Name
Title | ||
|---|---|---|
Distance regression by Gauss–Newton-type methods and iteratively re-weighted least-squares |
Abstract | ||
|---|---|---|
We discuss the problem of fitting a curve or surface to given measurement data. In many situations, the usual least-squares approach (minimization of the sum of squared norms of residual vectors) is not suitable, as it implicitly assumes a Gaussian distribution of the measurement errors. In those cases, it is more appropriate to minimize other functions (which we will call norm-like functions) of the residual vectors. This is well understood in the case of scalar residuals, where the technique of iteratively re-weighted least-squares, which originated in statistics (Huber in Robust statistics, 1981) is known to be a Gauss–Newton-type method for minimizing a sum of norm-like functions of the residuals. We extend this result to the case of vector-valued residuals. It is shown that simply treating the norms of the vector-valued residuals as scalar ones does not work. In order to illustrate the difference we provide a geometric interpretation of the iterative minimization procedures as evolution processes. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1007/s00607-009-0055-6 | Computing |
Keywords | DocType | Volume |
curve and surface fitting · iteratively re-weighted least squares · gauss-newton method · fitting by evolution | Journal | 86 |
Issue | ISSN | Citations |
2-3 | 1436-5057 | 3 |
PageRank | References | Authors |
0.41 | 9 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Martin Aigner | 1 | 3 | 0.41 |
| Bert Jüttler | 2 | 1148 | 96.12 |