Post date: 09-oct-2018 11:14:04

Title: Convutional Neural Networks

Date: 9-Octubre-2018, 13:00

Aula: 302, Aulario III

Material:

Speaker: Antonio García Marques

Abstract:

Convolutional neural networks (CNNs) have shown remarkable performance in a wide array of inference and reconstruction tasks. The objective of CNNs is to find a computationally feasible architecture capable of reproducing the behavior of a certain unknown function. One of the key for their success is that the structure of a CNN consist of a succession of layers, each of which performs simple operations which include a convolution, the application of a scalar nonlinearity, and the implementation of a pooling (downsampling) operator. Because the classical convolution and downsampling operations are defined for regular (grid-based) domains, CNNs have been applied to act on data modeled by such a regular structure, like time or images. However, an accurate description of modern datasets such as those in social and biological networks calls for more general irregular structures. Motivated by this, we describe two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs. The selection graph neural network (GNN) replaces linear time invariant filters with linear shift invariant graph filters to generate convolutional features and reinterprets pooling as a possibly nonlinear subsampling stage where nearby nodes pool their information in a set of preselected sample nodes. A key component of the architecture is to remember the position of sampled nodes to permit computation of convolutional features at deeper layers. The aggregation GNN diffuses the signal through the graph and stores the sequence of diffused components observed by a designated node. This procedure effectively aggregates all components into a stream of information having temporal structure to which the convolution and pooling stages of regular CNNs can be applied. A multinode version of aggregation GNNs is further introduced for operation in large scale graphs. An important property of selection and aggregation GNNs is that they reduce to conventional CNNs when particularized to time signals reinterpreted as graph signals in a circulant graph. Comparative numerical analyses are performed in a synthetic source localization application. Performance is evaluated for a text category classification problem using word proximity networks. Multinode aggregation GNNs are consistently the best performing GNN architecture.