Conference Paper

# Intersection and Signed-Intersection Kernels for Intervals.

DOI: 10.3233/978-1-58603-925-7-262 Conference: Artificial Intelligence Research and Development, Proceedings of the 11th International Conference of the Catalan Association for Artificial Intelligence, CCIA 2008, October 22-24, 2008, Sant Martí d'Empúries, Spain

Source: DBLP

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**ABSTRACT:**A training algorithm that maximizes the margin between the training patterns and the decision boundary is presented. The technique is applicable to a wide variety of classifiaction functions, including Perceptrons, polynomials, and Radial Basis Functions. The effective number of parameters is adjusted automatically to match the complexity of the problem. The solution is expressed as a linear combination of supporting patterns. These are the subset of training patterns that are closest to the decision boundary. Bounds on the generalization performance based on the leave-one-out method and the VC-dimension are given. Experimental results on optical character recognition problems demonstrate the good generalization obtained when compared with other learning algorithms. 108/1996; - [Show abstract] [Hide abstract]

**ABSTRACT:**The paper presents a diagrammatic representation of a standard interval space (the so-called “MR-diagram”), and shows how to represent and perform interval arithmetic and derive its various properties using the diagram. The representation is an extension and refinement of the IS-diagram representation devised earlier by the author to represent interval relations. First, the MR-diagram is defined together with appropriate graphical notions and constructions for basic interval relations and operations. Second, diagrammatic constructions for all standard arithmetic operations are presented. Several examples of the use of these constructions to aid reasoning about various simple, though nontrivial, properties of interval arithmetic are included in order to show how the representation facilitates both deeper understanding of the subject matter and reasoning about its properties.Linear Algebra and its Applications 02/2001; 324(1-3-324):55-80. · 0.98 Impact Factor -
##### Article: Functions of Positive and Negative Type, and their Connection with the Theory of Integral Equations

Phil. Trans. R. Soc. Lond. 209:415-446.

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