Adaptive networks consist of a collection of nodes with adaptation and learning abilities. The nodes interact with each other on a local level and diffuse information across the network to solve estimation and inference tasks in real-time. In this dissertation, we first examine and compare the mean-square performance of two main strategies for distributed estimation over networks: consensus strategies and diffusion strategies. The analysis confirms that diffusion networks converge faster and reach lower mean-square deviation than consensus networks, and that their mean-square stability is insensitive to the choice of the combination weights. In contrast, and surprisingly, it is shown that consensus networks can become unstable even if all individual nodes are stable and able to solve the estimation task on their own. This finding motivates us to focus on the study of diffusion networks. We incorporate node mobility into the design of the networks and demonstrate that the resulting strategies are well suited to model various types of self-organized behavior observed in biological networks.
We also examine the effect of heterogeneous sources of information on network performance. In one scenario, we consider two types of agents: informed and uninformed. Informed agents receive new data regularly and perform consultation and in-network processing tasks, while uninformed agents participate solely in the consultation tasks. It is established that if the set of informed agents is enlarged, the convergence rate of the network becomes faster albeit at the possible expense of some deterioration in mean-square performance. The arguments reveal an important interplay among three factors: the number and distribution of informed agents in the network, the convergence rate of the adaptation process, and the estimation accuracy in steady-state. In a second scenario, we study the situation in which the data observed by the agents may arise from two different distributions or models. We develop and study a procedure by which the entire network can be made to follow one objective or the other through a distributed and collaborative decision process. The results are useful to model situations where the agents in biological networks need to decide between multiple options, such as deciding between moving towards one food source or another or between moving towards a new hive or another.
The results in this dissertation reveal some interesting phenomena that relate to adaptation over networks: more information is not necessarily better and the way by which information is processed and propagated through the network matters: small variations can lead to catastrophic failures. The dissertation also reveals the convenience of using diffusion strategies to model sophisticated behavior exhibited by biological networks such as fish schooling and prey-predator behavior.
Acknowledgment This work was supported in part by the National Science Foundation under grants CCF-0942936 and CCF-1011918. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.