Data structures and algorithms for nearest neighbor search in general metric spaces
Peter N. Yianilos
- pp 311-321
Reads0
Chats0
TLDR
The up-tree (vantage point tree) is introduced in several forms, together‘ with &&ciated algorithms, as an improved method for these difficult search problems in general metric spaces.Abstract:
We consider the computational problem of finding nearest neighbors in general metric spaces. Of particular interest are spaces that may not be conveniently embedded or approximated in Euclidian space, or where the dimensionality of a Euclidian representation 1s very high. Also relevant are high-dimensional Euclidian settings in which the distribution of data is in some sense of lower dimension and embedded in the space. The up-tree (vantage point tree) is introduced in several forms, together‘ with &&ciated algorithms, as an improved method for these difficult search nroblems. Tree construcI tion executes in O(nlog(n i ) time, and search is under certain circumstances and in the imit, O(log(n)) expected time. The theoretical basis for this approach is developed and the results of several experiments are reported. In Euclidian cases, kd-tree performance is compared.read more
Citations
More filters
Proceedings ArticleDOI
Querying time-series streams
TL;DR: This paper proposes a novel tree maintenance mechanism for the problem of answering approximate k-Nearest Neighbor queries with a probabilistic guarantee on timeseries streams that offers an elegant compromise between the accuracy guarantee of query results and the cost of providing them.
Journal ArticleDOI
Comparing top-k XML lists
TL;DR: The first distance measures for ranked lists of sub-trees are presented, and under what conditions these measures are metrics are metrics, and algorithms to efficiently compute these distance measures are presented.
Proceedings ArticleDOI
Geometric multi-resolution analysis for dictionary learning
TL;DR: This paper describes how the GMRA correctly approximates a large class of plausible models (namely, the noisy manifolds) and proposes an efficient algorithm and theory for GMRA, a procedure for dictionary learning.
Manifold Learning and Dimensionality Reduction in Collective Motion
TL;DR: In this paper, the authors study mathematical aspects of the behaviors of animal groups, both to empirically reveal underlying simplicity, and to model possible mechanisms of them, and propose a method to detect phase transitions in a multi-agent system.
References
More filters
Book
Introduction to Statistical Pattern Recognition
TL;DR: This completely revised second edition presents an introduction to statistical pattern recognition, which is appropriate as a text for introductory courses in pattern recognition and as a reference book for workers in the field.
Journal ArticleDOI
Voronoi diagrams—a survey of a fundamental geometric data structure
TL;DR: The Voronoi diagram as discussed by the authors divides the plane according to the nearest-neighbor points in the plane, and then divides the vertices of the plane into vertices, where vertices correspond to vertices in a plane.
Journal ArticleDOI
An Algorithm for Finding Best Matches in Logarithmic Expected Time
TL;DR: An algorithm and data structure are presented for searching a file containing N records, each described by k real valued keys, for the m closest matches or nearest neighbors to a given query record.
Journal ArticleDOI
A Branch and Bound Algorithm for Computing k-Nearest Neighbors
TL;DR: The method of branch and bound is implemented in the present algorithm to facilitate rapid calculation of the k-nearest neighbors, by eliminating the necesssity of calculating many distances.