Abstract

Modern engineering systems collect large volumes of data measurements across diverse sensing modalities. These measurements can naturally be arranged in higher-order arrays of scalars which are commonly referred to as tensors. Tucker decomposition (TD) is a standard method for tensor analysis with applications in diverse fields of science and engineering. Despite its success, TD exhibits severe sensitivity against outliers —i.e., heavily corrupted entries that appear sporadically in modern datasets. We study L1-norm TD (L1-TD), a reformulation of TD that promotes robustness. For 3-way tensors, we show, for the first time, that L1-TD admits an exact solution via combinatorial optimization and present algorithms for its solution. We propose two novel algorithmic frameworks for approximating the exact solution to L1-TD, for general N-way tensors. We propose a novel algorithm for dynamic L1-TD —i.e., efficient and joint analysis of streaming tensors. Principal-Component Analysis (PCA) (a special case of TD) is also outlier responsive. We consider Lp-quasinorm PCA (Lp-PCA) for p

Library of Congress Subject Headings

Multisensor data fusion--Mathematics; Tensor algebra; Machine learning; Signal processing--Mathematics; Principal components analysis--Evaluation; High performance computing

Publication Date

4-2021

Document Type

Dissertation

Student Type

Graduate

Degree Name

Electrical and Computer Engineering (Ph.D)

Department, Program, or Center

Department of Electrical and Microelectronic Engineering (KGCOE)

Advisor

Panos P. Markopoulos

Advisor/Committee Member

Sohail Dianat

Advisor/Committee Member

Andreas Savakis

Campus

RIT – Main Campus

Plan Codes

ENGR-PHD

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