Neural Network-Based Gaussian Mixture Reduction

Gaussian mixtures (GMs) are a well-established
tool for the compact representation and processing of complex
probability distributions and are used, among other things, in
sensor data fusion. When fusing multiple GMs, the number
of components grows exponentially, increasing computational
and memory requirements. Reduction methods are therefore
necessary to replace a large GM with a compact approximation
having significantly fewer components. This paper provides
an overview of existing reduction methods as a benchmark.
Furthermore, a novel approach using neural network (NN) for
GM reduction is derived. This includes the training structure
of the NN, the per-sample fine-tuning and a hybrid approach
that combines the pretrained NN with a KMeans algorithm.
To overcome the issue of a collapsed NN initialization the
paper presents a dead-cluster recovery rule, which improves the
Integrated Squared Error (ISE). Both the benchmark methods
and the novel NN methods are compared in terms of their
runtime and accuracy for various dimensions and cardinalities.
The runtime of the NN with KMeans matches the runtime of
the cheapest classical method but surpasses these methods in
... mehr
terms of accuracy.