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Idempotent copulas with fractal support

Idempotent copulas with fractal support

引用

14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012

作者： Trutschnig, Wolfgang Research Unit for Intelligent Data Analysis and Graphical Els European Centre for Soft Computing Edificio de Investigación Calle Gonzalo Gutiérrez Quirós S/N 33600 Mieres Asturias Spain

ISBN: (纸本)9783642317149

In [7] Fredricks et al. showed that certain Iterated Function Systems (IFS) can be used to construct copulas with fractal support. Since, firstly, the same construction also works with respect to the D 1-metric on the space of copulas which is much stronger than the uniform metric and, secondly, the star product of copulas is (jointly) continuous with respect to this metric the IFS approach can also be used to construct idempotent copulas with fractal support. The main result of the paper is that for each open interval Iisin[1,2] there exists an idempotent copula A such that the Hausdorff dimension of the support of A is contained in the interval I. © 2012 Springer-Verlag Berlin Heidelberg.

关键词： Information management

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Computational Intelligence 1

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丛书名： Texts in Computer Science

1000年

作者： Rudolf Kruse Christian Moewes Pascal Held Christian Borgelt Frank Klawonn Matthias Steinbrecher

ISBN: (数字)9781447150138

ISBN: (纸本)9781447158493

This clearly-structured, classroom-tested textbook/reference presents a methodical introduction to the field of CI. Providing an authoritative insight into all that is necessary for the successful application of CI methods, the book describes fundamental concepts and their practical implementations, and explains the theoretical background underpinning proposed solutions to common problems. Only a basic knowledge of mathematics is required. Features: provides electronic supplementary material at an associated website, including module descriptions, lecture slides, exercises with solutions, and software tools; contains numerous examples and definitions throughout the text; presents self-contained discussions on artificial neural networks, evolutionary algorithms, fuzzy systems and Bayesian networks; covers the latest approaches, including ant colony optimization and probabilistic graphical models; written by a team of highly-regarded experts in CI, with extensive experience in both academia and industry.

关键词： Artificial Intelligence Mathematical and Computational Engineering

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Guide to intelligent data analysis 1

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丛书名： Texts in Computer Science

1000年

作者： Michael R. Berthold Christian Borgelt Frank Höppner Frank Klawonn

ISBN: (数字)9781848822603

ISBN: (纸本)9781447125723

Each passing year bears witness to the development of ever more powerful computers, increasingly fast and cheap storage media, and even higher bandwidth data connections. This makes it easy to believe that we can now – at least in principle – solve any problem we are faced with so long as we only have enough data. Yet this is not the case. Although large databases allow us to retrieve many different single pieces of information and to compute simple aggregations, general patterns and regularities often go undetected. Furthermore, it is exactly these patterns, regularities and trends that are often most valuable. To avoid the danger of “drowning in information, but starving for knowledge” the branch of research known as data analysis has emerged, and a considerable number of methods and software tools have been developed. However, it is not these tools alone but the intelligent application of human intuition in combination with computational power, of sound background knowledge with computer-aided modeling, and of critical reflection with convenient automatic model construction, that results in successful intelligent data analysis projects. Guide to intelligent data analysis provides a hands-on instructional approach to many basic data analysis techniques, and explains how these are used to solve data analysis problems. Topics and features: guides the reader through the process of data analysis, following the interdependent steps of project understanding, data understanding, data preparation, modeling, and deployment and monitoring; equips the reader with the necessary information in order to obtain hands-on experience of the topics under discussion; provides a review of the basics of classical statistics that support and justify many data analysis methods, and a glossary of statistical terms; includes numerous examples using R and KNIME, together with appendices introducing the open source software; integrates illustrations and case-study-style examplesto suppo

关键词： Artificial Intelligence

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