Multilayer Graph Node Kernels: Stacking While Maintaining Convexity

Nowadays, developing effective techniques able to deal with data coming from structured domains is becoming crucial. In this context kernel methods are the state-of-the-art tool widely adopted in real-world applications that involve learning on structured data. Contrarily, when one has to deal with unstructured domains, deep learning methods represent a competitive, or even better, choice. In this paper we propose a new family of kernels for graphs which exploits an abstract representation of the information inspired by the multilayer perceptron architecture. Our proposal exploits the advantages of the two worlds. From one side we exploit the potentiality of the state-of-the-art graph node kernels. From the other side we develop a multilayer architecture through a series of stacked kernel pre-image estimators, trained in an unsupervised fashion via convex optimization. The hidden layers of the proposed framework are trained in a forward manner and this allows us to avoid the greedy layerwise training of classical deep learning. Results on real world graph datasets confirm the quality of the proposal.