A Polygonal Line Algorithm for Constructing Principal Curves
Abstract
Principal curves have been defined as "self consistent" smooth curves which pass through the "middle" of a d-dimensional probability distri(cid:173) bution or data cloud. Recently, we [1] have offered a new approach by defining principal curves as continuous curves of a given length which minimize the expected squared distance between the curve and points of the space randomly chosen according to a given distribution. The new definition made it possible to carry out a theoretical analysis of learning principal curves from training data. In this paper we propose a practical construction based on the new definition. Simulation results demonstrate that the new algorithm compares favorably with previous methods both in terms of performance and computational complexity.
Cite
Text
Kégl et al. "A Polygonal Line Algorithm for Constructing Principal Curves." Neural Information Processing Systems, 1998.Markdown
[Kégl et al. "A Polygonal Line Algorithm for Constructing Principal Curves." Neural Information Processing Systems, 1998.](https://mlanthology.org/neurips/1998/kegl1998neurips-polygonal/)BibTeX
@inproceedings{kegl1998neurips-polygonal,
title = {{A Polygonal Line Algorithm for Constructing Principal Curves}},
author = {Kégl, Balázs and Krzyzak, Adam and Linder, Tamás and Zeger, Kenneth},
booktitle = {Neural Information Processing Systems},
year = {1998},
pages = {501-507},
url = {https://mlanthology.org/neurips/1998/kegl1998neurips-polygonal/}
}