Learning nonlinear manifolds from time series

Ruei Sung Lin, Che Bin Liu, Ming Hsuan Yang, Narendra Ahuja, Stephen Levinson

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

20 Citations (Scopus)

Abstract

There has been growing interest in developing nonlinear dimensionality reduction algorithms for vision applications. Although progress has been made in recent years, conventional nonlinear dimensionality reduction algorithms have been designed to deal with stationary, or independent and identically distributed data. In this paper, we present a novel method that learns nonlinear mapping from time series data to their intrinsic coordinates on the underlying manifold. Our work extends the recent advances in learning nonlinear manifolds within a global coordinate system to account for temporal correlation inherent in sequential data. We formulate the problem with a dynamic Bayesian network and propose an approximate algorithm to tackle the learning and inference problems. Numerous experiments demonstrate the proposed method is able to learn nonlinear manifolds from time series data, and as a result of exploiting the temporal correlation, achieve superior results.

Original languageEnglish
Title of host publicationComputer Vision - ECCV 2006, 9th European Conference on Computer Vision, Proceedings
Pages245-256
Number of pages12
Publication statusPublished - 2006 Jul 17
Event9th European Conference on Computer Vision, ECCV 2006 - Graz, Austria
Duration: 2006 May 72006 May 13

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3952 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference9th European Conference on Computer Vision, ECCV 2006
CountryAustria
CityGraz
Period06/5/706/5/13

Fingerprint

Time series
Temporal Correlation
Dimensionality Reduction
Time Series Data
Bayesian networks
Dynamic Bayesian Networks
Nonlinear Mapping
Approximate Algorithm
Identically distributed
Learning
Experiments
Demonstrate
Experiment

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Lin, R. S., Liu, C. B., Yang, M. H., Ahuja, N., & Levinson, S. (2006). Learning nonlinear manifolds from time series. In Computer Vision - ECCV 2006, 9th European Conference on Computer Vision, Proceedings (pp. 245-256). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3952 LNCS).
Lin, Ruei Sung ; Liu, Che Bin ; Yang, Ming Hsuan ; Ahuja, Narendra ; Levinson, Stephen. / Learning nonlinear manifolds from time series. Computer Vision - ECCV 2006, 9th European Conference on Computer Vision, Proceedings. 2006. pp. 245-256 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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Lin, RS, Liu, CB, Yang, MH, Ahuja, N & Levinson, S 2006, Learning nonlinear manifolds from time series. in Computer Vision - ECCV 2006, 9th European Conference on Computer Vision, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3952 LNCS, pp. 245-256, 9th European Conference on Computer Vision, ECCV 2006, Graz, Austria, 06/5/7.

Learning nonlinear manifolds from time series. / Lin, Ruei Sung; Liu, Che Bin; Yang, Ming Hsuan; Ahuja, Narendra; Levinson, Stephen.

Computer Vision - ECCV 2006, 9th European Conference on Computer Vision, Proceedings. 2006. p. 245-256 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3952 LNCS).

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

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Lin RS, Liu CB, Yang MH, Ahuja N, Levinson S. Learning nonlinear manifolds from time series. In Computer Vision - ECCV 2006, 9th European Conference on Computer Vision, Proceedings. 2006. p. 245-256. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).