Diffusion Adaptation over Networks
  Adaptive networks are well-suited to perform decentralized information processing and optimization tasks and to model various types of self-organized and complex behavior encountered in nature. Adaptive networks consist of a collection of agents with processing and learning abilities. The agents are linked together through a connection topology, and they cooperate with each other through local interactions to solve distributed optimization, estimation, and inference problems in real-time. The continuous diffusion of information across the network enables agents to adapt their performance in relation to streaming data and network conditions; it also results in improved adaptation and learning performance relative to non-cooperative agents. This article provides an overview of diffusion strategies for adaptation and learning over networks. The article is divided into several sections: 1. Motivation; 2. Mean-Square-Error Estimation; 3. Distributed Optimization via Diffusion Strategies; 4. Adaptive Diffusion Strategies; 5. Performance of Steepest-Descent Diffusion Strategies; 6. Performance of Adaptive Diffusion Strategies; 7. Comparing the Performance of Cooperative Strategies; 8. Selecting the Combination Weights; 9. Diffusion with Noisy Information Exchanges; 10. Extensions and Further Considerations; Appendix A: Properties of Kronecker Products; Appendix B: Graph Laplacian and Network Connectivity; Appendix C: Stochastic Matrices; Appendix D: Block Maximum Norm; Appendix E: Comparison with Consensus Strategies; References. 
Ali H. Sayed
cs.MA cs.LG