27 research outputs found
Fast Hierarchical Clustering and Other Applications of Dynamic Closest Pairs
We develop data structures for dynamic closest pair problems with arbitrary
distance functions, that do not necessarily come from any geometric structure
on the objects. Based on a technique previously used by the author for
Euclidean closest pairs, we show how to insert and delete objects from an
n-object set, maintaining the closest pair, in O(n log^2 n) time per update and
O(n) space. With quadratic space, we can instead use a quadtree-like structure
to achieve an optimal time bound, O(n) per update. We apply these data
structures to hierarchical clustering, greedy matching, and TSP heuristics, and
discuss other potential applications in machine learning, Groebner bases, and
local improvement algorithms for partition and placement problems. Experiments
show our new methods to be faster in practice than previously used heuristics.Comment: 20 pages, 9 figures. A preliminary version of this paper appeared at
the 9th ACM-SIAM Symp. on Discrete Algorithms, San Francisco, 1998, pp.
619-628. For source code and experimental results, see
http://www.ics.uci.edu/~eppstein/projects/pairs
Measuring the Difficulty of Distance-Based Indexing
Abstract. Data structures for similarity search are commonly evalu-ated on data in vector spaces, but distance-based data structures are also applicable to non-vector spaces with no natural concept of dimen-sionality. The intrinsic dimensionality statistic of Chávez and Navarro provides a way to compare the performance of similarity indexing and search algorithms across different spaces, and predict the performance of index data structures on non-vector spaces by relating them to equiv-alent vector spaces. We characterise its asymptotic behaviour, and give experimental results to calibrate these comparisons.