Abstract
Convolutional neural networks (CNN) have enabled major advances in image classification through convolution and pooling. In particular, image pooling transforms a connected discrete grid into a reduced grid with the same connectivity and allows reduction functions to take into account all the pixels of an image. However, a pooling satisfying such properties does not exist for graphs. Indeed, some methods are based on a vertex selection step which induces an important loss of information. Other methods learn a fuzzy clustering of vertex sets which induces almost complete reduced graphs. We propose to overcome both problems using a new pooling method, named MIVSPool. This method is based on a selection of vertices called surviving vertices using a Maximal Independent Vertex Set (MIVS) and an assignment of the remaining vertices to the survivors. Consequently, our method does not discard any vertex information nor artificially increase the density of the graph. Experimental results show an increase in accuracy for graph classification on various standard datasets.
The work reported in the paper was supported by French ANR grant #ANR-21-CE23-0025 CoDeGNN.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Balcilar, M., Renton, G., Héroux, P., Gaüzère, B., Adam, S., Honeine, P.: Analyzing the expressive power of graph neural networks in a spectral perspective. In: International Conference on Learning Representations (2021)
Bianchi, F.M., Grattarola, D., Livi, L., Alippi, C.: Hierarchical representation learning in graph neural networks with node decimation pooling. IEEE Trans. Neural Networks Learn. Syst. 33(5), 2195–2207 (2022)
Borgwardt, K.M., Ong, C.S., Schönauer, S., Vishwanathan, S., Smola, A.J., Kriegel, H.P.: Protein function prediction via graph kernels. Bioinformatics 21(suppl_1), 47–56 (2005)
Dobson, P.D., Doig, A.J.: Distinguishing enzyme structures from non-enzymes without alignments. J. Mol. Biol. 330(4), 771–783 (2003)
Gao, H., Ji, S.: Graph u-nets. In: International Conference on Machine Learning, pp. 2083–2092. PMLR (2019)
Hamilton, W., Ying, Z., Leskovec, J.: Inductive representation learning on large graphs. Adv. Neural. Inf. Process. Syst. 30, 1024–1034 (2017)
Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. In: International Conference on Learning Representations (ICLR) (2017)
Lee, J., Lee, I., Kang, J.: Self-attention graph pooling. In: International Conference on Machine Learning, pp. 3734–3743. PMLR (2019)
Meer, P.: Stochastic image pyramids. Compu. Vis. Graphics Image Process. 45(3), 269–294 (1989)
Nouranizadeh, A., Matinkia, M., Rahmati, M., Safabakhsh, R.: Maximum entropy weighted independent set pooling for graph neural networks. ArXiv abs/2107.01410 (2021)
Scarselli, F., Gori, M., Tsoi, A.C., Hagenbuchner, M., Monfardini, G.: The graph neural network model. IEEE Trans. Neural Netw. 20(1), 61–80 (2008)
Wale, N., Watson, I.A., Karypis, G.: Comparison of descriptor spaces for chemical compound retrieval and classification. Knowl. Inf. Syst. 14(3), 347–375 (2008)
Ying, Z., et al.: Hierarchical graph representation learning with differentiable pooling. Adv. Neural. Inf. Process. Syst. 31, 4805–4815 (2018)
Zhang, M., Cui, Z., Neumann, M., Chen, Y.: An end-to-end deep learning architecture for graph classification. Proc. AAAI Conf. Artif. Intell. 32(1), 4438–4445 (2018)
Zhang, Z., et al.: Hierarchical multi-view graph pooling with structure learning. IEEE Trans. Knowl. Data Eng. 35, 545–559 (2021)
Acknowledgements
The work was performed using computing resources of CRIANN (Normandy, France).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Stanovic, S., Gaüzère, B., Brun, L. (2022). Maximal Independent Vertex Set Applied to Graph Pooling. In: Krzyzak, A., Suen, C.Y., Torsello, A., Nobile, N. (eds) Structural, Syntactic, and Statistical Pattern Recognition. S+SSPR 2022. Lecture Notes in Computer Science, vol 13813. Springer, Cham. https://doi.org/10.1007/978-3-031-23028-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-031-23028-8_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-23027-1
Online ISBN: 978-3-031-23028-8
eBook Packages: Computer ScienceComputer Science (R0)