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第7讲 图卷积神经网络1
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沈华伟
中国科学院计算技术研究所
Graph
Convolutional Neural Networks
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Convolutional Neural Network
Convolutional neural network (CNN) gains great success on
Euclidean data, e.g., image, text, audio, and video
Image classification, object detection, machine translation
The power of CNN lies in
its ability to learn local stationary structures, via localized
convolution filter, and compose them to form multi-scale
hierarchical patterns
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M. M. Bronstein, J. Bruna, Y. LeCun, A. Szlam, P. Vandergheynst. Geometric deep learning: going beyond Euclidean
data. IEEE Signal Processing Magazine, 18-42, 2017.
Temporal convolutional networkConvolutional neural networks on image
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Convolutional Neural Network
Localized convolutional filters are translation- or shift-
invariant
Which are able to recognize identical features independently
of their spatial locations
One interesting problem is how to generalize convolution to
non-Euclidean domain, e.g., graph?
Irregular structure of graph poses challenges for defining
convolution for graph data
3
LeCun, Y., Bengio, Y., and Hinton, G. Deep learning. Nature, 521(7553):436, 2015
Template Matching
X-Shape
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From CNN to graph CNN
Convolution is well defined in Euclidean data, grid-like
network
Not straightforward to define convolution on irregular
network, widely observed in real world
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Grid-like network Irregular networks
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Convolution
Convolution is a mathematical operation on two functions,
and , to produce a third function .
Defined as the integral, in continuous case, or sum, in discrete case, of
the product of the two functions after one is reversed and shifted.
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Continuous case
Discrete case
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