Quantum Approaches for Medoid Clustering

Abstract

The $k$-medoids problem is an important problem in data clustering, which aims to partition a set of data points into $k$ clusters, where each cluster is represented by a medoid, i.e., a data point that is the most centrally located in the cluster. Quantum annealing might be helpful in finding the solution to this problem faster. In this paper we compare three approaches for using the quantum annealer and QUBO-formulations to solve the $k$-medoids problem. The first approach revolves around a QUBO that encodes the problem as a whole. This approach turns out not to scale well for bigger problem sizes. The QUBO in the second approach comes from the literature and solves only the problem of finding medoids: assigning the datapoints to clusters requires an additional step. The QUBO formulation in the third approach is the same as in the second, but with different penalty parameters. We show that the second and third approaches scale better in terms of complexity than the first approach. However, the original penalty parameters in approach 2 (i.e. those suggested in the literature) do not work well for bigger instances. Taking different parameters makes this approach much better in performance.