A New Probabilistic Distance Metric with Application in Gaussian Mixture Reduction

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.