Gradient Flow Based Matrix Joint Diagonalization for Independent Component Analysis

dc.contributor.advisorKrishnaprasad, P.S.en_US
dc.contributor.authorAfsari, Bijanen_US
dc.contributor.departmentISRen_US
dc.date.accessioned2007-05-23T10:15:54Z
dc.date.available2007-05-23T10:15:54Z
dc.date.issued2004en_US
dc.description.abstractIn this thesis, employing the theory of matrix Lie groups, we develop gradient based flows for the problem of Simultaneous or Joint Diagonalization (JD) of a set of symmetric matrices. This problem has applications in many fields especially in the field of Independent Component Analysis (ICA). We consider both orthogonal and non-orthogonal JD. We view the JD problem as minimization of a common quadric cost function on a matrix group. We derive gradient based flows together with suitable discretizations for minimization of this cost function on the Riemannian manifolds of O(n) and GL(n). We use the developed JD methods to introduce a new class of ICA algorithms that sphere the data, however do not restrict the subsequent search for the un-mixing matrix to orthogonal matrices. These methods provide robust ICA algorithms in Gaussian noise by making effective use of both second and higher order statistics.en_US
dc.format.extent1196064 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1903/6468
dc.language.isoen_USen_US
dc.relation.ispartofseriesISR; MS 2004-4en_US
dc.subjectIndependent Component Analysisen_US
dc.subjectOptimization on Lie groupsen_US
dc.titleGradient Flow Based Matrix Joint Diagonalization for Independent Component Analysisen_US
dc.typeThesisen_US

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