Social Learning over Weakly-Connected Graphs

In this paper, we study diffusion social learning over weakly-connected graphs. We show that the asymmetric flow of information hinders the learning abilities of certain agents regardless of their local observations. Under some circumstances that we clarify in this work, a scenario of total influence (or "mind-control") arises where a set of influential agents ends up shaping the beliefs of non-influential agents. We derive useful closed-form expressions that characterize this influence, and which can be used to motivate design problems to control it. We provide simulation examples to illustrate the results.Comment: To appear in 2017 in the IEEE Transactions on Signal and Information Processing over Network

Graph signal processing for machine learning: A review and new perspectives

The effective representation, processing, analysis, and visualization of large-scale structured data, especially those related to complex domains such as networks and graphs, are one of the key questions in modern machine learning. Graph signal processing (GSP), a vibrant branch of signal processing models and algorithms that aims at handling data supported on graphs, opens new paths of research to address this challenge. In this article, we review a few important contributions made by GSP concepts and tools, such as graph filters and transforms, to the development of novel machine learning algorithms. In particular, our discussion focuses on the following three aspects: exploiting data structure and relational priors, improving data and computational efficiency, and enhancing model interpretability. Furthermore, we provide new perspectives on future development of GSP techniques that may serve as a bridge between applied mathematics and signal processing on one side, and machine learning and network science on the other. Cross-fertilization across these different disciplines may help unlock the numerous challenges of complex data analysis in the modern age