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arXiv:2310.12153 · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings

Probabilistic Sampling of Balanced K-Means using Adiabatic Quantum Computing

Jan-Nico Zaech, Martin Danelljan, Tolga Birdal, Luc Van Gool

Published Jun 16, 2024• 4 citations
arXivHTMLPDF

Abstract

Adiabatic quantum computing (AQC) is a promising approach for discrete and often NP-hard optimization prob-lems. Current AQCs allow to implement problems of re-search interest, which has sparked the development of quan-tum representations for many computer vision tasks. De-spite requiring multiple measurements from the noisy AQC, current approaches only utilize the best measurement, dis-carding information contained in the remaining ones. In this work, we explore the potential of using this information for probabilistic balanced k-means clustering. Instead of discarding non-optimal solutions, we propose to use them to compute calibrated posterior probabilities with little ad-ditional compute cost. This allows us to identify ambiguous solutions and data points, which we demonstrate on a D-Wave AQC on synthetic tasks and real visual data.

DOI
10.1109/cvpr52733.2024.02475

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In this paper, we propose a new quantum version of the Balanced K-means algorithm in the D-wave quantum annealer. D-wave 2000Q quantum computer has been used by many papers in the last few years to solve optimization problems and for finding the global minimum of the balanced K-means optimization problem. However, in this paper, we modify the quadratic unconstrained binary optimization (QUBO) formulation of the Balanced K-means that has been proposed in a recent paper. Our modification is trained on different data sets: Iris, Wine and Breast Cancer. Also, we performed a comparative analysis between the two approaches (our approach and the paper's approach) to find the one that assigns the largest number of data to clusters and we also use the Davies-Bouldi metric to prove that our method gives the best clustering.
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