Fast, Large-Scale Transformation-Invariant Clustering

In previous work on "transformed mixtures of Gaussians" and "transformed hidden Markov models", we showed how the EM algorithm ina discrete latent variable model can be used to jointly normalize data (e.g., center images, pitch-normalize spectrograms) and learn a mixture model of the normalized data. The only input to the algorithm is the data, a list of possible transformations, and the number of clusters to find. The main criticism of this work was that the exhaustive computation of the posterior probabilities overtransformations would make scaling up to large feature vectors and large sets of transformations intractable. Here, we describe howa tremendous speedup is acheived through the use of a variational technique for decoupling transformations, and a fast Fourier transform method for computing posterior probabilities.