This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.
Browsing Institute for Systems Research Technical Reports by Author "Afsari, Bijan"
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.
We present a new scale-invariant cost function for non-orthogonal joint-diagonalization of a set of symmetric matrices with application to Independent Component Analysis (ICA). We derive two gradient minimization schemes to minimize this cost function. We also consider their performance in the context of an ICA algorithm based on non-orthogonal joint diagonalization.