Title :
A logarithmic cost function for principal singular component analysis
Author :
Hasan, Mohammed A.
Author_Institution :
Dept. of Electr. & Comput. Eng., Minnesota Univ., Duluth, MN
fDate :
March 31 2008-April 4 2008
Abstract :
An un-unconstrained optimization problem involving logarithmic cost function that incorporates a diagonal matrix is utilized for deriving gradient dynamical systems that converge to the principal singular components of arbitrary matrix. The equilibrium points of the resulting gradient systems are determined and their stability is thoroughly analyzed. Qualitative properties of the proposed systems are analyzed in detail including the limit of solutions as time approaches infinity. The performance of this system is also examined.
Keywords :
gradient methods; matrix algebra; numerical stability; optimisation; principal component analysis; diagonal matrix; gradient dynamical system; logarithmic cost function; principal singular component analysis; stability; unconstrained optimization; Asymptotic stability; Cost function; Differential equations; H infinity control; Lyapunov method; Matrix decomposition; Singular value decomposition; Stability analysis; Testing; SVD; asymptotic stability; global convergence; principal singular flow; unconstrained optimization;
Conference_Titel :
Acoustics, Speech and Signal Processing, 2008. ICASSP 2008. IEEE International Conference on
Conference_Location :
Las Vegas, NV
Print_ISBN :
978-1-4244-1483-3
Electronic_ISBN :
1520-6149
DOI :
10.1109/ICASSP.2008.4518014
