PUBO Formulation for MST and Application to Optimum-Path Forest

TL;DR

This paper introduces a quantum-inspired PUBO formulation for the MST problem in Optimum-Path Forest classifiers, improving scalability and maintaining accuracy on real datasets.

Contribution

It reformulates the MST as a PUBO problem and applies FALQON for optimization, reducing qubit requirements and addressing hardware scalability.

Findings

FALQON-optimized MST achieves accuracy comparable to classical Prim's algorithm.

PUBO formulation reduces qubit needs and eliminates auxiliary variables.

FALQON occasionally reaches local minima but with minimal impact on accuracy.

Abstract

The Optimum-Path Forest is a graph-based framework for designing classifiers that exploit inter-sample connectivity. A particular variant constructs decision boundaries based on prototypes computed by a Minimum Spanning Tree (MST) over the training data, which might become prohibitive for large-scale datasets. In this context, Quantum Machine Learning has emerged as a promising approach to overcome the high computational burden of combinatorial problems. We propose a quantum-inspired approach for prototype selection in OPF classifiers by reformulating the MST problem as a Polynomial Unconstrained Binary Optimization (PUBO) task and further employing the Feedback-Based Quantum Optimization (FALQON) algorithm for Hamiltonian minimization. The PUBO formulation reduces the need for qubits and eliminates the need for auxiliary variables, thereby addressing scalability constraints in current quantum hardware. Experiments on real-world datasets demonstrate that the FALQON-optimized MST achieves accuracies comparable to those of the classical Prim's algorithm while maintaining prototype quality. While FALQON occasionally reached local minima, it did not significantly impact the accuracy of the prototype selection process.