2019-Graph Neural Networks for IceCube Signal Classification-把节点
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Function Space Pooling For Graph Convolutional
Networks
Padraig Corcoran
School of Computer Science and Informatics
Cardiff University
May 16, 2019
Abstract
Convolutional layers in graph neural networks are a fundamental type
of layer which output a representation or embedding of each graph ver-
tex. The representation typically encodes information about the vertex in
question and its neighbourhood. If one wishes to perform a graph centric
task such as graph classification the set of vertex representations must be
integrated or pooled to form a graph representation. We propose a novel
pooling method which transforms a set of vertex representations into a
function space representation. Experiential results demonstrate that the
proposed method outperforms standard pooling methods of computing
the sum and mean vertex representation.
1 Introduction
Many real world data such as social networks, collections of documents and
chemical structures are naturally represented as graphs. Consequently there
exists great potential for the application of machine learning to graphs. Given
the great successes of neural networks or deep learning to the analysis of images,
there has recently been much research considering the application or general-
ization of neural networks to graphs. In many cases this has resulted in state
of the art performance in many tasks (Wu et al., 2019).
Graph convolutional is a neural network architecture commonly applied to
graphs. This architecture consists of a sequence of convolutional layers where
each layer iteratively updates a representation or embedding of each vertex.
This update is achieved through the application of an operation which consid-
ers the current representation of each vertex plus the current representation of
its adjacent neighbours (Gilmer et al., 2017). The output of a sequence of con-
volutional layers is a representation of each vertex which encodes properties of
the vertex in question and vertices in its neighbourhood.
If one wishes to perform a vertex centric task such as vertex classification,
then one may operate directly on the set of vertex representations output from
a sequence of convolutional layers. However, if one wishes to perform a graph
centric task such as graph classification, then the set of vertex representations
1
arXiv:1905.06259v1 [cs.LG] 15 May 2019
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