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Variance-based clustering methods and higher order data transformations and their applications

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TypeOfResource
Text
TitleInfo (ID = T-1)
Title
Variance-based clustering methods and higher order data transformations and their applications
SubTitle
PartName
PartNumber
NonSort
Identifier (displayLabel = ); (invalid = )
ETD_2045
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000051869
Language (objectPart = )
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eng
Genre (authority = marcgt)
theses
Subject (ID = SBJ-1); (authority = RUETD)
Topic
Computer Science
Subject (ID = SBJ-2); (authority = ETD-LCSH)
Topic
Multivariate analysis
Subject (ID = SBJ-3); (authority = ETD-LCSH)
Topic
Cluster analysis
Abstract
Two approaches have been proposed in statistical and machine learning communities in order to address the problem of uncovering clusters with complex structure. One approach relies on the development of clustering criteria that are able to accommodate increasingly complex characteristics of the data. The other approach is based on simplification of structure of data by mapping it to a different feature space via a non-linear function and then clustering in the new space.
This dissertation covers three related studies: development of a novel multi-dimensional clustering method, development of non-linear mapping functions that leverage higher-order co-occurrences between features in boolean data, and applications of these mapping functions for improving the performance of clustering methods. In particular, we treat clustering as a combinatorial optimization problem of finding a partition of the data so as to minimize a certain criterion. We develop a novel multi-dimensional clustering method based on a statistically-motivated criterion proposed by J. Neyman for stratified sampling from one-dimensional data. We show that this criterion is more reflective of the underlying data structure than the seemingly similar K-means criterion when second order variability is not homogeneous between constituent subgroups. Furthermore, experimental results demonstrate that generalization of the Neyman's criterion to multi-dimensional spaces and development of the associated clustering algorithm allow for statistically efficient estimation of the grand mean vector of a population.
In the framework of the mapping-based approach to discovering complex cluster structures, we introduced a novel adaptive non-linear data transformation termed Unsupervised Second Order Transformation (USOT). The novelties behind USOT are (a) that it leverages in a unsupervised manner, higher-order co-occurrences between features in boolean data, and (b) that it considers each feature in the context of probabilistic relationships with other features. In addition, USOT has two desirable properties. USOT adaptively selects features that would influence the mapping of a given feature, and preserves the interpretability of dimensions of the transformed space. Experimental results on text corpora and financial time series demonstrate that by leveraging higher-order co-occurrences between features, clustering methods achieved statistically significant improvements in USOT space over the original boolean space.
PhysicalDescription
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electronic resource
Extent
vii, 83 p. : ill.
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Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p. 78-82)
Note (type = statement of responsibility)
by Nikita I. Lytkin
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Lytkin
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Nikita I.
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author
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Nikita I. Lytkin
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Kulikowski
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Casimir
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chair
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Advisory Committee
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Casimir A Kulikowski
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Elgammal
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Ahmed
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internal member
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Advisory Committee
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Ahmed Elgammal
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Metaxas
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Dimitris
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internal member
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Advisory Committee
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Dimitris N Metaxas
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Behrens
NamePart (type = given)
Clifford
Role
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outside member
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Advisory Committee
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Clifford A Behrens
Name (ID = NAME-1); (type = corporate)
NamePart
Rutgers University
Role
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degree grantor
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Graduate School - New Brunswick
Role
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school
OriginInfo
DateCreated (point = ); (qualifier = exact)
2009
DateOther (qualifier = exact); (type = degree)
2009-10
Place
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xx
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
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TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T3B27VFQ
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

RightsDeclaration (AUTHORITY = GS); (ID = rulibRdec0006)
The author owns the copyright to this work
Copyright
Status
Copyright protected
Notice
Note
Availability
Status
Open
Reason
Permission or license
Note
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Name
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Lytkin
GivenName
Nikita
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Copyright holder
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DateTime
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Name
Nikita Lytkin
Affiliation
Rutgers University. Graduate School - New Brunswick
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Author Agreement License
Detail
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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Technical

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