Quantum Vision Clustering

TL;DR

Unsupervised visual clustering is addressed by casting the postprocessing component as a Quadratic Unconstrained Binary Optimization ($QUBO$) problem for Adiabatic Quantum Computing ($AQC$). The method maps cluster assignments to a binary matrix $\mathbf{U}$ and optimizes a combined objective $f = f_0 + f_1 + f_2$ that encodes cluster constraints, anchor assignments, and triplet relationships, thereby enabling quantum annealing on devices such as the D-Wave system. The paper introduces the first $QUBO$ based clustering formulation tailored for $AQC$, provides an Ising model representation suitable for current hardware, and reports competitive results against classical baselines with feasibility demonstrated on small instances. The work highlights potential quantum speedups for visual clustering and offers guidance for scalable future quantum clustering formulations as hardware capabilities advance.

Abstract

Unsupervised visual clustering has garnered significant attention in recent times, aiming to characterize distributions of unlabeled visual images through clustering based on a parameterized appearance approach. Alternatively, clustering algorithms can be viewed as assignment problems, often characterized as NP-hard, yet precisely solvable for small instances on contemporary hardware. Adiabatic quantum computing (AQC) emerges as a promising solution, poised to deliver substantial speedups for a range of NP-hard optimization problems. However, existing clustering formulations face challenges in quantum computing adoption due to scalability issues. In this study, we present the first clustering formulation tailored for resolution using Adiabatic quantum computing. An Ising model is introduced to represent the quantum mechanical system implemented on AQC. The proposed approach demonstrates high competitiveness compared to state-of-the-art optimization-based methods, even when utilizing off-the-shelf integer programming solvers. Lastly, this work showcases the solvability of the proposed clustering problem on current-generation real quantum computers for small examples and analyzes the properties of the obtained solutions

Figures (1)

• Figure 1: Overall system architecture. The blue box indicates the deep visual feature extraction step. Specifically, $\mathcal{D}$ is the set of N data points. $\mathcal{H}$ is the feature extraction module and $\mathcal{X}$ is the corresponding feature set of the datapoint $\mathcal{D}$. The red box is the deep unsupervised algorithm where $\mathcal{K}$ denotes the K-NN algorithm, $\mathcal{M}$ is the deep cluster algorithm, i.e., Clusformer and $\mathcal{P}$ indicates the post-unsupervised clustering step. The green box indicates our focus in this paper.