Structured Nonlinear Discriminant Analysis
Abstract
Many traditional machine learning and pattern recognition algorithms—as for example linear discriminant analysis (LDA) or principal component analysis (PCA)—optimize data representation with respect to an information theoretic criterion. For time series analysis these traditional techniques are typically insufficient. In this work we propose an extension to linear discriminant analysis that allows to learn a data representation based on an algebraic structure that is tailored for time series. Specifically we propose a generalization of LDA towards shift-invariance that is based on cyclic structures. We expand this framework towards more general structures, that allow to incorporate previous knowledge about the data at hand within the representation learning step. The effectiveness of this proposed approach is demonstrated on synthetic and real-world data sets. Finally, we show the interrelation of our approach to common machine learning and signal processing techniques.
Cite
Text
Bonenberger et al. "Structured Nonlinear Discriminant Analysis." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2022. doi:10.1007/978-3-031-26387-3_3Markdown
[Bonenberger et al. "Structured Nonlinear Discriminant Analysis." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2022.](https://mlanthology.org/ecmlpkdd/2022/bonenberger2022ecmlpkdd-structured/) doi:10.1007/978-3-031-26387-3_3BibTeX
@inproceedings{bonenberger2022ecmlpkdd-structured,
title = {{Structured Nonlinear Discriminant Analysis}},
author = {Bonenberger, Christopher M. A. and Ertel, Wolfgang and Schneider, Markus and Schwenker, Friedhelm},
booktitle = {European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases},
year = {2022},
pages = {38-54},
doi = {10.1007/978-3-031-26387-3_3},
url = {https://mlanthology.org/ecmlpkdd/2022/bonenberger2022ecmlpkdd-structured/}
}