Wasserstein Exponential Kernels

by   Henri De Plaen, et al.
KU Leuven

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.


page 4

page 5


Sliced Wasserstein Kernels for Probability Distributions

Optimal transport distances, otherwise known as Wasserstein distances, h...

Wasserstein Distance Measure Machines

This paper presents a distance-based discriminative framework for learni...

Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties

Optimal transport theory has recently found many applications in machine...

Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projections

It has been shown beneficial for many types of data which present an und...

Globally solving the Gromov-Wasserstein problem for point clouds in low dimensional Euclidean spaces

This paper presents a framework for computing the Gromov-Wasserstein pro...

Linear-time Learning on Distributions with Approximate Kernel Embeddings

Many interesting machine learning problems are best posed by considering...

Please sign up or login with your details

Forgot password? Click here to reset