Abstract
In recent years, graph neural network (GNN) has become the main stream for most of recent researches due to its powers in dealing with complex graph data learning problems. However, as most of the recent GNN-based architectures have been mainly designed to only evaluate direct relational structures between nodes. As the results, these techniques are unable to capture the sophisticated multi-way relationships in graph. The multi-way relationships can be represented by both explicit graph-based and complex topological structures. In general, the multi-way relationships in graph can be modelled as simplicial complexes, hyper-graphs, e.g., and can be efficiently preserved under the simplicial neural networks (SNN). There are several notable SNN-based architectures have been proposed recently, such as the well-known simplicial convolutional neural network (SCNN). The SNN-based techniques have shown the competitive performances in handling graph learning. However, most of recent proposed SNN-based architectures are designed upon the deep neural learning paradigm. Therefore, they still encountered several challenges with regard to the feature noise and data uncertainty. To overcome these limitations, in this paper, we proposed a novel integrated SNN and neuro-fuzzy network (NFN) graph embedding technique, called as: SFGE. Our SFGE model is designed to better capture the multi-way structural representation of graph by taking advances of different advanced graph-based and fuzzy-based neural learning techniques. By taking advances of neuro-fuzzy learning approach, our model can efficiently support to eliminate the feature uncertainty/ambiguity during the task-driven fine-tuning process. In addition, it also supports to better capture the rich multi-way relational structures of the input graphs under the topology-enhanced graph analysis approach. Extensive empirical studies within a real-world molecular graph dataset have effectiveness of our SFGE in dealing with graph classification task.







Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Data availability
There is no data associated with our studies in this paper.
Notes
AERU (University of Hertfordshire): https://sitem.herts.ac.uk/aeru/
ECOTOX: https://cfpub.epa.gov/ecotox
RDKit: https://www.rdkit.org/
References
Wu Z, Pan S, Chen F, Long G, Zhang C, Philip SY (2021) A comprehensive survey on graph neural networks. IEEE Trans Neural Netw Learn Syst 32(1):4–24
Han M, Wu H, Chen Z, Li M, Zhang X (2023) A survey of multi-label classification based on supervised and semi-supervised learning. Int J Mach Learn Cybern 14(3):697–724
Cui P, Wang X, Pei J, Zhu W (2018) A survey on network embedding. IEEE Trans Knowl Data Eng 31(5):833–852
Pham P, Do P (2020) W-Metagraph2Vec: a novel approval of enriched schematic topic-driven heterogeneous information network embedding. Int J Mach Learn Cybern 11(8):1855–1874
Pham P, Nguyen LT, Pedrycz W, Vo B (2022) Deep learning, graph-based text representation and classification: a survey, perspectives and challenges. Artif Intell Rev 56(6):4893–4927
Alzubi JA, Jain R, Nagrath P, Satapathy S, Taneja S, Gupta P (2021) Deep image captioning using an ensemble of CNN and LSTM based deep neural networks. J Intell Fuzzy Syst 40(4):5761–5769
Browne F, Wang H, Zheng H (2018) Investigating the impact human protein–protein interaction networks have on disease-gene analysis. Int J Mach Learn Cybern 9:455–464
Sharma A, Rani R (2020) Drug sensitivity prediction framework using ensemble and multi-task learning. Int J Mach Learn Cybern 11(6):1231–1240
Wei Y, Ma H, Wang Y, Li Z, Chang L (2023) Dual graph attention networks for multi-behavior recommendation. Int J Mach Learn Cybern 14(8):2831–846
Pham P, Nguyen LT, Nguyen NT, Pedrycz W, Yun U, Lin JCW, Vo B (2023) An approach to semantic-aware heterogeneous network embedding for recommender systems. IEEE Trans Cybern 53(9):6027–6040
Mikolov T, Chen K, Corrado G, Dean J (2013) Efficient estimation of word representations in vector space. ICLR
Pennington J, Socher R, Manning CD (2014) Glove: Global vectors for word representation. EMNLP, pp 1532–1543
Perozzi B, Al-Rfou R, Skiena S (2014) Deepwalk: Online learning of social representations. SIGKDD, pp 701–710
Grover A, Leskovec J (2016) Node2vec: Scalable feature learning for networks. SIGKDD, pp 855–864
Xu W, Guo D, Mi J, Qian Y, Zheng K, Ding W (2023) Two-way concept-cognitive learning via concept movement viewpoint. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2023.3235800
Alzubi JA, Alzubi OA, Beseiso M, Budati AK, Shankar K (2022) Optimal multiple key-based homomorphic encryption with deep neural networks to secure medical data transmission and diagnosis. Expert Syst 39(4):e12879
Guo D, Jiang C, Sheng R, Liu S (2022) A novel outcome evaluation model of three-way decision: a change viewpoint. Inf Sci 607:1089–1110
Alzubi OA, Alzubi JA, Alweshah M, Qiqieh I, Al-Shami S, Ramachandran M (2020) An optimal pruning algorithm of classifier ensembles: dynamic programming approach. Neural Comput Appl 32:16091–16107
Movassagh AA, Alzubi JA, Gheisari M, Rahimi M, Mohan S, Abbasi AA, Nabipour N (2021) Artificial neural networks training algorithm integrating invasive weed optimization with differential evolutionary model. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-020-02623-6
Kipf TN, Welling M (2017) Semi-supervised classification with graph convolutional networks. ICLR
Hamilton W, Ying Z, Leskovec J (2017) Inductive representation learning on large graphs, vol 30. NeurIPS
Veličković P, Cucurull G, Casanova A, Romero A, Lio P, Bengio Y (2018) Graph attention networks.ICLR
Feng W, Zhang J, Dong Y, Han Y, Luan H, Xu Q, Tang J (2020) Graph random neural networks for semi-supervised learning on graphs. NeurIPS 33:22092–22103
Brody S, Alon U, Yahav E (2022) How Attentive are Graph Attention Networks?. ICLR
Xu K, Hu W, Leskovec J, Jegelka S (2019) How Powerful are graph neural networks?. ICLR
Hu W, Liu B, Gomes J, Zitnik M, Liang P, Pande V, Leskovec J (2019) Strategies for pre-training graph neural networks. ICLR
Ying Z, You J, Morris C, Ren X, Hamilton W, Leskovec J (2018) Hierarchical graph representation learning with differentiable pooling. NeurIPS 31
Zhang M, Cui Z, Neumann M, Chen Y (2018) An end-to-end deep learning architecture for graph classification. AAAI 32(1)
Hofer C, Graf F, Rieck B, Niethammer M, Kwitt R (2020) Graph filtration learning. ICML, pp 4314–4323
Zhao Q, Ye Z, Chen C, Wang Y (2020) Persistence enhanced graph neural network. AISTATS, pp 2896–2906
Horn M, De Brouwer E, Moor M, Moreau Y, Rieck B, Borgwardt K (2022) Topological graph neural networks. ICLR
Hensel F, Moor M, Rieck B (2021) A survey of topological machine learning methods. Front Artif Intell 4:681108
Ebli S, Defferrard M, Spreemann G (2020) Simplicial neural networks. NeurIPS 2020 Workshop TDA and Beyond
Bunch E, You Q, Fung G, Singh V (2020) Simplicial 2-complex convolutional neural nets. NeurIPS 2020 Workshop TDA and Beyond
Yang M, Isufi E, Leus G (2022) Simplicial convolutional neural networks. ICASSP, pp 8847–8851
Cinque DM, Battiloro C, Di Lorenzo P (2023) Pooling strategies for simplicial convolutional networks. ICASSP, pp 1–5
Xu W, Yuan K, Li W, Ding W (2022) An emerging fuzzy feature selection method using composite entropy-based uncertainty measure and data distribution. IEEE Trans Emerg Topics Comput Intell 7(1):76–88
Xu W, Guo D, Qian Y, Ding W (2022) Two-way concept-cognitive learning method: a fuzzy-based progressive learning. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2022.3216110
Yuan K, Xu W, Li W, Ding W (2022) An incremental learning mechanism for object classification based on progressive fuzzy three-way concept. Inf Sci 584:127–147
Guo D, Xu W (2023) Fuzzy-based concept-cognitive learning: An investigation of novel approach to tumor diagnosis analysis. Inf Sci 639:118998
Guo D, Xu W, Qian Y, Ding W (2023) M-FCCL: Memory-based concept-cognitive learning for dynamic fuzzy data classification and knowledge fusion. Inf Fusion 100:101962
Zhang L, Shi Y, Chang YC, Lin CT (2023) Robust fuzzy neural network with an adaptive inference engine. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2023.3241170
Guo D, Xu W, Qian Y, Ding W (2023) Fuzzy-granular concept-cognitive learning via three-way decision: performance evaluation on dynamic knowledge discovery. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2023.3325952
Pham P, Nguyen LT, Nguyen NT, Kozma R, Vo B (2023) A hierarchical fused fuzzy deep neural network with heterogeneous network embedding for recommendation. Inf Sci 620:105–124
Pham P, Nguyen LT, Vo B, Yun U (2022) Bot2Vec: A general approach of intra-community oriented representation learning for bot detection in different types of social networks. Inf Syst 103:101771
Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez AN, Polosukhin, I (2017) Attention is all you need. NeurIPS 30
Lee J, Lee I, Kang J (2019) Self-attention graph pooling. ICML, pp 3734–3743
Yang M, Isufi E, Schaub MT, Leus G (2021) Finite impulse response filters for simplicial complexes. EUSIPCO, pp 2005–2009
Barbarossa S, Sardellitti S (2020) Topological signal processing over simplicial complexes. IEEE Trans Signal Process 68:2992–3007
Schaub MT, Zhu Y, Seby JB, Roddenberry TM, Segarra S (2021) Signal processing on higher-order networks: Livin’on the edge... and beyond. Signal Process 187:108149
Bodnar C, Frasca F, Wang Y, Otter N, Montufar GF, Lio P, Bronstein M (2021) Weisfeiler and lehman go topological: Message passing simplicial networks. ICML, pp 2005–2009
Giusti L, Battiloro C, Di Lorenzo P, Sardellitti S, Barbarossa S (2022) Simplicial attention networks. ICLR 2022 Workshop on Geometrical and Topological Representation Learning
Goldberg TE (2002) Combinatorial Laplacians of simplicial complexes. Senior Thesis, Bard College vol 6
Lim LH (2020) Hodge Laplacians on graphs. SIAM Rev 62(3):685–715
Wang F, Yang JF, Wang MY, Jia CY, Shi XX, Hao GF, Yang GF (2020) Graph attention convolutional neural network model for chemical poisoning of honey bees’ prediction. Sci Bull 65(14):1184–1191
Acknowledgements
This research is funded by HUTECH University, Ho Chi Minh City, Vietnam.
Funding
This research was funded by HUTECH University.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflicts of interest
Employment: Phu Pham is currently working as full-time researcher and lecturer at HUTECH University. Financial interests: Phu Pham has received research support from HUTECH University. Non-financial interests: None.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Pham, P. An integrated simplicial neural network with neuro-fuzzy network for graph embedding. Int. J. Mach. Learn. & Cyber. 16, 233–251 (2025). https://doi.org/10.1007/s13042-024-02201-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13042-024-02201-8