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Riemannian Optimization for Convex and Non-Convex Signal Processing and Machine Learning Applications


Douik, Ahmed (2020) Riemannian Optimization for Convex and Non-Convex Signal Processing and Machine Learning Applications. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/jt3c-0m30.


The performance of most algorithms for signal processing and machine learning applications highly depends on the underlying optimization algorithms. Multiple techniques have been proposed for solving convex and non-convex problems such as interior-point methods and semidefinite programming. However, it is well known that these algorithms are not ideally suited for large-scale optimization with a high number of variables and/or constraints. This thesis exploits a novel optimization method, known as Riemannian optimization, for efficiently solving convex and non-convex problems with signal processing and machine learning applications. Unlike most optimization techniques whose complexities increase with the number of constraints, Riemannian methods smartly exploit the structure of the search space, a.k.a., the set of feasible solutions, to reduce the embedded dimension and efficiently solve optimization problems in a reasonable time. However, such efficiency comes at the expense of universality as the geometry of each manifold needs to be investigated individually. This thesis explains the steps of designing first and second-order Riemannian optimization methods for smooth matrix manifolds through the study and design of optimization algorithms for various applications. In particular, the paper is interested in contemporary applications in signal processing and machine learning, such as community detection, graph-based clustering, phase retrieval, and indoor and outdoor location determination. Simulation results are provided to attest to the efficiency of the proposed methods against popular generic and specialized solvers for each of the above applications.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Riemannian manifolds, convex and non-convex optimization, graph-based clustering, phase retrieval, spatial localization.
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Electrical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Hassibi, Babak
Thesis Committee:
  • Vaidyanathan, P. P. (chair)
  • Kostina, Victoria
  • Tropp, Joel A.
  • Chandrasekaran, Venkat
  • Hassibi, Babak
Defense Date:27 May 2020
Record Number:CaltechTHESIS:06012020-120425051
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for ch. 6 adapted for ch. 1 adapted for ch. 3 adapted for ch. 3 adapted for ch. 4 adapted for ch. 4 adapted for ch. 5
Douik, Ahmed0000-0001-7791-9443
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13758
Deposited By: Ahmed Douik
Deposited On:09 Jun 2020 00:26
Last Modified:15 Jun 2020 18:05

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