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» Embedding a set of rational points in lower dimensions
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FOCS
1999
IEEE
13 years 9 months ago
Approximate Nearest Neighbor Algorithms for Hausdorff Metrics via Embeddings
Hausdorff metrics are used in geometric settings for measuring the distance between sets of points. They have been used extensively in areas such as computer vision, pattern recog...
Martin Farach-Colton, Piotr Indyk
JSCIC
2008
129views more  JSCIC 2008»
13 years 5 months ago
Level Set Equations on Surfaces via the Closest Point Method
Abstract Level set methods have been used in a great number of applications in R2 and R3 and it is natural to consider extending some of these methods to problems defined on surfac...
Colin B. Macdonald, Steven J. Ruuth
COMPGEOM
2008
ACM
13 years 7 months ago
Extremal problems on triangle areas in two and three dimensions
The study of extremal problems on triangle areas was initiated in a series of papers by Erdos and Purdy in the early 1970s. In this paper we present new results on such problems, ...
Adrian Dumitrescu, Micha Sharir, Csaba D. Tó...
CORR
2008
Springer
77views Education» more  CORR 2008»
13 years 5 months ago
Principal Graphs and Manifolds
In many physical statistical, biological and other investigations it is desirable to approximate a system of points by objects of lower dimension and/or complexity. For this purpo...
Alexander N. Gorban, Andrei Yu. Zinovyev
AAAI
2010
13 years 6 months ago
Conformal Mapping by Computationally Efficient Methods
Dimensionality reduction is the process by which a set of data points in a higher dimensional space are mapped to a lower dimension while maintaining certain properties of these p...
Stefan Pintilie, Ali Ghodsi