Learning from one example through shared densities on transforms
We define a process called congealing in which elements of a dataset (images) are brought into correspondence with each other jointly, producing a data-defined model. It is based upon minimizing the summed component-wise (pixel-wise) entropies over a continuous set of transforms on the data. One of the biproducts of this minimization is a set of transform, one associated with each original training sample. We then demonstrate a procedure for effectively bringing test data into correspondence with the data-defined model produced in the congealing process. Subsequently; we develop a probability density over the set of transforms that arose from the congealing process. We suggest that this density over transforms may be shared by many classes, and demonstrate how using this density as "prior knowledge" can be used to develop a classifier based on only a single training example for each class.