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    block this user Herve Abdi Trusted member

    Professor / herve@utdallas.edu

    The University of Teas at Dallas, School of Behavioral and brain Sciences, Richardson, TX 75080, USA

    A Widrow-Hoff Learning Rule for a Generalization of the Linear Auto-associator* 1

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    A generalization of the linear auto-associator that allows for differen- tial importance and nonindependence of both the stimuli and the units has been described previously by Abdi (1988). This model was shown to implement the general linear model of multivariate statistics. In this note, a proof is given that the WidrowHoff learning rule can be similarly generalized and that the weight matrix will converge to a generalized pseudo-inverse when the learning parameter is properly chosen. The value of the learning parameter is shown to be dependent only upon the (generalized) eigenvalues of the weight matrix and not upon the eigenvectors themselves. This proof provides a unified framework to support comparison of neural network models and the general linear model of multivariate statistics.

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    Description

    New Full text for this article was not available? Send a request to the author(s).
    Title : A Widrow-Hoff Learning Rule for a Generalization of the Linear Auto-associator* 1
    Author(s) : Herve Abdi, Dominique Valentin, Betty Edelman, AJ O'Toole
    Abstract : A generalization of the linear auto-associator that allows for differen- tial importance and nonindependence of both the stimuli and the units has been described previously by Abdi (1988). This model was shown to implement the general linear model of multivariate statistics. In this note, a proof is given that the WidrowHoff learning rule can be similarly generalized and that the weight matrix will converge to a generalized pseudo-inverse when the learning parameter is properly chosen. The value of the learning parameter is shown to be dependent only upon the (generalized) eigenvalues of the weight matrix and not upon the eigenvectors themselves. This proof provides a unified framework to support comparison of neural network models and the general linear model of multivariate statistics.
    Subject : unspecified
    Area : Other
    Language : English
    Year : 1996

    Affiliations :  The University of Teas at Dallas, School of Behavioral and brain Sciences, Richardson, TX 75080, USA
    Journal : Journal of Mathematical
    Volume : 182
    Issue : 0017
    Pages : 175-182
    Url : http://linkinghub.elsevier.com/retrieve/pii/S0022249696900176

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