Name
Abstract | ||
|---|---|---|
We study the problem of determining the one-dimensional structure that best represents a given data set. More precisely, we take a variational approach to approximating a given measure (data) by curves. We consider an objective functional whose minimizers are a regularization of principal curves and introduce a new functional which allows for multiple curves. We prove existence of minimizers and investigate their properties. While both of the functionals used are non-convex, we show that enlarging the configuration space to allow for multiple curves leads to a simpler energy landscape with fewer undesirable (high-energy) local minima. We provide an efficient algorithm for approximating minimizers of the functional and demonstrate its performance on real and synthetic data. The numerical examples illustrate the effectiveness of the proposed approach in the presence of substantial noise, and the viability of the algorithm for high-dimensional data. |
Year | DOI | Venue |
|---|---|---|
2015 | https://doi.org/10.1007/s10851-017-0730-8 | Journal of Mathematical Imaging and Vision |
Keywords | Field | DocType |
Principal curves,Geometry of data,Curve fitting,49M25,65D10,62G99,65D18,65K10,49Q20 | Family of curves,Mathematical analysis,Maxima and minima,Regularization (mathematics),Energy landscape,Mathematics,Principal curves,Computation,Configuration space | Journal |
Volume | Issue | ISSN |
abs/1512.05010 | 2 | 0924-9907 |
Citations | PageRank | References |
0 | 0.34 | 17 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Slav Kirov | 1 | 1 | 0.72 |
| Dejan Slepčev | 2 | 95 | 11.01 |