Principles of Information Filtering in Metric Spaces

Abstract

The traditional problem of similarity search requires to find, within a set of points, those that are closer to a query point $q$, according to a distance function $d$. In this paper we introduce the novel problem of metric filtering: in this scenario, each data point $x_i$ possesses its own distance function $d_i$ and the task is to find those points that are close enough, according to $d_i$, to a query point $q$. This minor difference in the problem formulation introduces a series of challenges from the point of view of efficient evaluation. We provide basic definitions and alternative pivot-based resolution strategies, presenting results from a preliminary experimentation that show how the proposed solutions are indeed effective in reducing evaluation costs.