GTM through time

Christopher M. Bishop, Geoffrey E. Hinton, Iain G. D. Strachan

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Abstract

    The standard GTM (generative topographic mapping) algorithm assumes that the data on which it is trained consists of independent, identically distributed (iid) vectors. For time series, however, the iid assumption is a poor approximation. In this paper we show how the GTM algorithm can be extended to model time series by incorporating it as the emission density in a hidden Markov model. Since GTM has discrete hidden states we are able to find a tractable EM algorithm, based on the forward-backward algorithm, to train the model. We illustrate the performance of GTM through time using flight recorder data from a helicopter.
    Original languageEnglish
    Title of host publicationFifth International Conference on Artificial Neural Networks
    Place of PublicationCambridge, US
    PublisherIEEE
    Pages111-116
    Number of pages6
    ISBN (Print)0852966903
    Publication statusPublished - 9 Jul 1997
    EventProceedings IEE Fifth International Conference on Artificial Neural Networks -
    Duration: 9 Jul 19979 Jul 1997

    Conference

    ConferenceProceedings IEE Fifth International Conference on Artificial Neural Networks
    Period9/07/979/07/97

    Fingerprint

    Time series
    Hidden Markov models
    Helicopters

    Bibliographical note

    Conference Publication No: 440 ©1997 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

    Keywords

    • Generative topographic mapping
    • identically distributed vectors
    • time series
    • Markov model
    • flight-recorder

    Cite this

    Bishop, C. M., Hinton, G. E., & Strachan, I. G. D. (1997). GTM through time. In Fifth International Conference on Artificial Neural Networks (pp. 111-116). Cambridge, US: IEEE.
    Bishop, Christopher M. ; Hinton, Geoffrey E. ; Strachan, Iain G. D. / GTM through time. Fifth International Conference on Artificial Neural Networks. Cambridge, US : IEEE, 1997. pp. 111-116
    @inbook{3d34fb2937ad47bf96be523bc9ffbece,
    title = "GTM through time",
    abstract = "The standard GTM (generative topographic mapping) algorithm assumes that the data on which it is trained consists of independent, identically distributed (iid) vectors. For time series, however, the iid assumption is a poor approximation. In this paper we show how the GTM algorithm can be extended to model time series by incorporating it as the emission density in a hidden Markov model. Since GTM has discrete hidden states we are able to find a tractable EM algorithm, based on the forward-backward algorithm, to train the model. We illustrate the performance of GTM through time using flight recorder data from a helicopter.",
    keywords = "Generative topographic mapping, identically distributed vectors, time series, Markov model, flight-recorder",
    author = "Bishop, {Christopher M.} and Hinton, {Geoffrey E.} and Strachan, {Iain G. D.}",
    note = "Conference Publication No: 440 {\circledC}1997 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.",
    year = "1997",
    month = "7",
    day = "9",
    language = "English",
    isbn = "0852966903",
    pages = "111--116",
    booktitle = "Fifth International Conference on Artificial Neural Networks",
    publisher = "IEEE",
    address = "United States",

    }

    Bishop, CM, Hinton, GE & Strachan, IGD 1997, GTM through time. in Fifth International Conference on Artificial Neural Networks. IEEE, Cambridge, US, pp. 111-116, Proceedings IEE Fifth International Conference on Artificial Neural Networks, 9/07/97.

    GTM through time. / Bishop, Christopher M.; Hinton, Geoffrey E.; Strachan, Iain G. D.

    Fifth International Conference on Artificial Neural Networks. Cambridge, US : IEEE, 1997. p. 111-116.

    Research output: Chapter in Book/Report/Conference proceedingChapter

    TY - CHAP

    T1 - GTM through time

    AU - Bishop, Christopher M.

    AU - Hinton, Geoffrey E.

    AU - Strachan, Iain G. D.

    N1 - Conference Publication No: 440 ©1997 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

    PY - 1997/7/9

    Y1 - 1997/7/9

    N2 - The standard GTM (generative topographic mapping) algorithm assumes that the data on which it is trained consists of independent, identically distributed (iid) vectors. For time series, however, the iid assumption is a poor approximation. In this paper we show how the GTM algorithm can be extended to model time series by incorporating it as the emission density in a hidden Markov model. Since GTM has discrete hidden states we are able to find a tractable EM algorithm, based on the forward-backward algorithm, to train the model. We illustrate the performance of GTM through time using flight recorder data from a helicopter.

    AB - The standard GTM (generative topographic mapping) algorithm assumes that the data on which it is trained consists of independent, identically distributed (iid) vectors. For time series, however, the iid assumption is a poor approximation. In this paper we show how the GTM algorithm can be extended to model time series by incorporating it as the emission density in a hidden Markov model. Since GTM has discrete hidden states we are able to find a tractable EM algorithm, based on the forward-backward algorithm, to train the model. We illustrate the performance of GTM through time using flight recorder data from a helicopter.

    KW - Generative topographic mapping

    KW - identically distributed vectors

    KW - time series

    KW - Markov model

    KW - flight-recorder

    UR - http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=607502&isnumber=13303

    UR - http://www.scopus.com/inward/record.url?scp=0030681437&partnerID=8YFLogxK

    M3 - Chapter

    SN - 0852966903

    SP - 111

    EP - 116

    BT - Fifth International Conference on Artificial Neural Networks

    PB - IEEE

    CY - Cambridge, US

    ER -

    Bishop CM, Hinton GE, Strachan IGD. GTM through time. In Fifth International Conference on Artificial Neural Networks. Cambridge, US: IEEE. 1997. p. 111-116