Gradient Flow Based Matrix Joint Diagonalization for Independent Component Analysis

Abstract

In 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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2004
Accession Number
ADA453259

Entities

People

  • Bijan Afsari

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Energy and Power Technologies
  • Sensors

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Differential Equations
  • Differential Geometry
  • Dynamic Range
  • Equations
  • Geometry
  • Lie Groups
  • Numerical Analysis
  • Order Statistics
  • Random Variables
  • Runge Kutta Method
  • Signal Processing
  • Statistics
  • Stochastic Processes
  • Theorems
  • Vector Spaces

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