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Two Topics in Data Analysis: Sample-...

Kuang, Simeng Max.

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Two Topics in Data Analysis: Sample-based Optimal Transport and Analysis of Turbulent Spectra from Ship Track Data.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Two Topics in Data Analysis: Sample-based Optimal Transport and Analysis of Turbulent Spectra from Ship Track Data./
Author:	Kuang, Simeng Max.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2017,
Description:	167 p.
Notes:	Source: Dissertation Abstracts International, Volume: 79-01(E), Section: B.
Contained By:	Dissertation Abstracts International79-01B(E).
Subject:	Applied mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10261148
ISBN:	9780355128314

Two Topics in Data Analysis: Sample-based Optimal Transport and Analysis of Turbulent Spectra from Ship Track Data.
Kuang, Simeng Max.

Two Topics in Data Analysis: Sample-based Optimal Transport and Analysis of Turbulent Spectra from Ship Track Data. - Ann Arbor : ProQuest Dissertations & Theses, 2017 - 167 p.

Source: Dissertation Abstracts International, Volume: 79-01(E), Section: B.

Thesis (Ph.D.)--New York University, 2017.

This thesis contains two topics in data analysis.

ISBN: 9780355128314Subjects--Topical Terms:

2122814
Applied mathematics.

Two Topics in Data Analysis: Sample-based Optimal Transport and Analysis of Turbulent Spectra from Ship Track Data.
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100 1 $a Kuang, Simeng Max. $3 3427141
245 1 0 $a Two Topics in Data Analysis: Sample-based Optimal Transport and Analysis of Turbulent Spectra from Ship Track Data.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2017
300 $a 167 p.
500 $a Source: Dissertation Abstracts International, Volume: 79-01(E), Section: B.
500 $a Adviser: Esteban G. Tabak.
502 $a Thesis (Ph.D.)--New York University, 2017.
520 $a This thesis contains two topics in data analysis.
520 $a The first topic consists of the introduction of algorithms for sample-based optimal transport and barycenter problems.
520 $a In chapter 1, a family of algorithms is introduced to solve both the L2 optimal transport problem and the Wasserstein barycenter problem. Starting from a theoretical perspective, the new algorithms are motivated from a key characterization of the barycenter measure, which suggests an update that reduces the total transportation cost and stops only when the barycenter is reached. A series of general theorems is given to prove the convergence of all the algorithms. We then extend the algorithms to solve sample-based optimal transport and barycenter problems, in which only finite sample sets are available instead of underlying probability distributions. A unique feature of the new approach is that it compares sample sets in terms of the expected values of a set of feature functions, which at the same time induce the function space of optimal maps and can be chosen by users to incorporate their prior knowledge of the data. All the algorithms are implemented and applied to various synthetic example and practical applications. On synthetic examples it is found that both the SOT algorithm and the SCB algorithm are able to find the true solution and often converge in a handful of iterations. On more challenging applications including Gaussian mixture models, color transfer and shape transform problems, the algorithms give very good results throughout despite the very different nature of the corresponding datasets.
520 $a In chapter 2, a preconditioning procedure is developed for the L2 and more general optimal transport problems. The procedure is based on a family of affine map pairs, which transforms the original measures into two new measures that are closer to each other, while preserving the optimality of solutions. It is proved that the preconditioning procedure minimizes the remaining transportation cost among all admissible affine maps. The procedure can be used on both continuous measures and finite sample sets from distributions. In numerical examples, the procedure is applied to multivariate normal distributions, to a two-dimensional shape transform problem and to color transfer problems.
520 $a For the second topic, we present an extension to anisotropic flows of the recently developed Helmholtz and wave-vortex decomposition method for one-dimensional spectra measured along ship or aircraft tracks in Buhler et al. (J. Fluid Mech., vol. 756, 2014, pp. 1007--1026). While in the original method the flow was assumed to be homogeneous and isotropic in the horizontal plane, we allow the flow to have a simple kind of horizontal anisotropy that is chosen in a self-consistent manner and can be deduced from the one-dimensional power spectra of the horizontal velocity fields and their cross-correlation. The key result is that an exact and robust Helmholtz decomposition of the horizontal kinetic energy spectrum can be achieved in this anisotropic flow setting, which then also allows the subsequent wave-vortex decomposition step. The new method is developed theoretically and tested with encouraging results on challenging synthetic data as well as on ocean data from the Gulf Stream.
590 $a School code: 0146.
650 4 $a Applied mathematics. $3 2122814
650 4 $a Physical oceanography. $3 3168433
690 $a 0364
690 $a 0415
710 2 $a New York University. $b Mathematics. $3 1019424
773 0 $t Dissertation Abstracts International $g 79-01B(E).
790 $a 0146
791 $a Ph.D.
792 $a 2017
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10261148