# Near-Optimal Comparison Based Clustering

arXiv: https://arxiv.org/abs/2010.03918 · HTML: https://mlsanity.com/paper/2010.03918/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2020.

## Built on by (most cited first, 3 of 3)

- [Graphon based Clustering and Testing of Networks: Algorithms and Theory](https://mlsanity.com/paper/2110.02722/) (2021)
- [Learning-Augmented Priority Queues](https://mlsanity.com/paper/2406.04793/) (2024)
- [A Revenue Function for Comparison-Based Hierarchical Clustering](https://mlsanity.com/paper/2211.16459/) (2022)

## Abstract (arXiv)

The goal of clustering is to group similar objects into meaningful partitions. This process is well understood when an explicit similarity measure between the objects is given. However, far less is known when this information is not readily available and, instead, one only observes ordinal comparisons such as "object i is more similar to j than to k." In this paper, we tackle this problem using a two-step procedure: we estimate a pairwise similarity matrix from the comparisons before using a clustering method based on semi-definite programming (SDP). We theoretically show that our approach can exactly recover a planted clustering using a near-optimal number of passive comparisons. We empirically validate our theoretical findings and demonstrate the good behaviour of our method on real data.