Gaussian Mixture Reduction Using Reverse Kullback-Leibler Divergence
This work addresses the problem of efficient mixture reduction for practitioners in fields like signal processing or machine learning, but it is incremental as it builds on prior KLD-based methods by adding pruning capability.
The authors tackled the problem of reducing Gaussian mixture models by proposing a greedy algorithm that can both prune and merge components using Kullback-Leibler divergence, resulting in a method that preserves peaks and is computationally efficient, with performance comparable to existing methods like Runnalls' and Williams' in numerical examples.
We propose a greedy mixture reduction algorithm which is capable of pruning mixture components as well as merging them based on the Kullback-Leibler divergence (KLD). The algorithm is distinct from the well-known Runnalls' KLD based method since it is not restricted to merging operations. The capability of pruning (in addition to merging) gives the algorithm the ability of preserving the peaks of the original mixture during the reduction. Analytical approximations are derived to circumvent the computational intractability of the KLD which results in a computationally efficient method. The proposed algorithm is compared with Runnalls' and Williams' methods in two numerical examples, using both simulated and real world data. The results indicate that the performance and computational complexity of the proposed approach make it an efficient alternative to existing mixture reduction methods.