6533b7dcfe1ef96bd1271d44
RESEARCH PRODUCT
A Widrow–Hoff Learning Rule for a Generalization of the Linear Auto-associator
Alice J. O'tooleHervé AbdiHervé AbdiDominique ValentinBetty Edelmansubject
General linear modelArtificial neural networkbusiness.industryGeneralizationApplied MathematicsGeneralized linear array modelMachine learningcomputer.software_genreGeneralized linear mixed modelHierarchical generalized linear modelLearning ruleApplied mathematicsArtificial intelligencebusinesscomputerGeneral PsychologyEigenvalues and eigenvectorsMathematicsdescription
Abstract A generalization of the linear auto-associator that allows for differential 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 Widrow–Hoff 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1996-06-01 | Journal of Mathematical Psychology |