We introduce an architecture based on deep hierarchical decompositions to learn effective representations of large graphs. Our framework extends classic R-decompositions used in kernel methods, enabling nested "part-of-part" relations. Unlike recursive neural networks, which unroll a template on input graphs directly, we unroll a neural network template over the decomposition hierarchy, allowing us to deal with the high degree variability that typically characterize social network graphs. Deep hierarchical decompositions are also amenable to domain compression, a technique that reduces both space and time complexity by exploiting symmetries. We show empirically that our approach is competitive with current state-of-the-art graph classification methods, particularly when dealing with social network datasets.
@cite_24: Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous node and edge attributes. Analogous to image-based convolutional networks that operate on locally connected regions of the input, we present a general approach to extracting locally connected regions from graphs. Using established benchmark data sets, we demonstrate that the learned feature representations are competitive with state of the art graph kernels and that their computation is highly efficient.
@math @cite_24 casts graphs into a format suitable for learning convolutional neural networks ( @math s): 1) graphs are decomposed into a fixed number of neighborhood subgraphs; 2) which are then casted to a fixed-size receptive field. Both 1) and 2) involve either padding or truncation in order to meet the fixed-size requirements. The truncation operation can be detrimental for the statistical performance of the downstream @math since it throws away part of the input graph. On the other hand @math is able to handle structured inputs of variable sizes without throwing away part of the them. And this is one of the reasons because @math has better statistical performance than @math (See ).