Paper Info
Title
Sensitivity Analysis for the Problem of Matrix Joint Diagonalization
Abstract
We investigate the sensitivity of the problem of nonorthogonal (matrix) joint diagonalization (NOJD). First, we consider the uniqueness conditions for the problem of exact joint diagonalization (EJD), which is closely related to the issue of uniqueness in tensor decompositions. As a byproduct, we derive the well-known identifiability conditions for independent component analysis (ICA) based on an EJD formulation of ICA. We next introduce some known cost functions for NOJD and derive flows based on these cost functions for NOJD. Then we define and investigate the noise sensitivity of the stationary points of these flows. We show that the condition number of the joint diagonalizer and uniqueness of the joint diagonalizer as measured by modulus of uniqueness (as defined in this paper) affect the sensitivity. We also investigate the effect of the number of matrices on the sensitivity. Our numerical experiments confirm the theoretical results.While this paper was under review a few of its results were presented in ICASSP07 conference in Honolulu, HI .
Year
DOI
Venue
2008
10.1137/060655997
SIAM J. Matrix Analysis Applications
Keywords
Field
DocType
sensitivity analysis,ejd formulation,matrix joint diagonalization,joint diagonalization,known cost function,uniqueness condition,cost function,noise sensitivity,icassp07 conference,joint diagonalizer,exact joint diagonalization,condition number,independent component analysis,perturbation analysis
Uniqueness,Condition number,Diagonalizable matrix,Matrix (mathematics),Mathematical analysis,Identifiability,Decomposition method (constraint satisfaction),Stationary point,Independent component analysis,Mathematics
Journal
Volume
Issue
ISSN
30
3
0895-4798
Citations 
PageRank 
References 
16
0.98
6
Authors
1
Name
Order
Citations
PageRank
Bijan Afsari113710.27