# Analogy-Based Preference Learning with Kernels

## TL;DR

This paper introduces an analogy kernel linking analogical reasoning to kernel methods, enabling a new preference learning approach with promising results across various domains.

## Contribution

It establishes a formal connection between analogical proportions and kernel functions, and develops a novel analogy kernel for preference learning with SVMs.

## Key findings

- The analogy kernel effectively measures analogical relationships.
- The proposed method achieves competitive accuracy on diverse datasets.
- Experimental results are promising across multiple application domains.

## Abstract

Building on a specific formalization of analogical relationships of the form "A relates to B as C relates to D", we establish a connection between two important subfields of artificial intelligence, namely analogical reasoning and kernel-based machine learning. More specifically, we show that so-called analogical proportions are closely connected to kernel functions on pairs of objects. Based on this result, we introduce the analogy kernel, which can be seen as a measure of how strongly four objects are in analogical relationship. As an application, we consider the problem of object ranking in the realm of preference learning, for which we develop a new method based on support vector machines trained with the analogy kernel. Our first experimental results for data sets from different domains (sports, education, tourism, etc.) are promising and suggest that our approach is competitive to state-of-the-art algorithms in terms of predictive accuracy.