Geoffrey E. Hinton, Michael Revow, Peter Dayan
We construct a mixture of locally linear generative models of a col(cid:173) lection of pixel-based images of digits, and use them for recogni(cid:173) tion. Different models of a given digit are used to capture different styles of writing, and new images are classified by evaluating their log-likelihoods under each model. We use an EM-based algorithm in which the M-step is computationally straightforward principal components analysis (PCA). Incorporating tangent-plane informa(cid:173) tion  about expected local deformations only requires adding tangent vectors into the sample covariance matrices for the PCA, and it demonstrably improves performance.