This paper proposes a method of ranking XML documents with respect to an Information Retrieval query by means of fuzzy logic. The proposed method allows imprecise queries to be evaluated against an XML document collection and it provides a model of ranking XML documents. In addition the proposed method enables sophisticated ranking of documents by employing proximity measures and the concept of...

The main bottleneck of the research in metric space searching is the so-called curse of dimensionality, which makes the task of searching some metric spaces intrinsically diicult, whatever algorithm is used. A recent trend to break this bottleneck resorts to probabilistic algorithms , where it has been shown that one can nd 99% of the elements at a fraction of the cost of the exact algorithm. T...

We develop an intuitive geometric interpretation of the standard support vector machine (SVM) for classification of both linearly separable and inseparable data and provide a rigorous derivation of the concepts behind the geometry. For the separable case finding the maximum margin between the two sets is equivalent to finding the closest points in the smallest convex sets that contain each clas...

In this paper we investigate the effects of replacing the objective function of a 0-1 Mixed-Integer Convex Program (MIP) with a “proximity” one, with the aim of enhancing the heuristic behavior of a black-box solver. The relationship of this approach with primal integer methods is also addressed. Promising computational results on different proof-of-concept implementations are presented, sugges...

Berinde [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum {bf 9} (2004), 43-53] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost $Theta$- contraction mappings andto prove some best proximity point results for t...

A characterization of the quotient proximity is given. It is used to find necessary and sufficient conditions for every proximity map on a space to be a topological quotient map. It is shown that a separated proximity space is compact iff every /7-map on X with separated range is a proximity quotient map. Introduction. In 1959 Katetov [3] introduced proximity quotient maps. They have since been...

An information retrieval (IR) engine can rank documents based on textual proximity of keywords within each document. In this paper we apply this notion to search across an entire database for objects that are \near" other relevant objects. Proximity search enables simple \focusing" queries based on general relationships among objects, helpful for interactive query sessions. We view the database...