6 research outputs found
Convolutional Neural Networks Via Node-Varying Graph Filters
Convolutional neural networks (CNNs) are being applied to an increasing
number of problems and fields due to their superior performance in
classification and regression tasks. Since two of the key operations that CNNs
implement are convolution and pooling, this type of networks is implicitly
designed to act on data described by regular structures such as images.
Motivated by the recent interest in processing signals defined in irregular
domains, we advocate a CNN architecture that operates on signals supported on
graphs. The proposed design replaces the classical convolution not with a
node-invariant graph filter (GF), which is the natural generalization of
convolution to graph domains, but with a node-varying GF. This filter extracts
different local features without increasing the output dimension of each layer
and, as a result, bypasses the need for a pooling stage while involving only
local operations. A second contribution is to replace the node-varying GF with
a hybrid node-varying GF, which is a new type of GF introduced in this paper.
While the alternative architecture can still be run locally without requiring a
pooling stage, the number of trainable parameters is smaller and can be
rendered independent of the data dimension. Tests are run on a synthetic source
localization problem and on the 20NEWS dataset.Comment: Submitted to DSW 2018 (IEEE Data Science Workshop
Convolutional Neural Network Architectures for Signals Supported on Graphs
Two architectures that generalize convolutional neural networks (CNNs) for
the processing of signals supported on graphs are introduced. We start with the
selection graph neural network (GNN), which 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
second architecture, dubbed 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 source
localization application over synthetic and real-world networks. Performance is
also evaluated for an authorship attribution problem and text category
classification. Multinode aggregation GNNs are consistently the best performing
GNN architecture.Comment: Submitted to IEEE Transactions on Signal Processin