Modelling the Manifolds of Images of Handwritten Digits

This paper describes two new methods for modelling 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 modelling 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.