Matrix formulation and singular-value decomposition algorithm for structured varimax rotation in multivariate singular spectrum analysis

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dc.creatorLeonardo L. Portes
dc.creatorLuis Antonio Aguirre
dc.date.accessioned2025-03-26T13:28:10Z
dc.date.accessioned2025-09-08T23:00:11Z
dc.date.available2025-03-26T13:28:10Z
dc.date.issued2016
dc.description.sponsorshipCNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico
dc.identifier.doi10.1103/PhysRevE.93.052216
dc.identifier.issn2470-0045
dc.identifier.urihttps://hdl.handle.net/1843/80929
dc.languageeng
dc.publisherUniversidade Federal de Minas Gerais
dc.relation.ispartofPhysical Review E
dc.rightsAcesso Restrito
dc.subjectEngenharia elétrica
dc.subjectSistemas lineares
dc.subjectEngenharia de sistemas
dc.subjectComputadores digitais
dc.subject.othermatrix formulation allows the simultaneous rotation of theM-SSA eigenvectors and the use of fast singular value decomposition algorithms
dc.subject.othermore complex chaotic funnel regime, theUVR impairs the ability of the M-SSA in the identification of different time scales, whereasthe SVR enhances it
dc.subject.othersynchronization phenomena in large systems
dc.titleMatrix formulation and singular-value decomposition algorithm for structured varimax rotation in multivariate singular spectrum analysis
dc.typeArtigo de periódico
local.citation.issue5
local.citation.spage052216
local.citation.volume93
local.description.resumoGroth and Ghil [Phys. Rev. E 84, 036206 (2011)] developed a modified varimax rotation aimed at enhancing the ability of the multivariate singular spectrum analysis (M-SSA) to characterize phase synchronization in systems of coupled chaotic oscillators. Due to the special structure of the M-SSA eigenvectors, the modification proposed by Groth and Ghil imposes a constraint in the rotation of blocks of components associated with the different subsystems. Accordingly, here we call it a structured varimax rotation (SVR). The SVR was presented as successive pairwise rotations of the eigenvectors. The aim of this paper is threefold. First, we develop a closed matrix formulation for the entire family of structured orthomax rotation criteria, for which the SVR is a special case. Second, this matrix approach is used to enable the use of known singular value algorithms for fast computation, allowing a simultaneous rotation of the M-SSA eigenvectors (a Python code is provided in the Appendix). This could be critical in the characterization of phase synchronization phenomena in large real systems of coupled oscillators. Furthermore, the closed algebraic matrix formulation could be used in theoretical studies of the (modified) M-SSA approach. Third, we illustrate the use of the proposed singular value algorithm for the SVR in the context of the two benchmark examples of Groth and Ghil: the Rössler system in the chaotic (i) phase-coherent and (ii) funnel regimes. Comparison with the results obtained with Kaiser's original (unstructured) varimax rotation (UVR) reveals that both SVR and UVR give the same result for the phase-coherent scenario, but for the more complex behavior (ii) only the SVR improves on the M-SSA.
local.publisher.countryBrasil
local.publisher.departmentENG - DEPARTAMENTO DE ENGENHARIA ELETRÔNICA
local.publisher.initialsUFMG
local.url.externahttps://journals.aps.org/pre/abstract/10.1103/PhysRevE.93.052216

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