Adaptive Quantum Optimized Centroid Initialization

TL;DR

The paper tackles the challenge of centroid initialization in prototype-based clustering by addressing slow convergence and local minima associated with random starts. It introduces Adaptive Quantum Optimized Centroid Initialization (AQOCI), an iterative, Gauss-Seidel-inspired enhancement of Quantum Optimized Centroid Initialization (QOCI) that uses adaptive scaling and a QUBO/Ising formulation to produce real-valued centroids under quantum annealing. Across Gaussian blob and MOTIF datasets, AQOCI achieves clustering metrics comparable to classical methods and often surpasses QOCI, while leveraging quantum-inspired optimization and block-wise execution to manage hardware-time constraints. The work demonstrates a practical pathway for integrating quantum annealing into centroid initialization, improving convergence and solution quality for prototype-based clustering under limited quantum resources.

Abstract

One of the major benefits of quantum computing is the potential to resolve complex computational problems faster than can be done by classical methods. There are many prototype-based clustering methods in use today, and selection of the starting nodes for the center points is often done randomly. For prototype-based clustering algorithms, this could lead to much slower convergence times. One of the causes of this may be prototype-based clustering accepting a local minima as a valid solution when there are possibly better solutions. Quantum computing, specifically quantum annealing, offers a solution to these problems by mapping the initial centroid problem to an Ising Hamiltonian where over time the lowest energy in the spectrum correlates to a valid, but better solution. A first approach to this problem utilizing quantum annealing was known as Quantum Optimized Centroid Initialization (QOCI), but this approach has some limitations both in results and performance. We will present a modification of QOCI known as Adaptive Quantum Optimized Centroid Initialization (AQOCI) which addresses many of the limitations in QOCI. The results presented are comparable to those obtained using classical techniques as well as being superior to those results found using QOCI.

Figures (12)

• Figure 1: Gaussian: Inertia
• Figure 2: Gaussian: Iterations
• Figure 3: Gaussian: Silhouette
• Figure 4: Gaussian: Homogeneity
• Figure 5: Gaussian: Completeness