Spline Embedding for Nonlinear Dimensionality Reduction
Abstract
This paper presents a new algorithm for nonlinear dimensionality reduction (NLDR). Smoothing splines are used to map the locally-coordinatized data points into a single global coordinate system of lower dimensionality. In this work setting, we can achieve two goals. First, a global embedding is obtained by minimizing the low-dimensional coordinate reconstruction error. Second, the NLDR algorithm can be naturally extended to deal with out-of-sample data points. Experimental results illustrate the validity of our method.
Cite
Text
Xiang et al. "Spline Embedding for Nonlinear Dimensionality Reduction." European Conference on Machine Learning, 2006. doi:10.1007/11871842_85Markdown
[Xiang et al. "Spline Embedding for Nonlinear Dimensionality Reduction." European Conference on Machine Learning, 2006.](https://mlanthology.org/ecmlpkdd/2006/xiang2006ecml-spline/) doi:10.1007/11871842_85BibTeX
@inproceedings{xiang2006ecml-spline,
title = {{Spline Embedding for Nonlinear Dimensionality Reduction}},
author = {Xiang, Shiming and Nie, Feiping and Zhang, Changshui and Zhang, Chunxia},
booktitle = {European Conference on Machine Learning},
year = {2006},
pages = {825-832},
doi = {10.1007/11871842_85},
url = {https://mlanthology.org/ecmlpkdd/2006/xiang2006ecml-spline/}
}