A Collective Neurodynamic Optimization Approach to Nonnegative Matrix Factorization.

Area of Science:

• Computational mathematics
• Artificial intelligence
• Optimization algorithms

Background:

• Nonnegative Matrix Factorization (NMF) is crucial for feature extraction but involves solving challenging nonconvex optimization problems.
• Existing methods struggle with the complexity of NMF's objective function and constraints.

Purpose of the Study:

• To present a novel Collective Neurodynamic Optimization (CNO) approach for addressing the global optimization challenges in NMF.
• To enhance the efficiency and effectiveness of NMF through a hybrid optimization strategy.

Main Methods:

• A hybrid system combining Recurrent Neural Networks (RNNs) for local search and Particle Swarm Optimization (PSO) with wavelet mutation for global guidance.
• RNNs perform precise local searches, while PSO directs them towards optimal solutions, enhanced by wavelet mutation for diversity.

Main Results:

• The proposed CNO approach demonstrates a high probability of achieving global optimality for NMF problems.
• Experimental results confirm the efficacy and superiority of CNO over state-of-the-art algorithms on benchmark nonconvex functions and NMF-based clustering tasks.

Conclusions:

• The Collective Neurodynamic Optimization approach offers a robust and effective solution for Nonnegative Matrix Factorization.
• CNO significantly advances the field of global optimization for complex, constrained problems.