The Experts below are selected from a list of 279 Experts worldwide ranked by ideXlab platform
George A Anastassiou - One of the best experts on this subject based on the ideXlab platform.
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FUZZY-RANDOM NEURAL NETWORK APPROXIMATION OPERATORS, Univariate Case
Fuzzy Mathematics: Approximation Theory, 2010Co-Authors: George A AnastassiouAbstract:In this chapter we study the rate of pointwise convergence in the q-mean to the Fuzzy-Random unit operator of very precise Univariate Fuzzy-Random neural network operators of Cardaliaguet. Euvrard and “Squashing” types. These Fuzzy-Random operators arise in a natural and common way among Fuzzy-Random neural networks. These rates are given through Probabilistic-Jackson type inequalities involving the Fuzzy-Random modulus of continuity of the engaged Fuzzy-Random function or its Fuzzy derivatives. Also several interesting results in Fuzzy-Random Analysis are given of independent merit, which are used then in the proofs of the main results of the chapter. This chapter follows [17].
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DEGREE OF APPROXIMATION OF FUZZY NEURAL NETWORK OPERATORS, Univariate Case
Fuzzy Mathematics: Approximation Theory, 2010Co-Authors: George A AnastassiouAbstract:In this chapter we study the rate of convergence to the unit operator of very specific well described Univariate Fuzzy neural network operators of Cardaliaguet–Euvrard and “Squashing” types. These Fuzzy operators arise in a very natural and common way among Fuzzy neural networks. The rates are given through Jackson type inequalities involving the Fuzzy modulus of continuity of the engaged Fuzzy valued function or its derivative in the Fuzzy sense. Also several interesting results in Fuzzy real analysis are presented to be used in the proofs of the main results. This chapter is based on [11].
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Partial shape preserving approximations by bivariate shepard operators
Computers & Mathematics with Applications, 2001Co-Authors: George A Anastassiou, Sorin G. GalAbstract:Abstract Extending the results from the Univariate Case in a paper by Gal and Szabados, in this paper, we prove that the bivariate Shepard interpolation operators preserve the monotonicity and the convexity of bivariate functions in neighborhoods of some points.
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CONVERGENCE OF GENERALIZED SINGULAR INTEGRALS TO THE UNIT, Univariate Case
Mathematical Inequalities & Applications, 2000Co-Authors: George A Anastassiou, Sorin G. GalAbstract:In a recent paper, the second author (see (2)) studied the degree of uniform approx- imation to the unit in terms of uniform moduli of smoothness, by the Jackson-type general- izations of Picard and of Gauss-Weierstrass singular integrals. In this paper we consider the L p -approximation, (1 p < +∞) by the above singular integrals in terms of the L p -moduli of smoothness, and both uniform and L p -approximation (in terms of the corresponding moduli of smoothness) by Jackson-type generalizations of the Poisson-Cauchy singular integrals.
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Some Shift-Invariant Integral Operators, Univariate Case, Revisited
Journal of Computational Analysis and Applications, 1999Co-Authors: George A AnastassiouAbstract:In recent articles the first author and H. Gonska [e.g., see G. Anastassiou, C. Cottin, and H. Gonska, Global smoothness of approximating functions, Analysis , 11, 43–57 (1991); G. Anastassiou and H. Gonska, On some shift-invariant integral operators, Univariate Case, Ann. Pol. Math. LXI.3, 225–243 (1995)] studied global smoothness preservation by some Univariate and multivariate linear operators over compact domains and ℝ^ n , n ≥ 1. In particular, they studied a very general positive linear integral type operator [e.g., see G. Anastassiou and H. Gonska, On some shift-invariant integral operators, Univariate Case, Ann. Pol. Math. LXI.3, 225–243 (1995)] over ℝ^ n that was introduced through a convolution-like integration of another general positive linear operator with a scaling-type function. In this article the authors, among others, extend and generalize [G. Anastassiou and H. Gonska, On some shift-invariant integral operators, Univariate Case, Ann. Pol. Math. LXI.3, 225–243 (1995)]. Also certain new similar but more general integral operators are introduced and studied. These operators arise in a natural way, and for all these sufficient conditions are given for shift invariance, preservation of higher-order global smoothness and sharpness of the related inequalities, convergence to the unit using the first modulus of continuity, shape preservation, and preservation of continuous probabilistic distribution functions. Several examples of very general specialized operators, old and new, are given that satisfy all the above properties.
A. Pisani - One of the best experts on this subject based on the ideXlab platform.
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A non-parametric and scale-independent method for cluster analysis – I. The Univariate Case
Monthly Notices of the Royal Astronomical Society, 1993Co-Authors: A. PisaniAbstract:The detection and analysis of structure and substructure in systems of galaxies is a well-known problem. Several methods of analysis exist with different ranges of applicability and giving different results. The aim of the present paper is to describe a general procedure of wide applicability that is based on a minimum number of general assumptions and gives an objective, testable, scale-independent and non-parametric estimate of the clustering pattern of a sample of observational data. The method follows the idea that the presence of a cluster in a data sample is indicated by a peak in the probability density underlying the data. There are two steps: the first is estimation of the probability density and the second is identification of the clusters
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a non parametric and scale independent method for cluster analysis i the Univariate Case
Monthly Notices of the Royal Astronomical Society, 1993Co-Authors: A. PisaniAbstract:The detection and analysis of structure and substructure in systems of galaxies is a well-known problem. Several methods of analysis exist with different ranges of applicability and giving different results. The aim of the present paper is to describe a general procedure of wide applicability that is based on a minimum number of general assumptions and gives an objective, testable, scale-independent and non-parametric estimate of the clustering pattern of a sample of observational data. The method follows the idea that the presence of a cluster in a data sample is indicated by a peak in the probability density underlying the data. There are two steps: the first is estimation of the probability density and the second is identification of the clusters
Foster Provost - One of the best experts on this subject based on the ideXlab platform.
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Classification in Networked Data : A Toolkit and a Univariate Case Study
Journal of Machine Learning Research, 2007Co-Authors: Sofus A. Macskassy, Foster ProvostAbstract:This paper is about classifying entities that are interlinked with entities for which the class is known. After surveying prior work, we present NetKit, a modular toolkit for classification in networked data, and a Case-study of its application to networked data used in prior machine learning research. NetKit is based on a node-centric framework in which classifiers comprise a local classifier, a relational classifier, and a collective inference procedure. Various existing node-centric relational learning algorithms can be instantiated with appropriate choices for these components, and new combinations of components realize new algorithms. The Case study focuses on Univariate network classification, for which the only information used is the structure of class linkage in the network (i.e., only links and some class labels). To our knowledge, no work previously has evaluated systematically the power of class-linkage alone for classification in machine learning benchmark data sets. The results demonstrate that very simple network-classification models perform quite well--well enough that they should be used regularly as baseline classifiers for studies of learning with networked data. The simplest method (which performs remarkably well) highlights the close correspondence between several existing methods introduced for different purposes--that is, Gaussian-field classifiers, Hopfield networks, and relational-neighbor classifiers. The Case study also shows that there are two sets of techniques that are preferable in different situations, namely when few versus many labels are known initially. We also demonstrate that link selection plays an important role similar to traditional feature selection.
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classification in networked data a toolkit and a Univariate Case study
2004Co-Authors: Sofus A. Macskassy, Foster ProvostAbstract:This paper presents NetKit, a modular toolkit for classification in networked data, and a Case-studyof its application to a collection of networked data sets used in prior machine learning research.Networked data are relational data where entities are interconnected, and this paper considers thecommon Case where entities whose labels are to be estimated are linked to entities for which thelabel is known. NetKit is based on a three-component framework, comprising a local classifier, arelational classifier, and a collective inference procedure. Various existing relational learning algorithmscan be instantiated with appropriate choices for these three components and new relationallearning algorithms can be composed by new combinations of components. The Case study demonstrateshow the toolkit facilitates comparison of different learning methods (which so far has beenlacking in machine learning research). It also shows how the modular framework allows analysisof subcomponents, to assess which, whether, and when particular components contribute to superiorperformance. The Case study focuses on the simple but important special Case of Univariatenetwork classification, for which the only information available is the structure of class linkage inthe network (i.e., only links and some class labels are available). To our knowledge, no work previouslyhas evaluated systematically the power of class-linkage alone for classification in machinelearning benchmark data sets. The results demonstrate clearly that simple network-classificationmodels perform remarkably wellâ"well enough that they should be used regularly as baseline classifiersfor studies of relational learning for networked data. The results also show that there are asmall number of component combinations that excel, and that different components are preferablein different situations, for example when few versus many labels are known.
Provostfoster - One of the best experts on this subject based on the ideXlab platform.
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Classification in Networked Data: A Toolkit and a Univariate Case Study
Journal of Machine Learning Research, 2007Co-Authors: A Macskassysofus, ProvostfosterAbstract:This paper is about classifying entities that are interlinked with entities for which the class is known. After surveying prior work, we present NetKit, a modular toolkit for classification in netw...
Sorin G. Gal - One of the best experts on this subject based on the ideXlab platform.
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Partial shape preserving approximations by bivariate shepard operators
Computers & Mathematics with Applications, 2001Co-Authors: George A Anastassiou, Sorin G. GalAbstract:Abstract Extending the results from the Univariate Case in a paper by Gal and Szabados, in this paper, we prove that the bivariate Shepard interpolation operators preserve the monotonicity and the convexity of bivariate functions in neighborhoods of some points.
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CONVERGENCE OF GENERALIZED SINGULAR INTEGRALS TO THE UNIT, Univariate Case
Mathematical Inequalities & Applications, 2000Co-Authors: George A Anastassiou, Sorin G. GalAbstract:In a recent paper, the second author (see (2)) studied the degree of uniform approx- imation to the unit in terms of uniform moduli of smoothness, by the Jackson-type general- izations of Picard and of Gauss-Weierstrass singular integrals. In this paper we consider the L p -approximation, (1 p < +∞) by the above singular integrals in terms of the L p -moduli of smoothness, and both uniform and L p -approximation (in terms of the corresponding moduli of smoothness) by Jackson-type generalizations of the Poisson-Cauchy singular integrals.
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General Theory of Global Smoothness Preservation by Singular Integrals, Univariate Case
Journal of Computational Analysis and Applications, 1999Co-Authors: George A Anastassiou, Sorin G. GalAbstract:In this article it is established that the well-known singular integrals of Picard, Poisson–Cauchy, Gauss–Weierstrass, and their Jackson-type generalizations fulfill the “global smoothness preservation” property, i.e., they “ripple” less than the function they are applied on, that is, producing a nice and fit approximation to the unit. The related results are established over various spaces of functions and the associated inequalities involve different types of corresponding moduli of smoothness. Several times these inequalities are proved to be sharp, namely, they are attained.
