Non-Linear Dimensionality Reduction: A Comparative Performance Analysis

Olivier Y. de Vel, Sofianto Li, Danny Coomans
Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics, PMLR R0:186-191, 1995.

Abstract

We present an analysis of the comparative performance of non-linear dimensionality reduction methods such as Non-Linear Mapping, NonMetric Multidimensional Scaling and the Kohonen Self-Organising Feature Map for which data sets of different dimensions are used. To obtain comparative measures of how well the mapping is performed, Procrustes analysis, the Spearman rank correlation coefficient and the scatter-plot diagram are used. Results indicate that, in low dimensions, Non-Linear Mapping has the best performance especially when measured in terms of the Spearman rank correlation coefficient. The output from the Kohonen SelfOrganising Feature Map is easier to interpret than the output from the other methods as it often provides a superior qualitative visual output. Also, the Kohonen Self-Organising Feature Map may outperform the other methods in a high-dimensional setting.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR0-vel95a, title = {Non-Linear Dimensionality Reduction: {A} Comparative Performance Analysis}, author = {de Vel, Olivier Y. and Li, Sofianto and Coomans, Danny}, booktitle = {Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics}, pages = {186--191}, year = {1995}, editor = {Fisher, Doug and Lenz, Hans-Joachim}, volume = {R0}, series = {Proceedings of Machine Learning Research}, month = {04--07 Jan}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/r0/vel95a/vel95a.pdf}, url = {https://proceedings.mlr.press/r0/vel95a.html}, abstract = {We present an analysis of the comparative performance of non-linear dimensionality reduction methods such as Non-Linear Mapping, NonMetric Multidimensional Scaling and the Kohonen Self-Organising Feature Map for which data sets of different dimensions are used. To obtain comparative measures of how well the mapping is performed, Procrustes analysis, the Spearman rank correlation coefficient and the scatter-plot diagram are used. Results indicate that, in low dimensions, Non-Linear Mapping has the best performance especially when measured in terms of the Spearman rank correlation coefficient. The output from the Kohonen SelfOrganising Feature Map is easier to interpret than the output from the other methods as it often provides a superior qualitative visual output. Also, the Kohonen Self-Organising Feature Map may outperform the other methods in a high-dimensional setting.}, note = {Reissued by PMLR on 01 May 2022.} }
Endnote
%0 Conference Paper %T Non-Linear Dimensionality Reduction: A Comparative Performance Analysis %A Olivier Y. de Vel %A Sofianto Li %A Danny Coomans %B Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 1995 %E Doug Fisher %E Hans-Joachim Lenz %F pmlr-vR0-vel95a %I PMLR %P 186--191 %U https://proceedings.mlr.press/r0/vel95a.html %V R0 %X We present an analysis of the comparative performance of non-linear dimensionality reduction methods such as Non-Linear Mapping, NonMetric Multidimensional Scaling and the Kohonen Self-Organising Feature Map for which data sets of different dimensions are used. To obtain comparative measures of how well the mapping is performed, Procrustes analysis, the Spearman rank correlation coefficient and the scatter-plot diagram are used. Results indicate that, in low dimensions, Non-Linear Mapping has the best performance especially when measured in terms of the Spearman rank correlation coefficient. The output from the Kohonen SelfOrganising Feature Map is easier to interpret than the output from the other methods as it often provides a superior qualitative visual output. Also, the Kohonen Self-Organising Feature Map may outperform the other methods in a high-dimensional setting. %Z Reissued by PMLR on 01 May 2022.
APA
de Vel, O.Y., Li, S. & Coomans, D.. (1995). Non-Linear Dimensionality Reduction: A Comparative Performance Analysis. Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research R0:186-191 Available from https://proceedings.mlr.press/r0/vel95a.html. Reissued by PMLR on 01 May 2022.

Related Material