Multimodal Manifold Analysis by Simultaneous Diagonalization of Laplacians

Davide Eynard, Artiom Kovnatsky, Michael M. Bronstein, Klaus Glashoff, Alexander M. Bronstein

Research output: Contribution to journalArticlepeer-review

Abstract

We construct an extension of spectral and diffusion geometry to multiple modalities through simultaneous diagonalization of Laplacian matrices. This naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of manifold learning, object classification, and clustering, showing that the joint spectral geometry better captures the inherent structure of multi-modal data. We also show the relation of many previous approaches for multimodal manifold analysis to our framework.

Original languageEnglish
Article number7053905
Pages (from-to)2505-2517
Number of pages13
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Volume37
Issue number12
DOIs
StatePublished - 1 Dec 2015
Externally publishedYes

Keywords

  • Joint diagonalization
  • Laplace-Beltrami operator
  • diffusion distances
  • dimensionality reduction
  • manifold alignment
  • manifold learning
  • multimodal clustering
  • multimodal data

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