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PK-TREE: A SPATIAL INDEX STRUCTURE FOR HIGH DIMENSIONAL POINT DATA

by Wei Wang, Jiong Yang, Richard Muntz
"... In this chapter we present the PK-tree which is an index structure for high dimensional point data. The proposed indexing structure can be viewed as combining aspects of the PR-quad or K-D tree but where unnecessary nodes are eliminated. The unnecessary nodes are typically the result of skew in the ..."
Abstract - Cited by 17 (1 self) - Add to MetaCart
In this chapter we present the PK-tree which is an index structure for high dimensional point data. The proposed indexing structure can be viewed as combining aspects of the PR-quad or K-D tree but where unnecessary nodes are eliminated. The unnecessary nodes are typically the result of skew

Distributed Computation of the knn Graph for Large High-Dimensional Point Sets

by Erion Plaku , Lydia E. Kavraki , 2007
"... High-dimensional problems arising from robot motion planning, biology, data mining, and geographic information systems often require the computation of k nearest neighbor (knn) graphs. The knn graph of a data set is obtained by connecting each point to its k closest points. As the research in the ab ..."
Abstract - Cited by 8 (0 self) - Add to MetaCart
High-dimensional problems arising from robot motion planning, biology, data mining, and geographic information systems often require the computation of k nearest neighbor (knn) graphs. The knn graph of a data set is obtained by connecting each point to its k closest points. As the research

Stratification learning: Detecting mixed density and dimensionality in high dimensional point clouds

by Gregory Randall, Gloria Haro, Gloria Haro, Gregory R, Guillermo Sapiro, Guillermo Sapiro - In Advances in NIPS 19 , 2006
"... The study of point cloud data sampled from a stratification, a collection of manifolds with possible different dimensions, is pursued in this paper. We present a technique for simultaneously soft clustering and estimating the mixed dimensionality and density of such structures. The framework is base ..."
Abstract - Cited by 20 (2 self) - Add to MetaCart
The study of point cloud data sampled from a stratification, a collection of manifolds with possible different dimensions, is pursued in this paper. We present a technique for simultaneously soft clustering and estimating the mixed dimensionality and density of such structures. The framework

The X-tree: An index structure for high-dimensional data

by Stefan Berchtold, Daniel A. Keim, Hans-peter Kriegel - In Proceedings of the Int’l Conference on Very Large Data Bases , 1996
"... In this paper, we propose a new method for index-ing large amounts of point and spatial data in high-dimensional space. An analysis shows that index structures such as the R*-tree are not adequate for indexing high-dimensional data sets. The major problem of R-tree-based index structures is the over ..."
Abstract - Cited by 592 (17 self) - Add to MetaCart
In this paper, we propose a new method for index-ing large amounts of point and spatial data in high-dimensional space. An analysis shows that index structures such as the R*-tree are not adequate for indexing high-dimensional data sets. The major problem of R-tree-based index structures

Estimating the Support of a High-Dimensional Distribution

by Bernhard Schölkopf, John C. Platt, John Shawe-taylor, Alex J. Smola, Robert C. Williamson , 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
Abstract - Cited by 783 (29 self) - Add to MetaCart
Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We

Efficient Clustering of High-Dimensional Data Sets with Application to Reference Matching

by Andrew McCallum , Kamal Nigam , Lyle H. Ungar , 2000
"... Many important problems involve clustering large datasets. Although naive implementations of clustering are computationally expensive, there are established efficient techniques for clustering when the dataset has either (1) a limited number of clusters, (2) a low feature dimensionality, or (3) a sm ..."
Abstract - Cited by 338 (15 self) - Add to MetaCart
technique for clustering these large, high-dimensional datasets. The key idea involves using a cheap, approximate distance measure to efficiently divide the data into overlapping subsets we call canopies. Then clustering is performed by measuring exact distances only between points that occur in a common

Shape Indexing Using Approximate Nearest-Neighbour Search in High-Dimensional Spaces

by Jeffrey S. Beis , David G. Lowe , 1997
"... Shape indexing is a way of making rapid associations between features detected in an image and object models that could have produced them. When model databases are large, the use of high-dimensional features is critical, due to the improved level of discrimination they can provide. Unfortunately, f ..."
Abstract - Cited by 311 (12 self) - Add to MetaCart
Shape indexing is a way of making rapid associations between features detected in an image and object models that could have produced them. When model databases are large, the use of high-dimensional features is critical, due to the improved level of discrimination they can provide. Unfortunately

Similarity search in high dimensions via hashing

by Aristides Gionis, Piotr Indyk, Rajeev Motwani , 1999
"... The nearest- or near-neighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search/index structures for performing similarity search over high-dimensional data, e.g., image dat ..."
Abstract - Cited by 641 (10 self) - Add to MetaCart
The nearest- or near-neighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search/index structures for performing similarity search over high-dimensional data, e.g., image

Laplacian eigenmaps and spectral techniques for embedding and clustering.

by Mikhail Belkin , Partha Niyogi - Proceeding of Neural Information Processing Systems, , 2001
"... Abstract Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami op erator on a manifold , and the connections to the heat equation , we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in ..."
Abstract - Cited by 668 (7 self) - Add to MetaCart
retrieval and data mining, one is often confronted with intrinsically low dimensional data lying in a very high dimensional space. For example, gray scale n x n images of a fixed object taken with a moving camera yield data points in rn: n2 . However , the intrinsic dimensionality of the space of all images

Efficient Variants of the ICP Algorithm

by Szymon Rusinkiewicz, Marc Levoy - INTERNATIONAL CONFERENCE ON 3-D DIGITAL IMAGING AND MODELING , 2001
"... The ICP (Iterative Closest Point) algorithm is widely used for geometric alignment of three-dimensional models when an initial estimate of the relative pose is known. Many variants of ICP have been proposed, affecting all phases of the algorithm from the selection and matching of points to the minim ..."
Abstract - Cited by 718 (5 self) - Add to MetaCart
The ICP (Iterative Closest Point) algorithm is widely used for geometric alignment of three-dimensional models when an initial estimate of the relative pose is known. Many variants of ICP have been proposed, affecting all phases of the algorithm from the selection and matching of points
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