Wasserstein Exponential Kernels
This work addresses the challenge of enhancing similarity measures in kernel methods for supervised learning tasks involving shapes and images, representing an incremental improvement over existing techniques.
The paper tackles the problem of improving kernel methods by replacing Euclidean distances with regularized Wasserstein distances in exponential kernels, showing that this approach yields smaller classification errors on small training sets of shapes compared to Euclidean-based classifiers.
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. Empirically, Wasserstein squared exponential kernels are shown to yield smaller classification errors on small training sets of shapes, compared to analogous classifiers using Euclidean distances.