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Dictionary learning and multidimensional processing for tensor data

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Title
Dictionary learning and multidimensional processing for tensor data
Name (type = personal)
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Shakeri
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Zahra
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1990-
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Zahra Shakeri
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author
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Waheed U.
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Waheed U. Bajwa
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Advisory Committee
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chair
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Sarwate
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Anand D.
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Anand D. Sarwate
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Advisory Committee
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internal member
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Petropulu
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Athina P.
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Athina P. Petropulu
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Advisory Committee
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internal member
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Eriksson
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Brian
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Brian Eriksson
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Advisory Committee
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outside member
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Rutgers University
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degree grantor
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School of Graduate Studies
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theses
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2019
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2019-10
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English
Abstract (type = abstract)
Modern machine learning and signal processing relies on finding meaningful and succinct representations of data. While most works in the literature have focused on finding representations of vector data, many of today's data are collected using various sensors and have a multidimensional structure. This dissertation addresses the problem of feature learning for tensor (i.e., multiway) data, which are defined as data having multiple modes. The work presented in this dissertation aims to study the theoretical and algorithmic aspects of dictionary learning from tensor data and further investigate the computational aspects of exploiting the structure of tensor data in wireless communication systems. The dissertation has been divided into three main parts.

The first part of the dissertation is focused on the theoretical aspects of Kronecker-structured dictionary learning from tensor data. Here, the structure of tensor data is exploited by requiring that the dictionary underlying the vectorized versions of tensor data samples be Kronecker structured. That is, it is comprised of coordinate dictionaries that independently transform various modes of the tensor data. The presented results are primarily stated in terms of lower and upper bounds on the sample complexity of dictionary learning, defined as the number of samples needed to reconstruct the true structured dictionary underlying the tensor data from noisy samples. These results highlight the effects of different parameters on the sample complexity of the problem and also bring out the potential advantages of structured dictionary learning from tensor data.

The second part of this dissertation focuses on extending the Kronecker-structured dictionary learning model to a less restrictive class of dictionaries referred to as low-separation-rank dictionary learning, while still exploiting the structure of tensor data in the underlying dictionary. Various computational algorithms are developed to learn such dictionaries in cases where tensor data are available in batch or are streaming in an online manner. Numerical experiments are provided to demonstrate the performance of the provided algorithms for synthetic tensor data representation and real-world image data denoising. These experiments highlight the advantages of the low-separation-rank dictionary learning model over Kronecker-structured dictionary learning for complex data classes such as images in the denoising problem.

The final part of the dissertation focuses on another application of sparse representations of tensor data and studies the sparse channel estimation problem in massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. By modeling the underlying wireless channel as a tensor, a sparse tensor recovery technique is used to estimate the channel using lower computational resources and storage at the receiver compared to vectorized representation methods. Numerical experiments are provided to compare the performance of the estimation algorithms corresponding to vectorized and tensor formulations. These results also highlight the effects of various training signal parameters on the channel estimation performance.
Subject (authority = RUETD)
Topic
Electrical and Computer Engineering
Subject (authority = local)
Topic
Dictionary learning
Subject (authority = LCSH)
Topic
Machine learning
RelatedItem (type = host)
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Title
Rutgers University Electronic Theses and Dissertations
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ETD_10082
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application/pdf
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text/xml
Extent
1 online resource (xiii, 167 pages) : illustrations
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
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School of Graduate Studies Electronic Theses and Dissertations
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rucore10001600001
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Identifier (type = doi)
doi:10.7282/t3-he9n-4916
Genre (authority = ExL-Esploro)
ETD doctoral
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The author owns the copyright to this work.
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Name
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Shakeri
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Zahra
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Type
Permission or license
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2019-06-18 18:12:11
AssociatedEntity
Name
Zahra Shakeri
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Copyright holder
Affiliation
Rutgers University. School of Graduate Studies
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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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Copyright protected
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Open
Reason
Permission or license
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2019-06-18T14:51:25
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2019-06-18T14:51:25
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