Efficient Clustering with Limited Distance Information

TL;DR

This paper introduces an efficient clustering method that requires only a small number of distance queries, leveraging one-vs-all queries, and demonstrates its effectiveness in protein sequence clustering with minimal distance information.

Contribution

The paper presents a novel algorithm for clustering with limited distance queries, achieving accurate results under certain structural assumptions, and applies it to protein sequence data.

Findings

Achieves accurate clustering with only O(k) distance queries

Effective in protein sequence clustering using sequence database searches

Produces clusterings close to manual classifications despite limited data

Abstract

Given a point set S and an unknown metric d on S, we study the problem of efficiently partitioning S into k clusters while querying few distances between the points. In our model we assume that we have access to one versus all queries that given a point s 2 S return the distances between s and all other points. We show that given a natural assumption about the structure of the instance, we can efficiently find an accurate clustering using only O(k) distance queries. We use our algorithm to cluster proteins by sequence similarity. This setting nicely fits our model because we can use a fast sequence database search program to query a sequence against an entire dataset. We conduct an empirical study that shows that even though we query a small fraction of the distances between the points, we produce clusterings that are close to a desired clustering given by manual classification.