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Title: Non-Unique Games Over Compact Groups and Applications
Authors: Chen, Yutong
Advisors: Singer, Amit
Contributors: Applied and Computational Mathematics Department
Keywords: cryo-EM
representation theory
semidefinite programming
Subjects: Mathematics
Issue Date: 2018
Publisher: Princeton, NJ : Princeton University
Abstract: Let G be a compact group and let fij 2 L2(G). We dene the Non-Unique Games (NUG) problem as nding g1; : : : ; gn 2 G to minimize Pn i;j=1 fij ô€€€ gigô€€€1 j . We devise a relaxation of the NUG problem to a semidenite program (SDP) by taking the Fourier transform of fij over G, which can then be solved eciently. The NUG framework can be seen as a generalization of the Unique Games problem and the little Grothendieck problem over the orthogonal group, and includes many practically relevant problems, such as the maximum likelihood estimator to registering bandlimited functions over the unit sphere in d-dimensions and orientation estimation in cryo-Electron Microscopy.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Applied and Computational Mathematics

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