Distortion-Free Nonlinear Dimensionality Reduction
Abstract
Nonlinear Dimensionality Reduction is an important issue in many machine learning areas where essentially low-dimensional data is nonlinearly embedded in some high-dimensional space. In this paper, we show that the existing Laplacian Eigenmaps method suffers from the distortion problem, and propose a new distortion-free dimensionality reduction method by adopting a local linear model to encode the local information. We introduce a new loss function that can be seen as a different way to construct the Laplacian matrix, and a new way to impose scaling constraints under the local linear model. Better low-dimensional embeddings are obtained via constrained concave convex procedure. Empirical studies and real-world applications have shown the effectiveness of our method.
Cite
Text
Jia et al. "Distortion-Free Nonlinear Dimensionality Reduction." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2008. doi:10.1007/978-3-540-87479-9_55Markdown
[Jia et al. "Distortion-Free Nonlinear Dimensionality Reduction." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2008.](https://mlanthology.org/ecmlpkdd/2008/jia2008ecmlpkdd-distortionfree/) doi:10.1007/978-3-540-87479-9_55BibTeX
@inproceedings{jia2008ecmlpkdd-distortionfree,
title = {{Distortion-Free Nonlinear Dimensionality Reduction}},
author = {Jia, Yangqing and Wang, Zheng and Zhang, Changshui},
booktitle = {European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases},
year = {2008},
pages = {564-579},
doi = {10.1007/978-3-540-87479-9_55},
url = {https://mlanthology.org/ecmlpkdd/2008/jia2008ecmlpkdd-distortionfree/}
}