Hankel based maximum margin classifiers: A connection between machine learning and wiener systems identification

F. Xiong, Y. Cheng, O. Camps, M. Sznaier, C. Lagoa

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

    3 Scopus citations

    Abstract

    This paper considers the problem of nonparametric identification ofWiener systems in cases where there is no a-priori available information on the dimension of the output of the linear dynamics. Thus, it can be considered as a generalization to the case of dynamical systems of non-linear manifold embedding methods recently proposed in the machine learning community. A salient feature of this framework is its ability to exploit both positive and negative examples, as opposed to classical identification techniques where usually only data known to have been produced by the unknown system is used. The main result of the paper shows that while in principle this approach leads to challenging non-convex optimization problems, tractable convex relaxations can be obtained by exploiting a combination of recent developments in polynomial optimization and matrix rank minimization. Further, since the resulting algorithm is based on identifying kernels, it uses only information about the covariance matrix of the observed data (as opposed to the data itself). Thus, it can comfortably handle cases such as those arising in computer vision applications where the dimension of the output space is very large (since each data point is a frame from a video sequence with thousands of pixels).

    Original languageEnglish (US)
    Title of host publication2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages6005-6010
    Number of pages6
    ISBN (Print)9781467357173
    DOIs
    StatePublished - Jan 1 2013
    Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
    Duration: Dec 10 2013Dec 13 2013

    Publication series

    NameProceedings of the IEEE Conference on Decision and Control
    ISSN (Print)0191-2216

    Other

    Other52nd IEEE Conference on Decision and Control, CDC 2013
    CountryItaly
    CityFlorence
    Period12/10/1312/13/13

    All Science Journal Classification (ASJC) codes

    • Control and Systems Engineering
    • Modeling and Simulation
    • Control and Optimization

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  • Cite this

    Xiong, F., Cheng, Y., Camps, O., Sznaier, M., & Lagoa, C. (2013). Hankel based maximum margin classifiers: A connection between machine learning and wiener systems identification. In 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013 (pp. 6005-6010). [6760837] (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6760837