Near-Optimal Comparison Based Clustering

Part of Advances in Neural Information Processing Systems 33 pre-proceedings (NeurIPS 2020)

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Authors

Michaël Perrot, Pascal Esser, Debarghya Ghoshdastidar

Abstract

<p>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.</p>