Learning Local Receptive Fields and their Weight Sharing Scheme on Graphs

We propose a simple and generic layer formulation that extends the properties of convolutional layers to any domain that can be described by a graph. Namely, we use the support of its adjacency matrix to design learnable weight sharing filters able to exploit the underlying structure of signals in the same fashion as for images. The proposed formulation makes it possible to learn the weights of the filter as well as a scheme that controls how they are shared across the graph. We perform validation experiments with image datasets and show that these filters offer performances comparable with convolutional ones.Comment: To appear in 2017, 5th IEEE Global Conference on Signal and Information Processing, 5 pages, 3 figures, 3 table

Kernel Graph Convolutional Neural Networks

Graph kernels have been successfully applied to many graph classification problems. Typically, a kernel is first designed, and then an SVM classifier is trained based on the features defined implicitly by this kernel. This two-stage approach decouples data representation from learning, which is suboptimal. On the other hand, Convolutional Neural Networks (CNNs) have the capability to learn their own features directly from the raw data during training. Unfortunately, they cannot handle irregular data such as graphs. We address this challenge by using graph kernels to embed meaningful local neighborhoods of the graphs in a continuous vector space. A set of filters is then convolved with these patches, pooled, and the output is then passed to a feedforward network. With limited parameter tuning, our approach outperforms strong baselines on 7 out of 10 benchmark datasets.Comment: Accepted at ICANN '1

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters

The rise of graph-structured data such as social networks, regulatory networks, citation graphs, and functional brain networks, in combination with resounding success of deep learning in various applications, has brought the interest in generalizing deep learning models to non-Euclidean domains. In this paper, we introduce a new spectral domain convolutional architecture for deep learning on graphs. The core ingredient of our model is a new class of parametric rational complex functions (Cayley polynomials) allowing to efficiently compute spectral filters on graphs that specialize on frequency bands of interest. Our model generates rich spectral filters that are localized in space, scales linearly with the size of the input data for sparsely-connected graphs, and can handle different constructions of Laplacian operators. Extensive experimental results show the superior performance of our approach, in comparison to other spectral domain convolutional architectures, on spectral image classification, community detection, vertex classification and matrix completion tasks