Patch-based data analysis using linear-projection diffusion

Moshe Salhov*, Guy Wolf, Amir Averbuch, Pekka Neittaanmäki

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


To process massive high-dimensional datasets, we utilize the underlying assumption that data on a manifold is approximately linear in sufficiently small patches (or neighborhoods of points) that are sampled with sufficient density from the manifold. Under this assumption, each patch can be represented by a tangent space of the manifold in its area and the tangential point of this tangent space. We use these tangent spaces, and the relations between them, to extend the scalar relations that are used by many kernel methods to matrix relations, which can encompass multidimensional similarities between local neighborhoods of points on the manifold. The properties of the presented construction are explored and its spectral decomposition is utilized to embed the patches of the manifold into a tensor space in which the relations between them are revealed. We present two applications that utilize the patch-to-tensor embedding framework: data classification and data clustering for image segmentation.

Original languageEnglish
Title of host publicationAdvances in Intelligent Data Analysis XI - 11th International Symposium, IDA 2012, Proceedings
Number of pages12
StatePublished - 2012
Event11th International Symposium on Intelligent Data Analysis, IDA 2012 - Helsinki, Finland
Duration: 25 Oct 201227 Oct 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7619 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference11th International Symposium on Intelligent Data Analysis, IDA 2012


  • Diffusion Maps
  • Dimensionality reduction
  • kernel PCA
  • manifold learning
  • patch processing
  • stochastic processing
  • vector processing


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