Associated Near Sets of Distance Functions in Pattern Analysis

This paper introduces description-based associated sets of distance functions, where members are topological structures helpful in pattern analysis and machine intelligence. An associated set of a function is a collection containing members with one or more common properties. This study has important implications in discerning patterns shared by members of an associated set. The focus in this paper is on defining and characterising distance functions relative to structures that are collections of sufficiently near (far) neighbourhoods, filters, grills and clusters. Naimpally-Peters-Tiwari distance functions themselves define approach spaces that generalise the traditional notion of a metric space. An important side-effect of this work is the discovery of various patterns that arise from the descriptions (perceptions) of associated set members. An application of the proposed approach is given in the context of camouflaged objects.