Nebojsa Jojic and Brendan J. Frey 1999.
Topographic transformation as a discrete latent variable.
In S. A. Solla, T. K. Leen and K.-R. Muller (eds)
Advances in Neural Information Processing Systems 12,
MIT Press, Cambridge, MA.
Invariance to topographic transformations such as translation and
shearing in an image has been successfully incorporated into feedforward
mechanisms, e.g., "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.
Compressed postscript,
uncompressed postscript.
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