An Unsupervised Algorithm For Learning Lie Group Transformations

We describe a method for learning Lie, or continuous transformation, group descriptions of the dynamics of natural scenes. Naively, doing so is made difficult by the O(N^6) computational complexity in the number of pixels N for learning of the Lie group operators, and an abundance of local minima while inferring transformations for specific image sequences. We present solutions to both of these difficulties, reducing learning to O(N^2) complexity via a re-parameterization of the Lie group operators, and introducing "blurring" operators that allows inference to escape local minima via a transformation specific reduction in scale. Both learning and inference is demonstrated using these extensions for the full set of affine transformations.