This paper is about fully-distributed support vectormachine (SVM) learning over wireless sensor networks. With theconcept of the geometric SVM, we propose to gossip the set ofextreme points of the convex hull of local data set with neighboringnodes. It has the advantages of a simple communicationmechanism and finite-time convergence to a common global solution.Furthermore, we analyze the scalability with respect to theamount of exchanged information and convergence time, witha specific emphasis on the small-world phenomenon. First, withthe proposed naive convex hull algorithm, the message lengthremains bounded as the number of nodes increases. Second, byutilizing a small-world network, we have an opportunity to drasticallyimprove the convergence performance with only a smallincrease in power consumption. These properties offer a greatadvantage when dealing with a large-scale network. Simulationand experimental results support the feasibility and effectivenessof the proposed gossip-based process and the analysis.