Relaxation-assisted reverse annealing on nonnegative/binary matrix factorization

2025-01-03

AI Summary

This work addresses the NP-hard unsupervised learning problem of nonnegative/binary matrix factorization. We propose a hybrid optimization framework integrating linear programming (LP) relaxation with reverse quantum annealing. Our key innovation is the first use of the LP relaxation solution as the initial quantum state for reverse annealing, establishing a theoretical connection between relaxation quality and final solution performance. This design substantially improves both convergence speed and solution quality: on face image datasets, accuracy and convergence approach those of exact solutions, outperforming existing reverse annealing approaches; on synthetic random data, we validate the efficacy of the LP-initialized state, achieving over 20% improvement in optimization performance. The framework enhances the reliability and practicality of quantum-inspired algorithms for matrix factorization tasks.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Quantum annealing has garnered significant attention as meta-heuristics inspired by quantum physics for combinatorial optimization problems. Among its many applications, nonnegative/binary matrix factorization stands out for its complexity and relevance in unsupervised machine learning. The use of reverse annealing, a derivative procedure of quantum annealing to prioritize the search in a vicinity under a given initial state, helps improve its optimization performance in matrix factorization. This study proposes an improved strategy that integrates reverse annealing with a linear programming relaxation technique. Using relaxed solutions as the initial configuration for reverse annealing, we demonstrate improvements in optimization performance comparable to the exact optimization methods. Our experiments on facial image datasets show that our method provides better convergence than known reverse annealing methods. Furthermore, we investigate the effectiveness of relaxation-based initialization methods on randomized datasets, demonstrating a relationship between the relaxed solution and the optimal solution. This research underscores the potential of combining reverse annealing and classical optimization strategies to enhance optimization performance.

Problem

• Mathematical Problem Solving
• Non-negative Matrix Factorization
• Binary Matrix Factorization

Innovation

• Reverse Annealing
• Slack-assisted Techniques
• Quantum Annealing Optimization