Name
Title | ||
|---|---|---|
Joint Low-Rank Factorizations With Shared And Unshared Components: Identifiability And Algorithms |
Abstract | ||
|---|---|---|
We study the joint low-rank factorization of the matrices X=[A B]G and Y=[A C]H, in which the columns of the shared factor matrix A correspond to vectorized rank-one matrices, the unshared factors B and C have full column rank, and the matrices G and H have full row rank. The objective is to find the shared factor A, given only X and Y. We first explain that if the matrix [A B C] has full column rank, then a basis for the column space of the shared factor matrix A can be obtained from the null space of the matrix [X Y]. This in turn implies that the problem of finding the shared factor matrix A boils down to a basic Canonical Polyadic Decomposition (CPD) problem that in many cases can directly he solved by means of an eigenvalue decomposition. Next, we explain that by taking the rank-one constraint of the columns of the shared factor matrix A into account when computing the null space of the matrix [X Y], more relaxed identifiability conditions can be obtained that do not require that [A B C] has full column rank. The benefit of the unconstrained null space approach is that it leads to simple algorithms while the benefit of the rank-one constrained null space approach is that it leads to relaxed identifiability conditions. Finally, a joint unbalanced orthogonal Procrustes and CPD fitting approach for computing the shared factor matrix A from noisy observation matrices X and Y will briefly he discussed. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.23919/EUSIPCO.2019.8903050 | 2019 27TH EUROPEAN SIGNAL PROCESSING CONFERENCE (EUSIPCO) |
Keywords | Field | DocType |
Coupled decompositions, canonical polyadic decomposition (CPD), joint low-rank tensor factorizations, joint unbalanced orthogonal Procrustes and CPD fitting, joint dimensionality reduction and CPD fitting | Kernel (linear algebra),Combinatorics,Identifiability,Matrix (mathematics),Column space,Eigendecomposition of a matrix,Factorization,SIMPLE algorithm,Mathematics,Procrustes | Conference |
ISSN | Citations | PageRank |
2076-1465 | 0 | 0.34 |
References | Authors | |
0 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mikael Sørensen | 1 | 0 | 0.68 |
| Nikolaos D. Sidiropoulos | 2 | 0 | 0.34 |