizan en el mercado bursátil. Estudiamos y clasifcamos las series temporales mediante el uso de una novedosa metodología basada en compresores de software. Este nuevo enfoque permite un estudio teórico de la formación de precios que demuestra resultados de divergencia entre precios reales de mercado y precios modelados mediante paseos aleatorios, apoyando así el desarrollo de modelos predictivos basados en el análisis de patrones históricos como los descritos en este documento. Además, esta metodología nos permite estudiar el comportamiento de series temporales de precios históricos en distintos sectores industriales mediante la búsqueda de patrones en empresas pertenecientes al mismo sector. Los resultados muestran agrupaciones que indican tendencias de mercado compartidas y ,por tanto, señalan que la inclusión de un análisis industrial puede reportar ventajas en la toma de decisiones de inversión. Comprobada la factibilidad de un sistema de predicción basado en series temporales y demostrada la existencia de tendencias macroeconómicas en las diferentes industrias, proponemos el desarrollo del sistema completo a través de diferentes etapas. Iterativamente y mediante varias aproximaciones, testeamos y analizamos las piezas que componen el sistema nal. Las primeras fases describen un sistema de comercio automatizado, basado en análisis técnico y fundamental de empresas, que presenta altos rendimientos y reduce el riesgo de pérdidas. El sistema utiliza un motor de optimización guiado por una versión modi cada de un algoritmo genético el la que presentamos operadores innovadores que proporcionan mecanismos para evitar una convergencia prematura del algoritmo y mejorar los resultados de rendimiento nales. Utilizando este mismo sistema de comercio automático proponemos técnicas de optimización novedosas en relación a uno de los problemas más característicos de estos sistemas, el tiempo de ejecución. Presentamos la paralelización del sistema de comercio automatizado mediante dos técnicas de computación paralela, computación distribuida y procesamiento grá co. Ambas arquitecturas presentan aceleraciones elevadas alcanzando los x50 y x256 respectivamente. Estápas posteriores presentan un cambio de metodologia de optimización, algoritmos genéticos por evolución gramatical, que nos permite comparar ambas estrategias e implementar características más avanzadas como reglas más complejas o la auto-generación de nuevos indicadores técnicos. Testearemos, con datos nancieros recientes, varios sistemas de comercio basados en diferentes funciones de aptitud, incluyendo una innovadora versión multi-objetivo, que nos permitirán analizar las ventajas de cada función de aptitud. Finalmente, describimos y testeamos la metodología del sistema de comercio automatizado basado en una doble capa de gramáticas evolutivas y que combina un análisis técnico, fundamental y macroeconómico en un análisis top-down híbrido. Los resultados obtenidos muestran rendimientos medios del 30% con muy pocas operaciones de perdidas.This thesis concerns to the implementation of a complex and pioneering automated trading system which uses three critical analysis to determine time-decisions and portfolios for investments. To this end, this work delves into automated trading systems and studies time series of historical prices related to companies listed in stock markets. Time series are studied using a novel methodology based on clusterings by software compressors. This new approach allows a theoretical study of price formation which shows results of divergence between market prices and prices modelled by random walks, thus supporting the implementation of predictive models based on the analysis of historical patterns. Furthermore, this methodology also provides us the tool to study behaviours of time series of historical prices from di erent industrial sectors seeking patterns among companies in the same industry. Results show clusters of companies pointing out market trends among companies developing similar activities, and suggesting a macroeconomic analysis to take advantage of investment decisions. Tested the feasibility of prediction systems based on analyses related to time series of historical prices and tested the existence of macroeconomic trends in the industries, we propose the implementation of a hybrid automated trading system through several stages which iteratively describe and test the components of the nal system. In the early stages, we implement an automated trading system based on technical and fundamental analysis of companies, it presents high returns and reducing losses. The implementation uses a methodology guided by a modi ed version of a genetic algorithm which presents novel genetic operators avoiding the premature convergence and improving nal results. Using the same automated trading system we propose novel optimization techniques related to one of the characteristic problems of these systems: the execution time. We present the parallelisation of the system using two parallel computing techniques, rst using distributed computation and, second, implementing a version for graphics processors. Both architectures achieve high speed-ups, reaching 50x and 256x respectively, thus, they present the necessary speed-ups required by systems analysing huge amount of nancial data. Subsequent stages present a transformation in the methodology, genetic algorithms for grammatical evolution, which allows us to compare the two evolutionary strategies and to implement more advanced features such as more complex rules or the self-generation of new technical indicators. In this context, we describe several automated trading system versions guided by di erent tness functions, including an innovative multi-objective version that we test with recent nancial data analysing the advantages of each tness function. Finally, we describe and test the methodology of an automated trading system based on a double layer of grammatical evolution combining technical, fundamental and macroeconomic analysis on a hybrid topdown analysis. The results show average returns of 30% with low number of negative operations.Depto. de Arquitectura de Computadores y AutomáticaFac. de InformáticaTRUEunpu