[en] Independent Component Analysis is a popular statistical method for separating a multivariate signal into additive components. It has been shown that the signal separation problem can be reduced to the joint diagonalization of the matrix slices of some higher-order cumulants of the signal. In this approach, the unknown mixing matrix can be computed directly from the obtained joint diagonalizer. Various iterative algorithms for solving the non-convex joint diagonalization problem exist, but they usually lack global optimality guarantees. In this paper, we introduce a procedure for computing an optimality gap for local optimal solutions. The optimality gap is then used to obtain an empirical error bound for the estimated mixing matrix. Finally, a class of simultaneous matrix decomposition problems that admit such relaxation procedure is identified.
Disciplines :
Mathematics
Author, co-author :
Colombo, Nicolo ; University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
Thunberg, Johan ; University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
Goncalves, Jorge ; University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
External co-authors :
no
Language :
English
Title :
Global Optimality Bounds for ICA Algorithms
Publication date :
2016
Event name :
22nd International Symposium on Mathematical Theory of Networks and Systems
Event date :
July 12-15
Main work title :
22nd International Symposium on Mathematical Theory of Networks and Systems
Peer reviewed :
Peer reviewed
FnR Project :
FNR8864515 - Set Convergence In Nonlinear Multi-agent Systems, 2014 (01/02/2015-31/01/2017) - Johan Thunberg