Deep Topological Embedding with Convolutional Neural Networks for Complex Network Classification

The classification of complex networks allows us to compare sets of networks based on their topological characteristics. By being able to compare sets of known networks to unknown ones, we can analyze real-world complex systems such as neural pathways, traffic flow, and social relations. However, most network-classification methods rely on vertex-level measures or they characterize single fixed-structure networks. Also, these approaches can be computationally costly when analyzing a large number of networks, as they need to learn the network embeds. To address these issues, we propose a hand-crafted embedding method called Deep Topological Embedding (DTE) that builds multidimensional and deep embeddings from networks, based on the joint distribution of vertex centrality, that combined represents the global structure of the network. The DTE can be approached as a two or three-dimensional visual representation of complex networks. In this sense, we present a convolutional architecture to classify DTE representations of different topological models. Our method achieves improved classification accuracy compared to related methods when tested on three benchmarks.