A sparse-grid-based out-of-sample extension for dimensionality reduction and clustering with Laplacian eigenmaps

Benjamin Peherstorfer, Dirk Pflüger, Hans Joachim Bungartz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Spectral graph theoretic methods such as Laplacian Eigenmaps are among the most popular algorithms for manifold learning and clustering. One drawback of these methods is, however, that they do not provide a natural out-of-sample extension. They only provide an embedding for the given training data. We propose to use sparse grid functions to approximate the eigenfunctions of the Laplace-Beltrami operator. We then have an explicit mapping between ambient and latent space. Thus, out-of-sample points can be mapped as well. We present results for synthetic and real-world examples to support the effectiveness of the sparse-grid-based explicit mapping.

Original languageEnglish (US)
Title of host publicationAI 2011
Subtitle of host publicationAdvances in Artificial Intelligence - 24th Australasian Joint Conference, Proceedings
Pages112-121
Number of pages10
DOIs
StatePublished - 2011
Event24th Australasian Joint Conference on Artificial Intelligence, AI 2011 - Perth, WA, Australia
Duration: Dec 5 2011Dec 8 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7106 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other24th Australasian Joint Conference on Artificial Intelligence, AI 2011
CountryAustralia
CityPerth, WA
Period12/5/1112/8/11

Keywords

  • clustering
  • manifold learning
  • sparse grids
  • spectral methods

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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