Lagrangian gradient for principal singular component analysis

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In this paper a framework for developing dynamical systems for solving optimization problems with orthogonal constraints are proposed. These systems are based on the Lagrangian gradient of the given constrained problem. By exploiting orthogonality and symmetry in the constraints, several dynamical systems for solving the same optimization problem are developed, and conditions for global stability of these systems are also given. As a special case, the reduced singular value decomposition is formulated as an optimization problem within this framework which resulted in a singular value dynamical system whose solution converges to the principal singular components of a given matrix.

Original languageEnglish (US)
Article number4253138
Pages (from-to)2315-2318
Number of pages4
JournalProceedings - IEEE International Symposium on Circuits and Systems
StatePublished - 2007
Event2007 IEEE International Symposium on Circuits and Systems, ISCAS 2007 - New Orleans, LA, United States
Duration: May 27 2007May 30 2007


  • Lagrangian gradient algorithms
  • Learning algorithms for optimization
  • Principal singular component analysis (PSCA)
  • Principal singular subspace (PSS)
  • Singular value decomposition (SVD)


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