1. A computer-implemented method for compressing multidimensional gaussian distributions with diagonal covariance matrices, the method comprising: with a computer, clustering a plurality of gaussian distributions in a multiplicity of clusters for each dimension, wherein each cluster is represented by a centroid, and wherein each centroid and each gaussian distribution includes a mean and a variance, and wherein clustering includes: calculating a mean for each centroid as a weighted average of the means of the plurality of gaussian distributions forming the cluster, the weighted average being based on a number of vectors that are matched to a gaussian in the plurality of gaussian distributions; and calculating a variance for each centroid as function of a weighted average of the variances of the plurality of gaussian distributions forming the cluster, the weighted average being based on a number of vectors that are matched to a gaussian in the plurality of gaussian distributions, and wherein a correction factor is included in calculating each variance, wherein the correction factor increases the variance corresponding to an error in quantizing the means; and providing an output from the computer indicative of the clustered gaussian distributions; wherein calculating a mean of each centroid includes using an equation of a form: μ n ⁡ [ d ] = ∑ k ∈ V n ⁢ C k ⁢ m k ⁡ [ d ] ∑ k ∈ V n ⁢ C k , and wherein calculating a variance of each centroid includes using a equation of a form: σ n 2 ⁡ [ d ] = ∑ k ∈ V n ⁢ C k [ ( υ k ⁡ [ d ] ) 2 + ( m k ⁡ [ d ] - μ n ⁡ [ d ] ) 2 ] ∑ k ∈ V n ⁢ C k , wherein C k is the “counts” of Gaussian k as seen in training, and V n is the plurality of Gaussians that are in cluster n.