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Abstract:
Invariance to topographic transformations such as translation
and shearing in an image has been successfully incorporated into
feedforward mechanisms, eg, "convolutional neural networks",
"tangent propagation". We describe a way to add transformation
invariance to a generative density model by approximating the
nonlinear transformation manifold by a discrete set of
transformations. An EM algorithm for the original model can be
extended to the new model by computing expectations over the set of
transformations. We show how to add a discrete transformation
variable to Gaussian mixture modeling, factor analysis and mixtures
of factor analysis. We give results on filtering microscopy images,
face and facial pose clustering, and handwritten digit modeling and
recognition.
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