Learning Convolutional Neural Networks for Graphs
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1 GA Learning Convolutional Neural Networks for Graphs Mathias Niepert Mohamed Ahmed Konstantin Kutzkov NEC Laboratories Europe
2 Representation Learning for Graphs Telecom Safety Transportation Industry Smart cities Intermediate Representation: Graphs? Deep Learning System (Edge) deployment Learning Convolutional Neural Networks for Graphs
3 Problem Definition Input: Finite collection of graphs Nodes of any two graphs are not necessarily in correspondence Nodes and edges may have attributes (discrete and continuous) Problem: Learn a representation for classification/regression Example: Graph classification problem class[ ] =? Learning Convolutional Neural Networks for Graphs
4 State of the Art: Graph Kernels Define kernel based on substructures Shortest paths Random walks Subtrees... Kernel is similarity function on pairs of graphs Count the number of common substructures Use graph kernels with SVMs 4 Learning Convolutional Neural Networks for Graphs
5 Patchy: Learning CNNs for Graphs 5 Learning Convolutional Neural Networks for Graphs
6 Patchy: Learning CNNs for Graphs node sequence selection (w=6 nodes) 6 Learning Convolutional Neural Networks for Graphs
7 Patchy: Learning CNNs for Graphs node sequence selection (w=6 nodes) 7 Learning Convolutional Neural Networks for Graphs
8 Patchy: Learning CNNs for Graphs node sequence selection (w=6 nodes) 8 Learning Convolutional Neural Networks for Graphs
9 Patchy: Learning CNNs for Graphs node sequence selection (w=6 nodes) 9 Learning Convolutional Neural Networks for Graphs
10 Patchy: Learning CNNs for Graphs node sequence selection (w=6 nodes) 10 Learning Convolutional Neural Networks for Graphs
11 Patchy: Learning CNNs for Graphs node sequence selection (w=6 nodes) 11 Learning Convolutional Neural Networks for Graphs
12 Patchy: Learning CNNs for Graphs neighborhood assembly (at least k=4 nodes) node sequence selection (w=6 nodes) 1 Learning Convolutional Neural Networks for Graphs
13 Patchy: Learning CNNs for Graphs neighborhood assembly (at least k=4 nodes) node sequence selection (w=6 nodes) 1 Learning Convolutional Neural Networks for Graphs
14 Patchy: Learning CNNs for Graphs neighborhood assembly (at least k=4 nodes) node sequence selection (w=6 nodes) 14 Learning Convolutional Neural Networks for Graphs
15 Patchy: Learning CNNs for Graphs neighborhood assembly (at least k=4 nodes) node sequence selection (w=6 nodes) 15 Learning Convolutional Neural Networks for Graphs
16 Patchy: Learning CNNs for Graphs neighborhood assembly (at least k=4 nodes) node sequence selection (w=6 nodes) 16 Learning Convolutional Neural Networks for Graphs
17 Patchy: Learning CNNs for Graphs neighborhood assembly (at least k=4 nodes) node sequence selection (w=6 nodes) 17 Learning Convolutional Neural Networks for Graphs
18 Patchy: Learning CNNs for Graphs neighborhood normalization (exactly k=4 nodes) neighborhood assembly (at least k=4 nodes) node sequence selection (w=6 nodes) 18 Learning Convolutional Neural Networks for Graphs
19 Patchy: Learning CNNs for Graphs Convolutional architecture a m a m a m normalized neighborhoods serve as receptive fields node and edge attributes correspond to channels neighborhood normalization 19 Learning Convolutional Neural Networks for Graphs
20 Node Sequence Selection We use centrality measures to generate the node sequences Nodes with similar structural roles are aligned across graphs node sequence selection A: Betweenness centrality B: Closeness centrality C: Eigenvector centrality D: Degree centrality 0 Learning Convolutional Neural Networks for Graphs
21 Neighborhood Assembly Simple breadth-first expansion until at least k nodes added, or no additional nodes to add neighborhood assembly 1 Learning Convolutional Neural Networks for Graphs
22 Graph Normalization Problem Nodes of any two graphs should have similar position in the adjacency matrices iff their structural roles are similar adjacency matrices under labeling 4 labeling method (centrality etc.) distance measures in matrix and graph space 1 normalization Result: For several distance measure pairs it is possible to efficiently compare labeling methods without supervision Example: A A 1 and edit distance on graphs Learning Convolutional Neural Networks for Graphs
23 Graph Normalization 1 Distance to root node Learning Convolutional Neural Networks for Graphs
24 Graph Normalization Centrality measures, etc. 1 Distance to root node 4 Learning Convolutional Neural Networks for Graphs
25 Graph Normalization Canonicalization (break ties) Centrality measures, etc. 1 Distance to root node 5 Learning Convolutional Neural Networks for Graphs
26 Computational Complexity At most linear in number of input graphs At most quadratic in number of nodes for each graph (depends on maximal node degree and centrality measure) 6 Learning Convolutional Neural Networks for Graphs
27 Convolutional Architecture v 1 v M field size: 4, stride: 4, filters: M Learning Convolutional Neural Networks for Graphs
28 Convolutional Architecture v 1 v M field size: 4, stride: 4, filters: M Learning Convolutional Neural Networks for Graphs
29 Convolutional Architecture v 1 v M v 1 v M field size: 4, stride: 4, filters: M Learning Convolutional Neural Networks for Graphs
30 Convolutional Architecture v 1 v N field size:, stride: 1, N filters v 1 v M v 1 v M field size: 4, stride: 4, filters: M Learning Convolutional Neural Networks for Graphs
31 Convolutional Architecture v 1 v N field size:, stride: 1, N filters v 1 v M v 1 v M field size: 4, stride: 4, filters: M Learning Convolutional Neural Networks for Graphs
32 Convolutional Architecture v 1 v N v 1 v N field size:, stride: 1, N filters v 1 v M v 1 v M field size: 4, stride: 4, filters: M Learning Convolutional Neural Networks for Graphs
33 Experiments - Graph Classification Finite collection of graphs and their class labels class = 1 class = 0 class = 1 Nodes of any two graphs are not necessarily in correspondence Nodes and edges may have attributes (discrete and continuous) Learn a function from graphs to class labels class[ ] =? Learning Convolutional Neural Networks for Graphs
34 Experiments - Convolutional Architecture softmax flatten, dense 18 units field size: 10, stride: 1, filters: field size: k, stride: k, filters: Learning Convolutional Neural Networks for Graphs
35 Classification Datasets MUTAG: Nitro compounds where classes indicate mutagenic effect on a bacterium (Salmonella Typhimurium) PTC: Chemical compounds where classes indicate carcinogenicity for male and female rats NCI: Chemical compounds where classes indicate activity against non-small cell lung cancer and ovarian cancer cell lines D&D: Protein structures where classes indicate whether structure is an enzyme or not... 5 Learning Convolutional Neural Networks for Graphs
36 Experiments - Graph Classification Q: How efficient and effective compared to graph kernels? Apply Patchy to typical graph classification benchmark data 6 Learning Convolutional Neural Networks for Graphs
37 Experiments - Visualization Q: What do learned edge filters look like? Restricted Boltzmann machine applied to graphs Receptive field size of hidden layer: 9 graphs sampled from RBM small instances of graphs weights of hidden nodes 7 Learning Convolutional Neural Networks for Graphs
38 Discussion Pros: Graph kernel design not required Outperforms graph kernels on several datasets (speed and accuracy) Incorporates node and edge features (discrete and continuous) Supports visualizations (graph motifs, etc.) Cons: Prone to overfitting on smaller data sets (graph kernel benchmarks) Shift from designing graph kernels to tuning hyperparameters Graph normalization not part of learning code to be released: patchy.neclab.eu 8 Learning Convolutional Neural Networks for Graphs
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