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We present several theoretical contributions which allow Lie groups to be fitto high dimensional datasets. Transformation operators are represented in theireigen-basis, reducing the computational complexity of parameter estimation tothat of training a linear transformation model. A transformation specific"blurring" operator is introduced that allows inference to escape local minimavia a smoothing of the transformation space. A penalty on traversed manifolddistance is added which encourages the discovery of sparse, minimal distance,transformations between states. Both learning and inference are demonstratedusing these methods for the full set of affine transformations on natural imagepatches. Transformation operators are then trained on natural video sequences.It is shown that the learned video transformations provide a better descriptionof inter-frame differences than the standard motion model based on rigidtranslation.

An Unsupervised Algorithm For Learning Lie Group Transformations