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Modeling the Manifolds of Images of Handwritten Digits

Geoffrey E. Hinton, Peter Dayan
and Michael Revow
Department of Computer Science
University of Toronto

Abstract

This paper describes two new methods for modeling the manifolds of digitised images of handwritten digits. The models allow a priori information about the structure of the manifolds to be combined with empirical data. Accurate modeling of the manifolds allows digits to be discriminated using the relative probability densities under the alternative models. One of the methods is grounded in principal components analysis, the other in factor analysis. Both methods are based on locally linear, low-dimensional approximations to the underlying data manifold. Links with other methods that model the manifold are discussed.

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IEEE Transactions on Neural Networks, 8 65-74

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