Relaxation-assisted reverse annealing on nonnegative/binary matrix factorization

Area of Science:

• Quantum computing and artificial intelligence
• Combinatorial optimization
• Machine learning

Background:

• Quantum annealing is a meta-heuristic for optimization problems.
• Nonnegative/binary matrix factorization is crucial in unsupervised machine learning.
• Reverse annealing improves matrix factorization optimization by focusing the search.

Purpose of the Study:

• To improve optimization performance in nonnegative/binary matrix factorization.
• To integrate reverse annealing with linear programming relaxation.
• To enhance convergence and solution quality.

Main Methods:

• Integrating reverse annealing with linear programming relaxation.
• Using relaxed solutions as initial configurations for reverse annealing.
• Experimenting on facial image and randomized datasets.

Main Results:

• The proposed method shows improved optimization performance, comparable to exact methods.
• Experiments demonstrate better convergence than existing reverse annealing methods.
• A relationship between relaxed solutions and optimal solutions is identified.

Conclusions:

• Combining reverse annealing with classical optimization strategies enhances performance.
• Relaxation-based initialization is effective for reverse annealing.
• This approach offers a promising direction for complex optimization tasks.