Learning a metric space for neighbourhood topology estimation. Application to manifold learning
- Karim Tamer Abou-Moustafa, AICML and Dept. of Computing Science
- Dale Schuurmans, AICML
- Frank Ferrie, McGill University
Manifold learning algorithms rely on a neighbourhood graph to provide an estimate of the data's local topology. Unfortunately, current methods for estimating local topology assume local Euclidean geometry and locally uniform data density, which often leads to poor data embeddings. We address these shortcomings by proposing a framework that combines local learning with parametric density estimation for local topology estimation. Given a data set $mathcal{D} subset mathcal{X}$, we first estimate a new metric space $(mathbb{X},d_{mathbb{X}})$ that characterizes the varying sample density of $mathcal{X}$ in $mathbb{X}$, then use $(mathbb{X},d_{mathbb{X}})$ as a new (pilot) input space for the graph construction step of the manifold learning process. The proposed framework results in significantly improved embeddings, which we demonstrated objectively by assessing clustering accuracy.
Citation
K. Abou-Moustafa, D. Schuurmans, F. Ferrie. "Learning a metric space for neighbourhood topology estimation. Application to manifold learning". Asian Conference on Machine Learning, (ed: Cheng Soon Ong and Tu Bao Ho), pp 1-16, November 2013.| Keywords: | Manifold learning, neighbourhood graphs, neighbourhood topology, divergence based graphs, low rank covariance matrix estimation |
| Category: | In Conference |
BibTeX
@incollection{Abou-Moustafa+al:ACML13,
author = {Karim Tamer Abou-Moustafa and Dale Schuurmans and Frank Ferrie},
title = {Learning a metric space for neighbourhood topology estimation.
Application to manifold learning},
Editor = {Cheng Soon Ong and Tu Bao Ho},
Pages = {1-16},
booktitle = {Asian Conference on Machine Learning},
year = 2013,
}Last Updated: October 25, 2013Submitted by Karim T. Abou-Moustafa
