Active Clustering: Robust and Efficient Hierarchical Clustering using Adaptively Selected Similarities

TL;DR

This paper introduces an active, adaptive hierarchical clustering method that efficiently determines cluster structures using significantly fewer pairwise similarities, even with some noisy data, reducing computational costs.

Contribution

The paper presents a novel active clustering algorithm that adaptively selects similarities, achieving accurate hierarchical clustering with fewer comparisons and robustness to noise.

Findings

Correct clustering possible with 3N log N similarities under certain conditions

Active selection reduces the number of similarities needed compared to random sampling

Method remains effective even with a fraction of anomalous similarities

Abstract

Hierarchical clustering based on pairwise similarities is a common tool used in a broad range of scientific applications. However, in many problems it may be expensive to obtain or compute similarities between the items to be clustered. This paper investigates the hierarchical clustering of N items based on a small subset of pairwise similarities, significantly less than the complete set of N(N-1)/2 similarities. First, we show that if the intracluster similarities exceed intercluster similarities, then it is possible to correctly determine the hierarchical clustering from as few as 3N log N similarities. We demonstrate this order of magnitude savings in the number of pairwise similarities necessitates sequentially selecting which similarities to obtain in an adaptive fashion, rather than picking them at random. We then propose an active clustering method that is robust to a limited fraction of anomalous similarities, and show how even in the presence of these noisy similarity values we can resolve the hierarchical clustering using only O(N log^2 N) pairwise similarities.