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Small and stable descriptors of dist...

Duke University., Computer Science.

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Small and stable descriptors of distributions for geometric statistical problems.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Small and stable descriptors of distributions for geometric statistical problems./
作者:	Phillips, Jeff M.
面頁冊數:	174 p.
附註:	Adviser: Pankaj K. Agarwal.
Contained By:	Dissertation Abstracts International70-03B.
標題:	Computer Science. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3349846
ISBN:	9781109061437

Small and stable descriptors of distributions for geometric statistical problems.
Phillips, Jeff M.

Small and stable descriptors of distributions for geometric statistical problems. - 174 p.

Adviser: Pankaj K. Agarwal.

Thesis (Ph.D.)--Duke University, 2009.

This thesis explores how to sparsely represent distributions of points for geometric statistical problems. A coreset C is a small summary of a point set P such that if a certain statistic is computed on P and C, then the difference in the results is guaranteed to be bounded by a parameter &egr;. Two examples of coresets are &egr;-samples and &egr;-kernels. An &egr;-sample can estimate the density of a point set in any range from a geometric family of ranges (e.g., disks, axis-aligned rectangles). An &egr;-kernel approximates the width of a point set in all directions. Both coresets have size that depends only on &egr;, the error parameter, not the size of the original data set. We demonstrate several improvements to these coresets and how they are useful for geometric statistical problems.

ISBN: 9781109061437Subjects--Topical Terms:

626642
Computer Science.

Small and stable descriptors of distributions for geometric statistical problems.
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245 1 0 $a Small and stable descriptors of distributions for geometric statistical problems.
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500 $a Source: Dissertation Abstracts International, Volume: 70-03, Section: B, page: 1762.
502 $a Thesis (Ph.D.)--Duke University, 2009.
520 $a This thesis explores how to sparsely represent distributions of points for geometric statistical problems. A coreset C is a small summary of a point set P such that if a certain statistic is computed on P and C, then the difference in the results is guaranteed to be bounded by a parameter &egr;. Two examples of coresets are &egr;-samples and &egr;-kernels. An &egr;-sample can estimate the density of a point set in any range from a geometric family of ranges (e.g., disks, axis-aligned rectangles). An &egr;-kernel approximates the width of a point set in all directions. Both coresets have size that depends only on &egr;, the error parameter, not the size of the original data set. We demonstrate several improvements to these coresets and how they are useful for geometric statistical problems.
520 $a We reduce the size of &egr;-samples for density queries in axis-aligned rectangles to nearly a square root of the size when the queries are with respect to more general families of shapes, such as disks. We also show how to construct &egr;-samples of probability distributions.
520 $a We show how to maintain "stable" &egr;-kernels, that is, if the point set P changes by a small amount, then the &egr;-kernel also changes by a small amount. This is useful in surveillance and tracking problems, and the stable properties leads to more efficient algorithms for maintaining &egr;-kernels.
520 $a We next study when the input point sets are uncertain and their uncertainty is modeled by probability distributions. Statistics on these point sets (e.g., radius of smallest enclosing ball) do not have exact answers, but rather distributions of answers. We describe data structures to represent approximations of these distributions and algorithms to compute them. We also show how to create distributions of &egr;-kernels and &egr;-samples for these uncertain data sets.
520 $a Finally, we examine a spatial anomaly detection problem: computing a spatial scan statistic. The input is a point set P and measurements on the point set. The spatial scan statistic finds the range (e.g., an axis-aligned bounding box) where the measurements inside the range are the most different from measurements outside of the range. We show how to compute this statistic efficiently while allowing for a bounded amount of approximation error. This result generalizes to several statistical models and types of input point sets.
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710 2 0 $a Duke University. $b Computer Science. $3 1019283
773 0 $t Dissertation Abstracts International $g 70-03B.
790 $a 0066
790 1 0 $a Agarwal, Pankaj K., $e advisor
790 1 0 $a Edelsbrunner, Herbert $e committee member
790 1 0 $a Gelfand, Alan E. $e committee member
790 1 0 $a Munagala, Kamesh $e committee member
790 1 0 $a Venkatasubramanian, Suresh $e committee member
791 $a Ph.D.
792 $a 2009
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