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Probabilistic distance clustering

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TypeOfResource
Text
TitleInfo (ID = T-1); (type = uniform)
Title
Probabilistic distance clustering
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.17142
Identifier
ETD_639
Language
LanguageTerm
English
Genre (authority = marcgt)
theses
Subject (ID = SBJ-1); (authority = RUETD)
Topic
Operations Research
Subject (ID = SBJ-2); (authority = ETD-LCSH)
Topic
Cluster analysis
Abstract
We present a new iterative method for probabilistic clustering of data. Given clusters, their centers, and the distances of data points from these centers, the probability of cluster membership at any point is assumed inversely proportional to the distance from (the center of) the cluster in question. This assumption is our working principle.
The method is a generalization, to several centers, of the Weiszfeld method for solving the Fermat-Weber location problem. At each iteration, the distances (Euclidean, Mahalanobis, etc.) from the cluster centers are computed for all data points, and the centers are updated as convex combinations of these points, with weights determined by the above principle. Computations stop when the centers stop moving.
Progress is monitored by the joint distance function (JDF), a measure of distance from all cluster centers, that evolves during the iterations, and captures the data in its low contours.
There are problems where the cluster sizes are given (as in capacitated facility location problems) and there are problems where the cluster sizes are unknowns to be estimated. The probabilistic distance clustering approach works well in both cases. The probabilistic distance clustering method adjusted for cluster size (called PDQ method) method is described, and applied to location problems, and mixtures of distributions, where it is a viable alternative to the EM method.
The method is simple, fast (requiring a small number of cheap iterations) and insensitive to outliers.
An important issue in clustering is the "right"number of clusters that best fits a data set. The JDF is used successfully to settle this issue and determine the correct number of clusters for a given data set.
PhysicalDescription
Extent
xiii, 124 pages
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Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p. 117-122).
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Iyigun
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Cem
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Cem Iyigun
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Prekopa
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Andras
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Andras Prekopa
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Boros
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Endre
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Endre Boros
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Ben-Israel
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Adi
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Adi Ben-Israel
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W. ART
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Rutgers University
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Graduate School - New Brunswick
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school
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DateCreated (qualifier = exact)
2008
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2008-01
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NjNbRU
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TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Identifier (type = doi)
doi:10.7282/T3JW8F81
Genre (authority = ExL-Esploro)
ETD doctoral
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The author owns the copyright to this work.
Copyright
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Copyright protected
Availability
Status
Open
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Name
CEM IYIGUN
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Affiliation
Rutgers University. Graduate School - New Brunswick
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Non-exclusive ETD license
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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