Sparse Coding and Dictionary Learning with Linear Dynamical Systems

Wenbing Huang, Fuchun Sun, Lele Cao, Deli Zhao, Huaping Liu, Mehrtash Harandi

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

    26 Citations (Scopus)

    Abstract

    Linear Dynamical Systems (LDSs) are the fundamental tools for encoding spatio-temporal data in various disciplines. To enhance the performance of LDSs, in this paper, we address the challenging issue of performing sparse coding on the space of LDSs, where both data and dictionary atoms are LDSs. Rather than approximate the extended observability with a finite-order matrix, we represent the space of LDSs by an infinite Grassmannian consisting of the orthonormalized extended observability subspaces. Via a homeomorphic mapping, such Grassmannian is embedded into the space of symmetric matrices, where a tractable objective function can be derived for sparse coding. Then, we propose an efficient method to learn the system parameters of the dictionary atoms explicitly, by imposing the symmetric constraint to the transition matrices of the data and dictionary systems. Moreover, we combine the state covariance into the algorithm formulation, thus further promoting the performance of the models with symmetric transition matrices. Comparative experimental evaluations reveal the superior performance of proposed methods on various tasks including video classification and tactile recognition.

    Original languageEnglish
    Title of host publicationProceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016
    PublisherIEEE Computer Society
    Pages3938-3947
    Number of pages10
    ISBN (Electronic)9781467388504
    DOIs
    Publication statusPublished - 9 Dec 2016
    Event29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016 - Las Vegas, United States
    Duration: 26 Jun 20161 Jul 2016

    Publication series

    NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
    Volume2016-December
    ISSN (Print)1063-6919

    Conference

    Conference29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016
    Country/TerritoryUnited States
    CityLas Vegas
    Period26/06/161/07/16

    Fingerprint

    Dive into the research topics of 'Sparse Coding and Dictionary Learning with Linear Dynamical Systems'. Together they form a unique fingerprint.

    Cite this