Manifold learning in regression tasks

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15 Citations (Scopus)

Abstract

The paper presents a new geometrically motivated method for nonlinear regression based on Manifold learning technique. The regression problem is to construct a predictive function which estimates an unknown smooth mapping f from q-dimensional inputs to m-dimensional outputs based on a training data set consisting of given ‘input-output’ pairs. The unknown mapping f determines q-dimensional manifold M(f) consisting of all the ‘input-output’ vectors which is embedded in (q+m)-dimensional space and covered by a single chart; the training data set determines a sample from this manifold. Modern Manifold Learning methods allow constructing the certain estimator M* from the manifold-valued sample which accurately approximates the manifold. The proposed method called Manifold Learning Regression (MLR) finds the predictive function fMLR to ensure an equality M(fMLR) = M*. The MLR simultaneously estimates the m×q Jacobian matrix of the mapping f.

Original languageEnglish
Title of host publicationStatistical Learning and Data Sciences - 3rd International Symposium, SLDS 2015, Proceedings
EditorsAlexander Gammerman, Vladimir Vovk, Harris Papadopoulos
PublisherSpringer Verlag
Pages414-423
Number of pages10
Volume9047
ISBN (Print)9783319170909
DOIs
Publication statusPublished - 2015
Externally publishedYes
Event3rd International Symposium on Statistical Learning and Data Sciences, SLDS 2015 - Egham, United Kingdom
Duration: 20 Apr 201523 Apr 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9047
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd International Symposium on Statistical Learning and Data Sciences, SLDS 2015
Country/TerritoryUnited Kingdom
CityEgham
Period20/04/1523/04/15

Keywords

  • Dimensionality reduction
  • Manifold learning
  • Manifold learning regression
  • Nonlinear regression
  • Tangent bundle manifold learning

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