Name
Abstract | ||
|---|---|---|
We consider the problem of fitting a discrete curve to time-labeled data points on the set Pn of all n-by-n symmetric positive-definite matrices. The quality of a curve is measured by a weighted sum of a term that penalizes its lack of fit to the data and a regularization term that penalizes speed and acceleration. The corresponding objective function depends on the choice of a Riemannian metric on Pn. We consider the Euclidean metric, the Log-Euclidean metric and the affine-invariant metric. For each, we derive a numerical algorithm to minimize the objective function. We compare these in terms of reliability and speed, and we assess the visual appear ance of the solutions on examples for n = 2. Notably, we find that the Log-Euclidean and the affine-invariant metrics tend to yield similar-and sometimes identical-results, while the former allows for much faster and more reliable algorithms than the latter. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1109/ICASSP.2011.5947287 | Acoustics, Speech and Signal Processing |
Keywords | Field | DocType |
curve fitting,matrix algebra,regression analysis,Log-Euclidean metric,Riemannian metric,affine-invariant metric,discrete curve fitting,discrete regression methods,positive-definite matrices,time-labeled data points,Positive-definite matrices,Riemannian metrics,finite differences,non-parametric regression | Mathematical optimization,Curve fitting,Matrix (mathematics),Nonparametric regression,Euclidean distance,Positive-definite matrix,Intrinsic metric,Lack-of-fit sum of squares,Manifold,Mathematics | Conference |
ISSN | ISBN | Citations |
1520-6149 E-ISBN : 978-1-4577-0537-3 | 978-1-4577-0537-3 | 2 |
PageRank | References | Authors |
0.36 | 4 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Boumal, Nicolas | 1 | 178 | 14.50 |
| Pierre-Antoine Absil | 2 | 10 | 1.77 |