A New Probabilistic Distance Metric With Application In Gaussian Mixture
  Reduction
Ahmad Sajedi Yuri A. Lawryshyn Konstantinos N. Plataniotis
This paper presents a new distance metric to compare two continuous
probability density functions. The main advantage of this metric is that,
unlike other statistical measurements, it can provide an analytic, closed-form
expression for a mixture of Gaussian distributions while satisfying all metric
properties. These characteristics enable fast, stable, and efficient
calculations, which are highly desirable in real-world signal processing
applications. The application in mind is Gaussian Mixture Reduction (GMR),
which is widely used in density estimation, recursive tracking, and belief
propagation. To address this problem, we developed a novel algorithm dubbed the
Optimization-based Greedy GMR (OGGMR), which employs our metric as a criterion
to approximate a high-order Gaussian mixture with a lower order. Experimental
results show that the OGGMR algorithm is significantly faster and more
efficient than state-of-the-art GMR algorithms while retaining the geometric
shape of the original mixture.