Optimal Transport for Kernel Gaussian Mixture Models
Jung Hun Oh Rena Elkin Anish Kumar Simhal Jiening Zhu Joseph O Deasy Allen Tannenbaum
The Wasserstein distance from optimal mass transport (OMT) is a powerful
mathematical tool with numerous applications that provides a natural measure of
the distance between two probability distributions. Several methods to
incorporate OMT into widely used probabilistic models, such as Gaussian or
Gaussian mixture, have been developed to enhance the capability of modeling
complex multimodal densities of real datasets. However, very few studies have
explored the OMT problems in a reproducing kernel Hilbert space (RKHS), wherein
the kernel trick is utilized to avoid the need to explicitly map input data
into a high-dimensional feature space. In the current study, we propose a
Wasserstein-type metric to compute the distance between two Gaussian mixtures
in a RKHS via the kernel trick, i.e., kernel Gaussian mixture models.