NDLI: A relaxation-based approach for the orthogonal Procrustes problem with data uncertainties

Content Provider	IEEE Xplore Digital Library
Author	Ahmed, S. Jaimoukha, I.M.
Copyright Year	2012
Description	Author affiliation: Department of Electrical and Electronic Engineering, Imperial College London, UK (Ahmed, S.; Jaimoukha, I.M.)
Abstract	The orthogonal Procrustes problem (OPP) deals with matrix approximations. The solution of this problem gives an orthogonal matrix to best transform one data matrix to another, in a Frobenius norm sense. In this work, we use semidefinite relaxation (SDR) to find the solutions of different OPP formulations. For the standard problem formulation, this approach yields an exact solution, i.e. no relaxation gap. We also address uncertainties in the data matrices and formulate a min-max robust problem. The robust problem, being non-convex, turns out to be a difficult optimization problem; however, it is relatively straight forward to approximate it into a convex optimization problem using SDR. Our preliminary results on robust problem show that the solution of the relaxed uncertain problem does not guarantee zero relaxation gap, and as a result, we cannot always find a solution, which satisfies the orthogonality constraint. In such cases we use orthogonalization, which gives the nearest orthogonal matrix from the SDR based solution. All these relaxed formulations, can be easily converted into a semidefinite program (SDP), for which polynomial time efficient algorithms exists. For the nominal problems, the presented approach may not be computationally efficient than other existing methods. In this work, our main contribution is to demonstrate that the SDR approach provides a unified framework to solve not only the standard OPP but can also solve the problems with uncertainties in the data matrices, which other existing approaches cannot handle.
Starting Page	906
Ending Page	911
File Size	550850
Page Count	6
File Format	PDF
ISBN	9781467315593
e-ISBN	9781467315609
e-ISBN	9781467315586
DOI	10.1109/CONTROL.2012.6334752
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-09-03
Publisher Place	United Kingdom
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Uncertainty Transforms Cameras Robustness Standards Optimization Singular value decomposition
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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