Counting Distance Permutations

Distance permutation indexes support fast proximity searching in high-dimensional metric spaces. Given some fixed reference sites, for each point in a database the index stores a permutation naming the closest site, the second-closest, and so on. We examine how many distinct permutations can occur as a function of the number of sites and the size of the space. We give theoretical results for tree metrics and vector spaces with L1, L2, and L∞ metrics, improving on the previous best known storage space in the vector case. We also give experimental results and commentary on the number of distance permutations that actually occur in a variety of vector, string, and document databases. Key words: metric space, nearest neighbour, Voronoi diagram, distance permutation

• Type: Conference
• Year: 2008
• Where: SISAP
• Authors: Matthew Skala
• Keywords: Data Mining, Distance Permutation, Distance Permutation Indexes, Metric Space, SISAP 2008