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Learning the nonlinear geometric structure of high-dimensional data

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TitleInfo
Title
Learning the nonlinear geometric structure of high-dimensional data
SubTitle
models, algorithms, and applications
Name (type = personal)
NamePart (type = family)
Wu
NamePart (type = given)
Tong
NamePart (type = date)
1987-
DisplayForm
Tong Wu
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Bajwa
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Waheed
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Waheed Bajwa
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Advisory Committee
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chair
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
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Graduate School - New Brunswick
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Text
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theses
OriginInfo
DateCreated (qualifier = exact)
2017
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2017-05
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2017
Place
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xx
Language
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eng
Abstract (type = abstract)
Modern information processing relies on the axiom that high-dimensional data lie near low-dimensional geometric structures. The work presented in this thesis aims to develop new models and algorithms for learning the geometric structures underlying data and to exploit the application of geometry learning in image and video analytics. The first part of the thesis revisits the problem of data-driven learning of these geometric structures and puts forth two new nonlinear geometric models for data describing "related" objects/phenomena. The first one of these models straddles the two extremes of the subspace model and the union-of-subspaces model, and is termed the emph{metric-constrained union-of-subspaces} (MC-UoS) model. The second one of these models---suited for data drawn from a mixture of nonlinear manifolds---generalizes the kernel subspace model, and is termed the emph{metric-constrained kernel union-of-subspaces} (MC-KUoS) model. The main contributions in this regard are threefold. First, we motivate and formalize the problems of MC-UoS and MC-KUoS learning. Second, we present algorithms that efficiently learn an MC-UoS or an MC-KUoS underlying data of interest. Third, we extend these algorithms to the case when parts of the data are missing. The second part of the thesis considers the problem of learning meaningful human action attributes from video data. Representation of human actions as a sequence of human body movements or action attributes enables the development of models for human activity recognition and summarization. We first propose a hierarchical union-of-subspaces model and an approach called hierarchical sparse subspace clustering (HSSC) is developed to learn this model from the data in an unsupervised manner by capturing the variations or movements of each action in different subspaces. We then present an extension of the low-rank representation (LRR) model, termed the emph{clustering-aware structure-constrained low-rank representation} (CS-LRR) model, for unsupervised learning of human action attributes from video data. The CS-LRR model is based on the union-of-subspaces framework, and integrates spectral clustering into the LRR optimization problem for better subspace clustering results. We also introduce a hierarchical subspace clustering approach, termed hierarchical CS-LRR, to learn the attributes without the need for a priori specification of their number. By visualizing and labeling these action attributes, the hierarchical model can be used to semantically summarize long video sequences of human actions at multiple resolutions. A human action or activity can also be uniquely represented as a sequence of transitions from one action attribute to another, which can then be used for human action recognition.
Subject (authority = RUETD)
Topic
Electrical and Computer Engineering
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Title
Rutgers University Electronic Theses and Dissertations
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ETD_8094
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electronic resource
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application/pdf
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text/xml
Extent
1 online resource (viii, 106 p. : ill.)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Tong Wu
RelatedItem (type = host)
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/T3C250C1
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

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The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Wu
GivenName
Tong
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2017-04-17 16:26:43
AssociatedEntity
Name
Tong Wu
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
Type
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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.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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