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Divergence Based Graph Estimation for Manifold Learning

Full Text: aboumoustafa_globalsip.pdf PDF

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 embeddings of the data. 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 $mathbb{X}$, and then use $(mathbb{X},d_{mathbb{X}})$ as a new (pilot) input space for manifold learning. The proposed framework results in significantly improved embeddings, which we demonstrated objectively by assessing clustering accuracy.

Citation

K. Abou-Moustafa, F. Ferrie, D. Schuurmans. "Divergence Based Graph Estimation for Manifold Learning". IEEE Global Conference on Signal and Information Processing, December 2013.

Keywords: Manifold learning, divergence measures, neighbourhood graphs, graph topology estimation, divergence based graphs
Category: In Conference

BibTeX

@incollection{Abou-Moustafa+al:IEEEGLOBSIP13,
  author = {Karim Tamer Abou-Moustafa and Frank Ferrie and Dale Schuurmans},
  title = {Divergence Based Graph Estimation for Manifold Learning},
  booktitle = {IEEE Global Conference on Signal and Information Processing},
  year = 2013,
}

Last Updated: October 25, 2013
Submitted by Karim T. Abou-Moustafa

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