SENSITIVITY ANALYSIS FOR THE PROBLEM OF MATRIX JOINT DIAGONALIZATION

被引:47
|
作者
Afsari, Bijan [1 ]
机构
[1] Univ Maryland, Dept Appl Math, College Pk, MD 20740 USA
关键词
joint diagonalization; independent component analysis (ICA); simultaneous diagonalization; sensitivity analysis; perturbation analysis; CANDECOMP/PARAFAC; tensor decompositions;
D O I
10.1137/060655997
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 de. ne 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 the 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.
引用
收藏
页码:1148 / 1171
页数:24
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