On the effects of topology and node distribution on learning over complex adaptive networks

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 through their collaborations, as dictated by the network topology and by the spatial distribution of the nodes. In this work, we consider two types of nodes: informed and uninformed. The former collect data and perform processing, while the latter only participate in the processing tasks. We examine the performance of adaptive networks as a function of the fraction of informed nodes. The results reveal an interesting trade-off between convergence and performance. The analysis indicates that the larger the proportion of informed nodes in a network, the faster the convergence rate is at the expense of a deterioration in the mean-square-error performance. The conclusion suggests an important interplay relating the number of informed nodes, the desired convergence rate, and the desired estimation accuracy.