A Geometric Algorithm for Scalable Multiple Kernel Learning

TL;DR

This paper introduces a geometric approach to Multiple Kernel Learning that reformulates the problem as a kernel distance maximization, enabling scalable and efficient optimization with strong theoretical guarantees.

Contribution

It presents a novel geometric formulation of MKL, reducing it to a simple, provably convergent optimization routine that scales to larger datasets.

Findings

Our method is significantly faster than previous MKL algorithms.

It achieves competitive or better performance compared to uniform kernel combinations.

The approach provides strong theoretical convergence and quality guarantees.

Abstract

We present a geometric formulation of the Multiple Kernel Learning (MKL) problem. To do so, we reinterpret the problem of learning kernel weights as searching for a kernel that maximizes the minimum (kernel) distance between two convex polytopes. This interpretation combined with novel structural insights from our geometric formulation allows us to reduce the MKL problem to a simple optimization routine that yields provable convergence as well as quality guarantees. As a result our method scales efficiently to much larger data sets than most prior methods can handle. Empirical evaluation on eleven datasets shows that we are significantly faster and even compare favorably with a uniform unweighted combination of kernels.