Wasserstein Exponential Kernels

Understand

In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel.

• Recently, other distances relying on optimal transport theory - such as the Wasserstein distance between probability distributions - have shown their practical relevance for different machine learning techniques.
• In this paper, we study the use of exponential kernels defined thanks to the regularized Wasserstein distance and discuss their positive definiteness.
• More specifically, we define Wasserstein feature maps and illustrate their interest for supervised learning problems involving shapes and images.