# On Pairwise Clustering with Side Information

## TL;DR

This paper models pairwise clustering as a transductive prediction problem with hidden similarities and optional side-information, providing algorithms with tight bounds on misclassification and analyzing their performance.

## Contribution

It introduces a novel transductive framework for pairwise clustering that incorporates side-information and offers two algorithms with theoretical performance guarantees.

## Key findings

- SACA is a simple, fast agglomerative clustering algorithm.
- RGCA leverages side-information for improved clustering bounds.
- The paper provides tight bounds on misclassification errors.

## Abstract

Pairwise clustering, in general, partitions a set of items via a known similarity function. In our treatment, clustering is modeled as a transductive prediction problem. Thus rather than beginning with a known similarity function, the function instead is hidden and the learner only receives a random sample consisting of a subset of the pairwise similarities. An additional set of pairwise side-information may be given to the learner, which then determines the inductive bias of our algorithms. We measure performance not based on the recovery of the hidden similarity function, but instead on how well we classify each item. We give tight bounds on the number of misclassifications. We provide two algorithms. The first algorithm SACA is a simple agglomerative clustering algorithm which runs in near linear time, and which serves as a baseline for our analyses. Whereas the second algorithm, RGCA, enables the incorporation of side-information which may lead to improved bounds at the cost of a longer running time.