2021-03-18-cai21a.md

title	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Identification of Matrix Joint Block Diagonalization	Given a set $\mathcal{C}=\{C_i\}_{i=1}^m$ of square matrices, the matrix blind joint block diagonalization problem (BJBDP) is to find a full column rank matrix $A$ such that $C_i=A\Sigma_iA^{\T}$ for all $i$, where $\Sigma_i$’s are all block diagonal matrices with as many diagonal blocks as possible. The BJBDP plays an important role in independent subspace analysis. This paper considers the identification problem for BJBDP, that is, under what conditions and by what means, we can identify the diagonalizer $A$ and the block diagonal structure of $\Sigma_i$, especially when there is noise in $C_i$’s. In this paper, we propose a “bi-block diagonalization” method to solve BJBDP, and establish sufficient conditions for when the method is able to accomplish the task. Numerical simulations validate our theoretical results. To the best of the authors’ knowledge, current numerical methods for BJBDP have no theoretical guarantees for the identification of the exact solution, whereas our method does.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	cai21a	0	Identification of Matrix Joint Block Diagonalization	1495	1503	1495-1503	1495	false	Cai, Yunfeng and Li, Ping	given family Yunfeng Cai given family Ping Li	2021-03-18		Proceedings of The 24th International Conference on Artificial Intelligence and Statistics	130	inproceedings	date-parts 2021 3 18	http://proceedings.mlr.press/v130/cai21a/cai21a.pdf	label link Supplementary PDF http://proceedings.mlr.press/v130/cai21a/cai21a-supp.pdf