Local Gradient Descent Methods for GMM Simplification

Gaussian mixture model simplification is a powerful technique for reducing the number of components of an existing mixture model without having to re-cluster the original data set. Instead, a simplified GMM with fewer components is computed by minimizing some distance metric between the two models. In this paper, we derive an analytical expression for the difference between the probability density functions of two GMMs along with its gradient information. We minimize the objective function using gradient descent and K-means. Both synthetic and non-synthetic test cases are used in the experiments.