527 research outputs found
Hierarchical Graph Convolutional Networks for Semi-supervised Node Classification
Graph convolutional networks (GCNs) have been successfully applied in node
classification tasks of network mining. However, most of these models based on
neighborhood aggregation are usually shallow and lack the "graph pooling"
mechanism, which prevents the model from obtaining adequate global information.
In order to increase the receptive field, we propose a novel deep Hierarchical
Graph Convolutional Network (H-GCN) for semi-supervised node classification.
H-GCN first repeatedly aggregates structurally similar nodes to hyper-nodes and
then refines the coarsened graph to the original to restore the representation
for each node. Instead of merely aggregating one- or two-hop neighborhood
information, the proposed coarsening procedure enlarges the receptive field for
each node, hence more global information can be captured. The proposed H-GCN
model shows strong empirical performance on various public benchmark graph
datasets, outperforming state-of-the-art methods and acquiring up to 5.9%
performance improvement in terms of accuracy. In addition, when only a few
labeled samples are provided, our model gains substantial improvements.Comment: 8 pages, 3 figures, 3 tables, accepted by International Joint
Conference on Artificial Intelligence (IJCAI-19
Graph Convolutional Networks with EigenPooling
Graph neural networks, which generalize deep neural network models to graph
structured data, have attracted increasing attention in recent years. They
usually learn node representations by transforming, propagating and aggregating
node features and have been proven to improve the performance of many graph
related tasks such as node classification and link prediction. To apply graph
neural networks for the graph classification task, approaches to generate the
\textit{graph representation} from node representations are demanded. A common
way is to globally combine the node representations. However, rich structural
information is overlooked. Thus a hierarchical pooling procedure is desired to
preserve the graph structure during the graph representation learning. There
are some recent works on hierarchically learning graph representation analogous
to the pooling step in conventional convolutional neural (CNN) networks.
However, the local structural information is still largely neglected during the
pooling process. In this paper, we introduce a pooling operator \pooling
based on graph Fourier transform, which can utilize the node features and local
structures during the pooling process. We then design pooling layers based on
the pooling operator, which are further combined with traditional GCN
convolutional layers to form a graph neural network framework \m for graph
classification. Theoretical analysis is provided to understand \pooling from
both local and global perspectives. Experimental results of the graph
classification task on commonly used benchmarks demonstrate the
effectiveness of the proposed framework
Classifying Signals on Irregular Domains via Convolutional Cluster Pooling
We present a novel and hierarchical approach for supervised classification of
signals spanning over a fixed graph, reflecting shared properties of the
dataset. To this end, we introduce a Convolutional Cluster Pooling layer
exploiting a multi-scale clustering in order to highlight, at different
resolutions, locally connected regions on the input graph. Our proposal
generalises well-established neural models such as Convolutional Neural
Networks (CNNs) on irregular and complex domains, by means of the exploitation
of the weight sharing property in a graph-oriented architecture. In this work,
such property is based on the centrality of each vertex within its
soft-assigned cluster. Extensive experiments on NTU RGB+D, CIFAR-10 and 20NEWS
demonstrate the effectiveness of the proposed technique in capturing both local
and global patterns in graph-structured data out of different domains.Comment: 12 pages, 6 figures. To appear in the Proceedings of the 22nd
International Conference on Artificial Intelligence and Statistics (AISTATS)
2019, Naha, Okinawa, Japan. PMLR: Volume 8
Octree guided CNN with Spherical Kernels for 3D Point Clouds
We propose an octree guided neural network architecture and spherical
convolutional kernel for machine learning from arbitrary 3D point clouds. The
network architecture capitalizes on the sparse nature of irregular point
clouds, and hierarchically coarsens the data representation with space
partitioning. At the same time, the proposed spherical kernels systematically
quantize point neighborhoods to identify local geometric structures in the
data, while maintaining the properties of translation-invariance and asymmetry.
We specify spherical kernels with the help of network neurons that in turn are
associated with spatial locations. We exploit this association to avert dynamic
kernel generation during network training that enables efficient learning with
high resolution point clouds. The effectiveness of the proposed technique is
established on the benchmark tasks of 3D object classification and
segmentation, achieving new state-of-the-art on ShapeNet and RueMonge2014
datasets.Comment: Accepted in IEEE CVPR 2019. arXiv admin note: substantial text
overlap with arXiv:1805.0787
Representation Learning on Graphs: Methods and Applications
Machine learning on graphs is an important and ubiquitous task with
applications ranging from drug design to friendship recommendation in social
networks. The primary challenge in this domain is finding a way to represent,
or encode, graph structure so that it can be easily exploited by machine
learning models. Traditionally, machine learning approaches relied on
user-defined heuristics to extract features encoding structural information
about a graph (e.g., degree statistics or kernel functions). However, recent
years have seen a surge in approaches that automatically learn to encode graph
structure into low-dimensional embeddings, using techniques based on deep
learning and nonlinear dimensionality reduction. Here we provide a conceptual
review of key advancements in this area of representation learning on graphs,
including matrix factorization-based methods, random-walk based algorithms, and
graph neural networks. We review methods to embed individual nodes as well as
approaches to embed entire (sub)graphs. In doing so, we develop a unified
framework to describe these recent approaches, and we highlight a number of
important applications and directions for future work.Comment: Published in the IEEE Data Engineering Bulletin, September 2017;
version with minor correction
3DTI-Net: Learn Inner Transform Invariant 3D Geometry Features using Dynamic GCN
Deep learning on point clouds has made a lot of progress recently. Many point
cloud dedicated deep learning frameworks, such as PointNet and PointNet++, have
shown advantages in accuracy and speed comparing to those using traditional 3D
convolution algorithms. However, nearly all of these methods face a challenge,
since the coordinates of the point cloud are decided by the coordinate system,
they cannot handle the problem of 3D transform invariance properly. In this
paper, we propose a general framework for point cloud learning. We achieve
transform invariance by learning inner 3D geometry feature based on local graph
representation, and propose a feature extraction network based on graph
convolution network. Through experiments on classification and segmentation
tasks, our method achieves state-of-the-art performance in rotated 3D object
classification, and achieve competitive performance with the state-of-the-art
in classification and segmentation tasks with fixed coordinate value
Convolutional Neural Network on Semi-Regular Triangulated Meshes and its Application to Brain Image Data
We developed a convolution neural network (CNN) on semi-regular triangulated
meshes whose vertices have 6 neighbours. The key blocks of the proposed CNN,
including convolution and down-sampling, are directly defined in a vertex
domain. By exploiting the ordering property of semi-regular meshes, the
convolution is defined on a vertex domain with strong motivation from the
spatial definition of classic convolution. Moreover, the down-sampling of a
semi-regular mesh embedded in a 3D Euclidean space can achieve a down-sampling
rate of 4, 16, 64, etc. We demonstrated the use of this vertex-based graph CNN
for the classification of mild cognitive impairment (MCI) and Alzheimer's
disease (AD) based on 3169 MRI scans of the Alzheimer's Disease Neuroimaging
Initiative (ADNI). We compared the performance of the vertex-based graph CNN
with that of the spectral graph CNN.Comment: conferenc
Enhancing Geometric Deep Learning via Graph Filter Deconvolution
In this paper, we incorporate a graph filter deconvolution step into the
classical geometric convolutional neural network pipeline. More precisely,
under the assumption that the graph domain plays a role in the generation of
the observed graph signals, we pre-process every signal by passing it through a
sparse deconvolution operation governed by a pre-specified filter bank. This
deconvolution operation is formulated as a group-sparse recovery problem, and
convex relaxations that can be solved efficiently are put forth. The
deconvolved signals are then fed into the geometric convolutional neural
network, yielding better classification performance than their unprocessed
counterparts. Numerical experiments showcase the effectiveness of the
deconvolution step on classification tasks on both synthetic and real-world
settings.Comment: 5 pages, 8 figures, to appear in the proceedings of the 2018 6th IEEE
Global Conference on Signal and Information Processing, November 26-29, 2018,
Anaheim, California, US
A Comprehensive Survey on Graph Neural Networks
Deep learning has revolutionized many machine learning tasks in recent years,
ranging from image classification and video processing to speech recognition
and natural language understanding. The data in these tasks are typically
represented in the Euclidean space. However, there is an increasing number of
applications where data are generated from non-Euclidean domains and are
represented as graphs with complex relationships and interdependency between
objects. The complexity of graph data has imposed significant challenges on
existing machine learning algorithms. Recently, many studies on extending deep
learning approaches for graph data have emerged. In this survey, we provide a
comprehensive overview of graph neural networks (GNNs) in data mining and
machine learning fields. We propose a new taxonomy to divide the
state-of-the-art graph neural networks into four categories, namely recurrent
graph neural networks, convolutional graph neural networks, graph autoencoders,
and spatial-temporal graph neural networks. We further discuss the applications
of graph neural networks across various domains and summarize the open source
codes, benchmark data sets, and model evaluation of graph neural networks.
Finally, we propose potential research directions in this rapidly growing
field.Comment: Minor revision (updated tables and references
Graph Attribute Aggregation Network with Progressive Margin Folding
Graph convolutional neural networks (GCNNs) have been attracting increasing
research attention due to its great potential in inference over graph
structures. However, insufficient effort has been devoted to the aggregation
methods between different convolution graph layers. In this paper, we introduce
a graph attribute aggregation network (GAAN) architecture. Different from the
conventional pooling operations, a graph-transformation-based aggregation
strategy, progressive margin folding, PMF, is proposed for integrating graph
features. By distinguishing internal and margin elements, we provide an
approach for implementing the folding iteratively. And a mechanism is also
devised for preserving the local structures during progressively folding. In
addition, a hypergraph-based representation is introduced for transferring the
aggregated information between different layers. Our experiments applied to the
public molecule datasets demonstrate that the proposed GAAN outperforms the
existing GCNN models with significant effectiveness
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