Name
Abstract | ||
|---|---|---|
The problem of approximate joint diagonalization of a set of matrices is instrumental in numerous statistical signal processing applications. For nonorthogonal joint diagonalization based on the weighted least-squares (WLS) criterion, the trivial (zero) solution can simply be avoided by adopting some constraint on the diagonalizing matrix or penalty terms. However, the resultant algorithms may converge to some undesired degenerate solutions (nonzero but singular or ill-conditioned solutions). This paper discusses and analyzes the problem of degenerate solutions in detail. To solve this problem, a novel nonleast-squares criterion for approximate nonorthogonal joint diagonalization is proposed and an efficient algorithm, called fast approximate joint diagonalization (FAJD), is developed. As compared with the existing nonorthogonal diagonalization algorithms, the new algorithm can not only avoid the trivial solution but also any degenerate solutions. Theoretical analysis shows that the FAJD algorithm has some advantages over the existing nonorthogonal diagonalization algorithms. Simulation results are presented to demonstrate the efficiency of this paper's algorithm |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1109/TSP.2006.889983 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
nonorthogonal joint diagonalization,ill-conditioned solution,existing nonorthogonal diagonalization algorithm,resultant algorithm,degenerate solution,fajd algorithm,approximate nonorthogonal joint diagonalization,approximate joint diagonalization,novel nonleast-squares criterion,new algorithm,efficient algorithm,nonorthogonal joint diagonalization free,matrix decomposition,signal processing,machine learning,nonlinear optimization,statistical signal processing,algorithm design and analysis,blind source separation,independent component analysis | Degenerate energy levels,Mathematical optimization,Orthogonal diagonalization,Algorithm design,Matrix (mathematics),Matrix decomposition,Nonlinear programming,Blind signal separation,Source separation,Mathematics | Journal |
Volume | Issue | ISSN |
55 | 5 | 1053-587X |
Citations | PageRank | References |
69 | 3.11 | 15 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xi-Lin Li | 1 | 547 | 34.85 |
| Xianda Zhang | 2 | 809 | 68.13 |