# Learning to Link

## TL;DR

This paper introduces a data-driven approach to simultaneously learn the best clustering algorithm and distance metric tailored to specific applications, improving clustering performance through efficient algorithms and empirical validation.

## Contribution

It proposes a novel method for joint algorithm and metric learning for clustering, optimizing performance for specific tasks using parameterized linkage algorithms and convex combination of distance functions.

## Key findings

- Significant performance improvements in clustering accuracy.
- Effective algorithms for joint learning of algorithms and metrics.
- Empirical results demonstrate practical benefits.

## Abstract

Clustering is an important part of many modern data analysis pipelines, including network analysis and data retrieval. There are many different clustering algorithms developed by various communities, and it is often not clear which algorithm will give the best performance on a specific clustering task. Similarly, we often have multiple ways to measure distances between data points, and the best clustering performance might require a non-trivial combination of those metrics. In this work, we study data-driven algorithm selection and metric learning for clustering problems, where the goal is to simultaneously learn the best algorithm and metric for a specific application. The family of clustering algorithms we consider is parameterized linkage based procedures that includes single and complete linkage. The family of distance functions we learn over are convex combinations of base distance functions. We design efficient learning algorithms which receive samples from an application-specific distribution over clustering instances and simultaneously learn both a near-optimal distance and clustering algorithm from these classes. We also carry out a comprehensive empirical evaluation of our techniques showing that they can lead to significantly improved clustering performance.