NDLI: Gershgorin Analysis of Random Gramian Matrices With Application to MDS Tracking

Content Provider	IEEE Xplore Digital Library
Author	Macagnano, D. de Abreu, G.T.F.
Copyright Year	1991
Abstract	We offer a redesigned form of the multidimensional scaling (MDS) algorithm suitable to the simultaneous tracking of a large number of targets with no a priori mobility models. First, we employ an extreme-value and asymptotic take on the theory of Gershgorin spectrum bounds to perform a detailed statistical analysis of the spectrum of random N × N Gramian matrices which arise from dynamic constructions of MDS kernels where the diagonalizer of a previous kernel is used to construct the next one. The analysis reveals that even if the subspace distance between consecutive kernels is relatively large, the dominant eigenspace of dynamic MDS kernels are, with a high probability quantified analytically, associated with its first rows. This feature is exploited further to design a statistically optimized and truncated variation of the Jacobi algorithm, which converges to the dominant eigenspace of a dynamic MDS kernel as fast as the overall optimal Jacobian, but without the exhaustive search for the elements to be annihilated at each rotation as required in the latter. Under the fact that the Euclidean double-centered kernels of the classic MDS method are asymptotically Gramian, and the knowledge of Nyström-inspired methods to compensate for data erasures, the technique presented yields a very efficient (fast) MDS-based multitarget tracking algorithm which achieves a remarkably low complexity of order O(√(N)), and which is robust to arbitrary statistics of the target's dynamics.
Sponsorship	IEEE Signal Processing Society
Starting Page	1785
Ending Page	1800
Page Count	16
File Size	911642
File Format	PDF
ISSN	1053587X
Volume Number	59
Issue Number	4
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-04-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Kernel Heuristic algorithms Signal processing algorithms Jacobian matrices Algorithm design and analysis Matrix decomposition Target tracking range-based measurements Gershgorin discs Jacobi algorithm multidimensional scaling (MDS) multitarget tracking
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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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