Results 11  20
of
818
RapidlyExploring Random Trees: Progress and Prospects
 Algorithmic and Computational Robotics: New Directions
, 2000
"... this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints. ..."
Abstract

Cited by 260 (25 self)
 Add to MetaCart
this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints.
Geometric Range Searching and Its Relatives
 CONTEMPORARY MATHEMATICS
"... ... process a set S of points in so that the points of S lying inside a query R region can be reported or counted quickly. Wesurvey the known techniques and data structures for range searching and describe their application to other related searching problems. ..."
Abstract

Cited by 257 (41 self)
 Add to MetaCart
... process a set S of points in so that the points of S lying inside a query R region can be reported or counted quickly. Wesurvey the known techniques and data structures for range searching and describe their application to other related searching problems.
An Efficient kMeans Clustering Algorithm: Analysis and Implementation
, 2000
"... Kmeans clustering is a very popular clustering technique, which is used in numerous applications. Given a set of n data points in R d and an integer k, the problem is to determine a set of k points R d , called centers, so as to minimize the mean squared distance from each data point to its ..."
Abstract

Cited by 241 (4 self)
 Add to MetaCart
Kmeans clustering is a very popular clustering technique, which is used in numerous applications. Given a set of n data points in R d and an integer k, the problem is to determine a set of k points R d , called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for kmeans clustering is Lloyd's algorithm. In this paper we present a simple and efficient implementation of Lloyd's kmeans clustering algorithm, which we call the filtering algorithm. This algorithm is very easy to implement. It differs from most other approaches in that it precomputes a kdtree data structure for the data points rather than the center points. We establish the practical efficiency of the filtering algorithm in two ways. First, we present a datasensitive analysis of the algorithm's running time. Second, we have implemented the algorithm and performed a number of empirical studies, both on synthetically generated data and on real...
Fast approximate nearest neighbors with automatic algorithm configuration
 In VISAPP International Conference on Computer Vision Theory and Applications
, 2009
"... nearestneighbors search, randomized kdtrees, hierarchical kmeans tree, clustering. For many computer vision problems, the most time consuming component consists of nearest neighbor matching in highdimensional spaces. There are no known exact algorithms for solving these highdimensional problems ..."
Abstract

Cited by 211 (2 self)
 Add to MetaCart
nearestneighbors search, randomized kdtrees, hierarchical kmeans tree, clustering. For many computer vision problems, the most time consuming component consists of nearest neighbor matching in highdimensional spaces. There are no known exact algorithms for solving these highdimensional problems that are faster than linear search. Approximate algorithms are known to provide large speedups with only minor loss in accuracy, but many such algorithms have been published with only minimal guidance on selecting an algorithm and its parameters for any given problem. In this paper, we describe a system that answers the question, “What is the fastest approximate nearestneighbor algorithm for my data? ” Our system will take any given dataset and desired degree of precision and use these to automatically determine the best algorithm and parameter values. We also describe a new algorithm that applies priority search on hierarchical kmeans trees, which we have found to provide the best known performance on many datasets. After testing a range of alternatives, we have found that multiple randomized kd trees provide the best performance for other datasets. We are releasing public domain code that implements these approaches. This library provides about one order of magnitude improvement in query time over the best previously available software and provides fully automated parameter selection. 1
ANN: library for approximate nearest neighbor searching. http://www.cs.umd.edu/ ~mount/ANN
, 1998
"... ..."
Efficient Search for Approximate Nearest Neighbor in High Dimensional Spaces
, 1998
"... We address the problem of designing data structures that allow efficient search for approximate nearest neighbors. More specifically, given a database consisting of a set of vectors in some high dimensional Euclidean space, we want to construct a spaceefficient data structure that would allow us to ..."
Abstract

Cited by 196 (9 self)
 Add to MetaCart
We address the problem of designing data structures that allow efficient search for approximate nearest neighbors. More specifically, given a database consisting of a set of vectors in some high dimensional Euclidean space, we want to construct a spaceefficient data structure that would allow us to search, given a query vector, for the closest or nearly closest vector in the database. We also address this problem when distances are measured by the L 1 norm, and in the Hamming cube. Significantly improving and extending recent results of Kleinberg, we construct data structures whose size is polynomial in the size of the database, and search algorithms that run in time nearly linear or nearly quadratic in the dimension (depending on the case; the extra factors are polylogarithmic in the size of the database). Computer Science Department, Technion  IIT, Haifa 32000, Israel. Email: eyalk@cs.technion.ac.il y Bell Communications Research, MCC1C365B, 445 South Street, Morristown, NJ ...
Ranking in Spatial Databases
, 1995
"... An algorithm for ranking spatial objects according to increasing distance from a query object is introduced and analyzed. The algorithm makes use of a hierarchical spatial data structure. The intended application area is a database environment, where the spatial data structure serves as an index. T ..."
Abstract

Cited by 190 (21 self)
 Add to MetaCart
An algorithm for ranking spatial objects according to increasing distance from a query object is introduced and analyzed. The algorithm makes use of a hierarchical spatial data structure. The intended application area is a database environment, where the spatial data structure serves as an index. The algorithm is incremental in the sense that objects are reported one by one, so that a query processor can use the algorithm in a pipelined fashion for complex queries involving proximity. It is well suited for k nearest neighbor queries, and has the property that k needs not be fixed in advance.
Two Algorithms for NearestNeighbor Search in High Dimensions
, 1997
"... Representing data as points in a highdimensional space, so as to use geometric methods for indexing, is an algorithmic technique with a wide array of uses. It is central to a number of areas such as information retrieval, pattern recognition, and statistical data analysis; many of the problems aris ..."
Abstract

Cited by 179 (0 self)
 Add to MetaCart
Representing data as points in a highdimensional space, so as to use geometric methods for indexing, is an algorithmic technique with a wide array of uses. It is central to a number of areas such as information retrieval, pattern recognition, and statistical data analysis; many of the problems arising in these applications can involve several hundred or several thousand dimensions. We consider the nearestneighbor problem for ddimensional Euclidean space: we wish to preprocess a database of n points so that given a query point, one can efficiently determine its nearest neighbors in the database. There is a large literature on algorithms for this problem, in both the exact and approximate cases. The more sophisticated algorithms typically achieve a query time that is logarithmic in n at the expense of an exponential dependence on the dimension d; indeed, even the averagecase analysis of heuristics such as kd trees reveals an exponential dependence on d in the query time. In this wor...
Indexdriven similarity search in metric spaces
 ACM Transactions on Database Systems
, 2003
"... Similarity search is a very important operation in multimedia databases and other database applications involving complex objects, and involves finding objects in a data set S similar to a query object q, based on some similarity measure. In this article, we focus on methods for similarity search th ..."
Abstract

Cited by 149 (6 self)
 Add to MetaCart
Similarity search is a very important operation in multimedia databases and other database applications involving complex objects, and involves finding objects in a data set S similar to a query object q, based on some similarity measure. In this article, we focus on methods for similarity search that make the general assumption that similarity is represented with a distance metric d. Existing methods for handling similarity search in this setting typically fall into one of two classes. The first directly indexes the objects based on distances (distancebased indexing), while the second is based on mapping to a vector space (mappingbased approach). The main part of this article is dedicated to a survey of distancebased indexing methods, but we also briefly outline how search occurs in mappingbased methods. We also present a general framework for performing search based on distances, and present algorithms for common types of queries that operate on an arbitrary “search hierarchy. ” These algorithms can be applied on each of the methods presented, provided a suitable search hierarchy is defined.
Cover trees for nearest neighbor
 In Proceedings of the 23rd international conference on Machine learning
, 2006
"... ABSTRACT. We present a tree data structure for fast nearest neighbor operations in generalpoint metric spaces. The data structure requires space regardless of the metric’s structure. If the point set has an expansion constant � in the sense of Karger and Ruhl [KR02], the data structure can be const ..."
Abstract

Cited by 148 (0 self)
 Add to MetaCart
ABSTRACT. We present a tree data structure for fast nearest neighbor operations in generalpoint metric spaces. The data structure requires space regardless of the metric’s structure. If the point set has an expansion constant � in the sense of Karger and Ruhl [KR02], the data structure can be constructed in � time. Nearest neighbor queries obeying the expansion bound require � time. In addition, the nearest neighbor of points can be queried in time. We experimentally test the algorithm showing speedups over the brute force search varying between 1 and 2000 on natural machine learning datasets. 1.