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Multiple Manifold Learning by Nonlinear Dimensionality Reduction

  • Juliana Valencia-Aguirre
  • Andrés Álvarez-Meza
  • Genaro Daza-Santacoloma
  • Carlos Acosta-Medina
  • César Germán Castellanos-Domínguez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7042)

Abstract

Methods for nonlinear dimensionality reduction have been widely used for different purposes, but they are constrained to single manifold datasets. Considering that in real world applications, like video and image analysis, datasets with multiple manifolds are common, we propose a framework to find a low-dimensional embedding for data lying on multiple manifolds. Our approach is inspired on the manifold learning algorithm Laplacian Eigenmaps - LEM, computing the relationships among samples of different datasets based on an intra manifold comparison to unfold properly the data underlying structure. According to the results, our approach shows meaningful embeddings that outperform the results obtained by the conventional LEM algorithm and a previous close related work that analyzes multiple manifolds.

Keywords

Manifold learning multiple manifolds laplacian eigenmaps video analysis 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Juliana Valencia-Aguirre
    • 1
  • Andrés Álvarez-Meza
    • 1
  • Genaro Daza-Santacoloma
    • 2
  • Carlos Acosta-Medina
    • 1
    • 3
  • César Germán Castellanos-Domínguez
    • 1
  1. 1.Signal Processing and Recognition GroupUniversidad Nacional de ColombiaManizalesColombia
  2. 2.Faculty of Electronic EngineeringUniversidad Antonio NariñoBogotáColombia
  3. 3.Scientific Computing and Mathematical Modeling GroupUniversidad Nacional de ColombiaManizalesColombia

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