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Compactifications of Discrete Spaces
"... Compactifications of an infinite discrete spaceD are discussed. Equivalent conditions are obtained for a compactification of D to be totally disconnected. The existance of infinite compactifications of D which are totally disconnected is proved. ..."
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Compactifications of an infinite discrete spaceD are discussed. Equivalent conditions are obtained for a compactification of D to be totally disconnected. The existance of infinite compactifications of D which are totally disconnected is proved.
ON ALMOST DISCRETE SPACE
"... Abstract. Let C(X) be the ring of real continuous functions on a completely regular Hausdorff space. In this paper an almost discrete space is determined by the algebraic structure of C(X). The intersection of essential weak ideal in C(X) is also studied. 1. ..."
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Abstract. Let C(X) be the ring of real continuous functions on a completely regular Hausdorff space. In this paper an almost discrete space is determined by the algebraic structure of C(X). The intersection of essential weak ideal in C(X) is also studied. 1.
Continuous Motion in Discrete Space
 Principles of Knowledge Representation and Reasoning: Proceedings of the Seventh International Conference (KR2000
, 2000
"... A number of situations arise in the context of knowledge representation where some notion of continuity is desired within a framework that is itself discrete. We survey some varieties of discrete space that have been proposed, and show that they can all be described as instances of a general n ..."
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Cited by 6 (0 self)
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A number of situations arise in the context of knowledge representation where some notion of continuity is desired within a framework that is itself discrete. We survey some varieties of discrete space that have been proposed, and show that they can all be described as instances of a general
DIMENSION ON DISCRETE SPACES.
, 1993
"... In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by means of axioms, and the axioms are based on an obvious geomet ..."
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In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by means of axioms, and the axioms are based on an obvious
Discrete spacetime
"... One conceivable hypothesis on the structure of space in the microcosmos, conceived as a collection of disconnected elements in space (points) which cannot be distinguished by observations. An acceptable formalization of discrete spacetime can be given in terms of topological spaces in which the con ..."
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One conceivable hypothesis on the structure of space in the microcosmos, conceived as a collection of disconnected elements in space (points) which cannot be distinguished by observations. An acceptable formalization of discrete spacetime can be given in terms of topological spaces in which
Convolution Kernels on Discrete Structures
, 1999
"... We introduce a new method of constructing kernels on sets whose elements are discrete structures like strings, trees and graphs. The method can be applied iteratively to build a kernel on an infinite set from kernels involving generators of the set. The family of kernels generated generalizes the fa ..."
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Cited by 510 (0 self)
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We introduce a new method of constructing kernels on sets whose elements are discrete structures like strings, trees and graphs. The method can be applied iteratively to build a kernel on an infinite set from kernels involving generators of the set. The family of kernels generated generalizes
Convexity in Discrete Space
"... Abstract. This paper looks at axioms for convexity, and shows how they can be applied to discrete spaces. Two structures for a discrete geometry are considered: oriented matroids, and cell complexes. Oriented matroids are shown to have a structure which naturally satisfies the axioms for being a con ..."
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Cited by 1 (0 self)
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Abstract. This paper looks at axioms for convexity, and shows how they can be applied to discrete spaces. Two structures for a discrete geometry are considered: oriented matroids, and cell complexes. Oriented matroids are shown to have a structure which naturally satisfies the axioms for being a
Regularization on discrete spaces
 Pattern Recognition
, 2005
"... Abstract. We consider the classification problem on a finite set of objects. Some of them are labeled, and the task is to predict the labels of the remaining unlabeled ones. Such an estimation problem is generally referred to as transductive inference. It is wellknown that many meaningful inductive ..."
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Cited by 44 (1 self)
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inductive or supervised methods can be derived from a regularization framework, which minimizes a loss function plus a regularization term. In the same spirit, we propose a general discrete regularization framework defined on finite object sets, which can be thought of as discrete analogue of classical
Supervised and unsupervised discretization of continuous features
 in A. Prieditis & S. Russell, eds, Machine Learning: Proceedings of the Twelfth International Conference
, 1995
"... Many supervised machine learning algorithms require a discrete feature space. In this paper, we review previous work on continuous feature discretization, identify de ning characteristics of the methods, and conduct an empirical evaluation of several methods. We compare binning, an unsupervised dis ..."
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Cited by 534 (11 self)
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Many supervised machine learning algorithms require a discrete feature space. In this paper, we review previous work on continuous feature discretization, identify de ning characteristics of the methods, and conduct an empirical evaluation of several methods. We compare binning, an unsupervised
Results 1  10
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893,046