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      Topology adaptive graph convolutional networks

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          Abstract

          Convolution acts as a local feature extractor in convolutional neural networks (CNNs). However, the convolution operation is not applicable when the input data is supported on an irregular graph such as with social networks, citation networks, or knowledge graphs. This paper proposes the topology adaptive graph convolutional network (TAGCN), a novel graph convolutional network that generalizes CNN architectures to graph-structured data and provides a systematic way to design a set of fixed-size learnable filters to perform convolutions on graphs. The topologies of these filters are adaptive to the topology of the graph when they scan the graph to perform convolution, replacing the square filter for the grid-structured data in traditional CNNs. The outputs are the weighted sum of these filters' outputs, extraction of both vertex features and strength of correlation between vertices. It can be used with both directed and undirected graphs. The proposed TAGCN not only inherits the properties of convolutions in CNN for grid-structured data, but it is also consistent with convolution in traditional signal processing. We apply TAGCN to semi-supervised learning problems for graph vertex classification; experiments on a number of data sets demonstrate that our method outperforms the existing graph convolutional neural networks and achieves state-of-the-art performance for each data set tested.

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          Big Data Analysis with Signal Processing on Graphs: Representation and processing of massive data sets with irregular structure

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            Discrete signal processing on graphs: Graph filters

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              Spectral Projector-Based Graph Fourier Transforms

              The paper presents the graph Fourier transform (GFT) of a signal in terms of its spectral decomposition over the Jordan subspaces of the graph adjacency matrix \(A\). This representation is unique and coordinate free, and it leads to unambiguous definition of the spectral components ("harmonics") of a graph signal. This is particularly meaningful when \(A\) has repeated eigenvalues, and it is very useful when \(A\) is defective or not diagonalizable (as it may be the case with directed graphs). Many real world large sparse graphs have defective adjacency matrices. We present properties of the GFT and show it to satisfy a generalized Parseval inequality and to admit a total variation ordering of the spectral components. We express the GFT in terms of spectral projectors and present an illustrative example for a real world large urban traffic dataset.
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                Author and article information

                Journal
                27 October 2017
                Article
                1710.10370
                5f542c02-1240-4cdc-98af-8dbd5012e4de

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                cs.LG stat.ML

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