In this paper we study the generalized Erdös-Falconer distance problems in the finite field setting. The generalized distances are defined in terms of polynomials, and various formulas for sizes of distance sets are obtained. In particular, we develop a simple formula for estimating the cardinality of distance sets determined by diagonal polynomials. As a result, we generalize the spherical dis...

Many cognitive theories of judgement and decision making assume that choice options are evaluated relative to other available options. The extent to which the preference for one option is influenced by other available options will often depend on how similar the options are to each other, where similarity is assumed to be a decreasing function of the distance between options. We examine how the...

1 This paper brieey reviews the two currently dominant paradigms in machine learning-the connectionist network (CN) models and symbol processing (SP) systems; argues for the centrality of knowledge representation frameworks in learning; examines a range of representations in increasing order of complexity and measures of similarity or distance that are appropriate for each of them; introduces t...

Information entropy and its extension, which are important generalization of entropy, have been applied in many research domains today. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional relative entropy. We presented the structure of generalized relative entropy after the discussion of defects in relative entropy. Moreover, some properties o...

A distance for mixed nominal, ordinal and continuous data is developed by applying the Kullback–Leibler divergence to the general mixed-data model, an extension of the general location model that allows for ordinal variables to be incorporated in the model. The distance obtained can be considered as a generalization of the Mahalanobis distance to data with a mixture of nominal, ordinal and cont...

Generalized maps are widely used to model the topology of nD objects (such as images) by means of incidence and adjacency relationships between cells (vertices, edges, faces, volumes, ...). In this paper, we define a first error-tolerant distance measure for comparing generalized maps, which is an important issue for image processing and analysis. This distance measure is defined by means of th...

Implicit surfaces are often designed through the definition and addition of offset surfaces. These are typically defined using a skeleton of primitives such as points and lines. A predefined offset from the skeleton determines the surface. Implied in this commonly used technique is the computation of the distance from the skeleton. It is natural to use the Euclidean definition of distance. In t...