Multi-Criteria Attention-Based Graph Neural Network: A Heterogeneous Representation Learning Framework Abstract. for Logistics System Optimization
الموضوعات :
Mohammad Shahbazi
1
,
Hamid Tohidi
2
,
Majid Nojavan
3
1 - School of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
2 - School of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
3 - School of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
الکلمات المفتاحية: Machine learning, Deep learning, Representation learning, Heterogeneous systems, Logistics optimization,
ملخص المقالة :
Modeling the intricate relationships within complex logistics systems is essential for op- timizing various operations—such as routing, scheduling, and distribution—in modern supply chains. These systems often exhibit significant diversity in their facilities, transportation modes, and capacity constraints, introducing a phenomenon known as “heterogeneity,” which complicates the modeling pro- cess. To simplify calculations, some researchers assume homogeneous systems, overlooking critical variability in nodes (e.g., warehouses, distribution centers) and edges (e.g., transportation routes, capac- ities). However, ignoring this heterogeneity can lead to a marked decrease in model accuracy.
A representation learning method specifically tailored for heterogeneous logistics systems is proposed here, preserving the multifaceted relationships among components and enhancing model performance in real-world scenarios. Two novel extensions refine the underlying graph-based deep learning architecture by incorporating techniques from deep learning, graph probability models, and machine learning. The approach is evaluated on a representative logistics network dataset, with precision, F1 score, and recall as performance metrics. Experimental results indicate that this method outperforms existing methods by providing higher precision, enabling more accurate classification of system components and better extraction of relationships within complex logistics networks.
[1] Y. Bengio, A. Courville, and P. Vincent, "Representation learning: A review and new per- spectives," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 35, no. 8, pp. 1798–1828, Aug. 2013. doi: 10.1109/TPAMI.2013.50
[2] J. Han, "Mining heterogeneous information networks by exploring the power of links," in Discovery Science. Berlin, Germany: Springer, 2009, pp. 13–30. doi: 10.1007/978-3-642- 04955-63
[3] L. Getoor and C. P. Diehl, "Link mining: A survey," SIGKDD Explorer Newsletter, vol. 7, no. 2, pp. 3–12, Dec. 2005. doi: 10.1145/1089815.1089817
[4] E. Otte and R. Rousseau, "Social network analysis: a powerful strategy, also for the informa- tion science," Journal of Information Science, vol. 28, no. 6, pp. 441–453, Dec. 2002. doi: 10.1177/016555150202800601
[5] S. Chakrabarti, Mining the Web: Analysis of Hypertext and Semi Structured Data, Aug. 2002. doi: 10.1007/3-540-45778-81 3
[6] T. Lewis, Network Science: Theory and Applications, Wiley, 2013. doi: 10.1002/9781118670008
[7] D. J. Cook and L. B. Holdelder, "Graph-based data mining," IEEE Intelligent Systems, vol. 15, no.
2, pp. 32–41, Mar./Apr. 2000. doi: 10.1109/5254.846291
[8] P. Pham, L. T. T. Nguyen, B. Vo, and U. Yun, "Bot2Vec: A general approach of intra-community oriented representation learning for bot detection in different types of social networks," IEEE Access, vol. 10, pp. 12162–12174, 2022. doi: 10.1109/ACCESS.2021.3067189
[9] Y. Sun and J. Han, "Mining heterogeneous information networks: A structural analysis approach," SIGKDD Explorer Newsletter, vol. 14, no. 2, pp. 20–28, Dec. 2013. doi: 10.1145/2541141.2541145
[10] M. Nazari, A. Oroojlooy, L. V. Snyder, and M. Takáč, "Reinforcement Learning for Solving the Vehicle Routing Problem," in NeurIPS, pp. 9839–9849, 2018.
[11] J.Chen,H.Zhou,S.Xie,andS.Sun,"LearningtoOptimizeCapacitatedVehicleRoutingProblems with Heterogeneous Demands via Graph Neural Networks," European Journal of Operational Research, vol. 292, no. 3, pp. 887–901, 2021. doi: 10.1016/j.ejor.2020.11.033
[12] Z.Chen,Y.Liu,andQ.Song,"Agraphneuralnetworkapproachforsolvingcapacitatedvehiclerout- ing problems," Computers & Operations Research, vol. 140, 2022. doi: 10.1016/j.cor.2022.105643
[13] Y. Sun, J. Han, X. Yan, P. Yu, and T. Wu, "Pathsim: Meta path-based top-k similarity search in heterogeneous information networks," in Proceedings of the VLDB Endowment, vol. 4, no. 11, pp. 992–1003, Aug. 2011. doi: 10.14778/2078331.2078334
[14] W. Wang, T. Tang, F. Xia, Z. Gong, Z. Chen, and H. Liu, "Collaborative filtering with network representation learning for citation recommendation," IEEE Transactions on Big Data, vol. 6, no. 2, pp. 283–294, Apr.–Jun. 2020. doi: 10.1109/TBDATA.2018.2839571
10
[15] L.Guo,H.Yin,T.Chen,X.Zhang,andK.Zheng,"Hierarchicalhyperedgeembedding-basedrepre- sentation learning for group recommendation," CoRR, abs/2103.13506, Mar. 2021. doi: 2103.13506
[16] Y. Xu, E. Wang, Y. Yang, and Y. Chang, "A unified collaborative representation learning for neural network based recommender systems," IEEE Transactions on Knowledge and Data Engineering, 2021 (Early Access). doi: 10.1109/TKDE.2021.3061575
[17] D. Zhou, Z. Xu, W. Li, X. Xie, and S. Peng, "MultiDTI: Drug-target interaction prediction based on multi-modal representation learning to bridge the gap between new chemical entities and known heterogeneous network," IEEE Access, vol. 9, pp. 60596–60606, 2021. doi: 10.1109/AC- CESS.2021.3072153
[18] M.M.Li,K.Huang,andM.Zitnik,"Representationlearningfornetworksinbiologyandmedicine: Advancements, challenges, and opportunities," IEEE Access, vol. 9, pp. 40539–40555, 2021. doi: 10.1109/ACCESS.2021.3065465
[19] M. Girvan and M. E. J. Newman, "Community structure in social and biological networks," Proceedings of the National Academy of Sciences, vol. 99, pp. 7821–7826, 2002. doi: 10.1073/pnas.122653799
[20] M. Valueva, N. Nagornov, P. Lyakhov, G. Valuev, and N. Chervyakov, "Application of the residue number system to reduce hardware costs of the convolutional neural network imple- mentation," Mathematics and Computers in Simulation, vol. 177, pp. 232–243, 2020. doi: 10.1016/j.matcom.2020.07.006
[21] W. Zhang, K. Itoh, J. Tanida, and Y. Ichioka, "Parallel distributed processing model with local space-invariant interconnections and its optical architecture," Applied Optics, vol. 29, no. 32, pp. 4790–4799, Nov. 1990. doi: 10.1364/AO.29.004790
[22] R. Salakhutdinov and G. Hinton, "Semantic hashing," International Journal of Approximate Rea- soning, vol. 50, no. 7, pp. 969–978, 2009. doi: 10.1016/j.ijar.2008.11.006
[23] S. Cao, W. Lu, and Q. Xu, "Grarep: Learning graph representations with global structural infor- mation," in Proceedings of the 24th ACM International Conference on Information and Knowledge Management, 2015, pp. 891–900. doi: 10.1145/2806416.2806512
[24] M. E. J. Newman, "Finding community structure in networks using the eigenvectors of matrices," Physical Review E, vol. 74, no. 3, Sep. 2006. doi: 10.1103/PhysRevE.74.036104
[25] P. Vincent, H. Larochelle, I. Lajoie, Y. Bengio, and P.-A. Manzagol, "Stacked denoising autoen- coders: Learning useful representations in a deep network with a local denoising criterion," Journal of Machine Learning Research, vol. 11, pp. 3371–3408, 2010.
[26] R.-E. Fan, K.-W. Chang, C.-J. Hsieh, X.-R. Wang, and C.-J. Lin, "Liblinear: A library for large linear classification," The Journal of Machine Learning Research, vol. 9, pp. 1871–1874, 2008. doi: 10.1145/2001269.2001293
[27] Q. V. Le and T. Mikolov, "Distributed representations of sentences and documents," in CoRR, vol. abs/1405.4053, 2014. doi: 10.3115/1963501.1963531
11
[28] N.Djuric,H.Wu,V.Radosavljevic,M.Grbovic,andN.Bhamidipati,"Hierarchicalneurallanguage models for joint representation of streaming documents and their content," in Proceedings of the 24th International Conference on World Wide Web, 2015. doi: 10.1145/2736277.2741093
[29] A. Vaswani, N. Shazeer, N. Parmar, et al., "Attention is all you need," in CoRR, abs/1706.03762, 2017. doi: 10.1145/3292500.3330644
[30] C.Yang,Z.Liu,D.Zhao,M.Sun,andE.Y.Chang,"Networkrepresentationlearningwithrichtext information," in Proceedings of the 24th International Conference on Artificial Intelligence, 2015, pp. 2111–2117. doi: 10.1145/2806416.2806458
[31] L. Tang and H. Liu, "Relational learning via latent social dimensions," in Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2009, pp. 817–826. doi: 10.1145/1557019.1557107
[32] T. Mikolov, K. Chen, G. Corrado, and J. Dean, "Efficient estimation of word representations in vector space," in Proceedings of 1st International Conference on Learning Representations (ICLR), 2013.
[33] T. Mikolov, I. Sutskever, K. Chen, G. Corrado, and J. Dean, "Distributed representations of words and phrases and their compositionality," in Proceedings of the 26th International Conference on Neural Information Processing Systems, 2013, pp. 3111–3119.
[34] B. Perozzi, R. Al-Rfou, and S. Skiena, "Deepwalk: Online learning of social representations," in CoRR, abs/1403.6652, 2014. doi: 10.1145/2736277.2741093
[35] A. Grover and J. Leskovec, "node2vec: Scalable feature learning for networks," in CoRR, abs/1607.00653, 2016. doi: 10.1145/3097983.3098135
[36] J. Li, J. Zhu, and B. Zhang, "Discriminative deep random walk for network classification," in Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics, 2016. doi: 10.18653/v1/P16-1119
[37] J.Chen,Q.Zhang,andX.Huang,"Incorporategroupinformationtoenhancenetworkembedding," in Proceedings of the 25th ACM International on Conference on Information and Knowledge Management, 2016, pp. 1901–1904. doi: 10.1145/2983323.2983888
[38] M.Gong,C.Yao,Y.Xie,andM.Xu,"Semi-supervisednetworkembeddingwithtextinformation," Pattern Recognition, vol. 104, pp. 337–347, 2020. doi: 10.1016/j.patcog.2020.107311
[39] C. Li, S. Wang, D. Yang, Z. Li, Y. Yang, X. Zhang, and J. Zhou, "Ppne: Property preserving network embedding," in Database Systems for Advanced Applications, pp. 163–179, 2017. doi: 10.1007/978-3-319-56608-51 2
[40] S. Pan, J. Wu, X. Zhu, C. Zhang, and Y. Wang, "Tri-party deep network representation," in Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, 2016, pp. 1895–1901. doi: 10.24963/ijcai.2016/278
12
[41] C. Zhou, Y. Liu, X. Liu, Z. Liu, and J. Gao, "Scalable graph embedding for asymmetric proximity," in Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, 2017, pp. 2942–2948. doi: 10.1609/aaai.v31i1.31115019
[42] D. Zhang, J. Yin, X. Zhu, and C. Zhang, "User Profile Preserving Social Network Embedding," in Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, 2017, pp. 3378–3384. doi: 10.24963/ijcai.2017/469
[43] S. Wang, J. Tang, C. Aggarwal, and H. Liu, "Linked document embedding for classification," in Proceedings of the 25th ACM International on Conference on Information and Knowledge Management, pp. 115–124, 2016. doi: 10.1145/2983323.2983742
[44] S. Wang, J. Tang, F. Morstatter, and H. Liu, "Paired restricted Boltzmann machine for linked data," in Proceedings of the 25th ACM International on Conference on Information and Knowledge Management, pp. 1753–1762, 2016. doi: 10.1145/2983323.2983769
[45] G. E. Hinton, "Reducing the dimensionality of data with neural networks," Science, vol. 313, no. 5786, pp. 504–507, Jul. 2006. doi: 10.1126/science.1127647
[46] H. Wang, J. Wang, J. Wang, M. Zhao, W. Zhang, F. Zhang, X. Xie, and M. Guo, "Graphgan: Graph representation learning with generative adversarial nets," in CoRR, abs/1711.08267, 2017. doi: 10.1145/3192448.3192454
[47] I.J.Goodfellow,J.Pouget-Abadie,M.Mirza,etal.,"Generativeadversarialnets,"inProceedingsof the 27th International Conference on Neural Information Processing Systems, 2014, pp. 2672–2680. doi: 10.1145/2969033.2969125
[48] R. B. Joshi and S. Mishra, "Learning graph representations," CoRR, abs/2102.02026, 2021.
[49] D. Wang, P. Cui, and W. Zhu, "Structural deep network embedding," in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1225– 1234, 2016. doi: 10.1145/2939672.2939754
[50] H. Chen, B. Perozzi, Y. Hu, and S. Skiena, "HARP: hierarchical representation learning for net- works," CoRR, abs/1706.07845, 2017.
[51] L. Tang and H. Liu, "Leveraging social media networks for classification," Data Mining and Knowledge Discovery, vol. 23, no. 3, pp. 447–478, Jan. 2011. doi: 10.1007/s10618-010-0197-8
[52] M.Ou,P.Cui,J.Pei,Z.Zhang,andW.Zhu,"Asymmetrictransitivitypreservinggraphembedding," in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1105–1114, 2016. doi: 10.1145/2939672.2939811
[53] C. Donnat, M. Zitnik, D. Hallac, and J. Leskovec, "Spectral graph wavelets for structural role similarity in networks," in Proceedings of the International Conference on Learning Representations (ICLR), 2018, abs/1710.10321.
[54] X. Wang, P. Cui, J. Wang, J. Pei, W. Zhu, and S. Yang, "Community Preserving Network Em- bedding," in Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, 2017, pp. 203–209. doi: 10.1609/aaai.v31i1.3012
13
[55] D. Zhang, J. Yin, X. Zhu, and C. Zhang, "Homophily, Structure, and Content Augmented Network Representation Learning," in IEEE 16th International Conference on Data Mining (ICDM), 2016. doi: 10.1109/ICDM.2016.0082
[56] C. Tu, W. Zhang, Z. Liu, and M. Sun, "Max-Margin DeepWalk: Discriminative Learning of Network Representation," in Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, 2016, pp. 3889–3895. doi: 10.24963/ijcai.2016/539
[57] D.Zhang,J.Yin,X.Zhu,andC.Zhang,"CollectiveClassificationviaDiscriminativeMatrixFactor- ization on Sparsely Labeled Networks," in Proceedings of the 25th ACM International Conference on Information and Knowledge Management, 2016, pp. 1563–1572. doi: 10.1145/2983323.2983729
[58] X. Huang, J. Li, and X. Hu, "Label Informed Attributed Network Embedding," in Proceedings of the Tenth ACM International Conference on Web Search and Data Mining, 2017, pp. 731–739. doi: 10.1145/3018661.3018733
[59] C.Zhou,Y.Liu,X.Liu,Z.Liu,andJ.Gao,"ScalableGraphEmbeddingforAsymmetricProximity," in Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, 2017, pp. 2942–2948. doi: 10.1609/aaai.v31i1.31115019
[60] Y. Dong, N. V. Chawla, and A. Swami, "Metapath2vec: Scalable representation learning for heterogeneous networks," in Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 135–144, 2017. doi: 10.1145/3097983.3098036
[61] S. Shi, B. Hu, W. X. Zhao, and P. S. Yu, "Heterogeneous information network embedding for recommendation," in CoRR, abs/1711.10730, 2017. doi: 10.1109/TKDE.2019.2919125
[62] M. Schlichtkrull, T. N. Kipf, P. Bloem, R. van den Berg, I. Titov, and M. Welling, "Modeling relational data with graph convolutional networks," IEEE Access, vol. 6, pp. 46069–46080, 2018. doi: 10.1109/ACCESS.2018.2842263
[63] J. Chen, S. Yang, and Z. Wang, "Multi-view representation learning for data stream clustering," IEEE Access, vol. 10, pp. 2945–2960, 2022. doi: 10.1109/ACCESS.2021.3069892
[64] Q.Luo,D.Yu,A.M.VeraVenkataSai,Z.Cai,andX.Cheng,"Asurveyofstructuralrepresentation learning for social networks," IEEE Access, vol. 10, pp. 24669–24683, 2022. doi: 10.1109/AC- CESS.2022.3088288
[65] X. Wang, P. Cui, J. Wang, J. Pei, W. Zhu, and S. Yang, "Community Preserving Network Em- bedding," in Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, 2017, pp. 203–209. doi: 10.1609/aaai.v31i1.3012
[66] S. Cao, W. Lu, and Q. Xu, "Deep Neural Networks for Learning Graph Representations," in Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, 2016, pp. 1145–1152. doi: 10.1007/978-3-319-71249-91
[67] R. Feng, Y. Yang, W. Hu, F. Wu, and Y. Zhuang, "Representation learning for scale-free networks," CoRR, abs/1711.10755, 2017. doi: 10.1145/3308558.3313377
14
[68] Z. Yang, W. W. Cohen, and R. Salakhutdinov, "Revisiting semi-supervised learning with graph embeddings," in CoRR, abs/1603.08861, 2016. doi: 10.1145/3045390.3045594
[69] X. Wang, H. Ji, C. Shi, B. Wang, Y. Ye, P. Cui, and P. S. Yu, "Heterogeneous graph attention net- work," in The World Wide Web Conference, 2019, pp. 2022–2032. doi: 10.1145/3308558.3313417
[70] X. Wang, H. Ji, C. Shi, B. Wang, P. Cui, P. S. Yu, and Y. Ye, "Heterogeneous graph attention network," in CoRR, vol. abs/1903.07293, 2019. doi: 10.1145/3292500.3330851
[71] H. Hong, H. Guo, Y. Lin, X. Yang, Z. Li, and J. Ye, "An attention-based graph neu- ral network for heterogeneous structural learning," in CoRR, vol. abs/1912.10832, 2019. doi: 10.1145/3442381.3449843
[72] P. Vincent, H. Larochelle, I. Lajoie, Y. Bengio, and P.-A. Manzagol, "Stacked denoising au- toencoders: Learning useful representations in a deep network with a local denoising crite- rion," Journal of Machine Learning Research, vol. 11, no. 110, pp. 3371–3408, 2010. doi: 10.5555/1756006.1953039
[73] H. H. Song, T. W. Cho, V. Dave, Y. Zhang, and L. Qiu, "Scalable proximity estimation and link prediction in online social networks," in Proceedings of the 9th ACM SIGCOMM Conference on Internet Measurement, 2009, pp. 322–335. doi: 10.1145/1644893.1644928
[74] M. Belkin and P. Niyogi, "Laplacian eigenmaps and spectral techniques for embedding and clus- tering," in Proceedings of the 14th International Conference on Neural Information Processing Systems, 2001, pp. 585–591. doi: 10.1016/j.patcog.2007.03.014
[75] J. Mairal, J. Ponce, G. Sapiro, A. Zisserman, and F. Bach, "Supervised dictionary learning," in Advances in Neural Information Processing Systems, vol. 21, 2009. doi: 10.5555/2984093.2984214
[76] J. Zhu, A. Ahmed, and E. P. Xing, "Medlda: Maximum margin supervised topic models," Journal of Machine Learning Research, vol. 13, no. 74, pp. 2237–2278, 2012. doi: 10.5555/2984093.2984214
[77] Q. V. Le and T. Mikolov, "Distributed representations of sentences and documents," in CoRR, vol. abs/1405.4053, 2014. doi: 10.3115/1963501.1963531
[78] D. P. Kingma and J. Ba, "Adam: A Method for Stochastic Optimization," in 3rd International Conference on Learning Representations, 2015. doi: 10.1145/3045118.3045167
[79] N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, "Dropout: A simple way to prevent neural networks from overfitting," Journal of Machine Learning Research, vol. 15, no. 56, pp. 1929–1958, 2014. doi: 10.1007/s10994-015-5521-0
[80] K. He, X. Zhang, S. Ren, and J. Sun, "Deep residual learning for image recognition," in CoRR, vol. abs/1512.03385, 2015. doi: 10.1109/CVPR.2016.90
[81] Y. Dong, N. V. Chawla, and A. Swami, "Metapath2vec: Scalable representation learning for heterogeneous networks," in Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 135–144, 2017. doi: 10.1145/3097983.3098036
15
[82] C. Shi, B. Hu, W. X. Zhao, and P. S. Yu, "Heterogeneous information network embedding for recommendation," in CoRR, abs/1711.10730, 2017. doi: 10.1109/TKDE.2019.2919125
[83] M. Schlichtkrull, T. N. Kipf, P. Bloem, R. van den Berg, I. Titov, and M. Welling, "Modeling relational data with graph convolutional networks," IEEE Access, vol. 6, pp. 46069–46080, 2018. doi: 10.1109/ACCESS.2018.2842263
[84] D. P. Kingma and J. Ba, "Adam: A Method for Stochastic Optimization," in 3rd International Conference on Learning Representations, 2015. doi: 10.1145/3045118.3045167
[85] N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, "Dropout: A simple way to prevent neural networks from overfitting," Journal of Machine Learning Research, vol. 15, no. 56, pp. 1929–1958, 2014. doi: 10.1007/s10994-015-5521-0
[86] K. He, X. Zhang, S. Ren, and J. Sun, "Deep residual learning for image recognition," in CoRR, vol. abs/1512.03385, 2015. doi: 10.1109/CVPR.2016.90
[87] J. Tang, J. Zhang, L. Yao, J. Li, L. Zhang, and Z. Su, "Arnetminer: Extraction and mining of academic social networks," in Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 990–998, 2008. doi: 10.1145/1401890.1402024
[88] Y. Zhang, R. Jin, and Z.-H. Zhou, "Understanding bag-of-words model: a statistical framework," International Journal of Machine Learning and Cybernetics, vol. 1, no. 1–4, pp. 43–52, Aug. 2010. doi: 10.1007/s13042-010-0001-0
[89] M. Schlichtkrull, T. N. Kipf, P. Bloem, R. van den Berg, I. Titov, and M. Welling, "Modeling relational data with graph convolutional networks," IEEE Access, vol. 6, pp. 46069–46080, 2018. doi: 10.1109/ACCESS.2018.2842263
[90] J. Chen, S. Yang, and Z. Wang, "Multi-view representation learning for data stream clustering," IEEE Access, vol. 10, pp. 2945–2960, 2022. doi: 10.1109/ACCESS.2021.3069892
[91] Q.Luo,D.Yu,A.M.VeraVenkataSai,Z.Cai,andX.Cheng,"Asurveyofstructuralrepresentation learning for social networks," IEEE Access, vol. 10, pp. 24669–24683, 2022. doi: 10.1109/AC- CESS.2022.3088288
[92] E. Wang, Q. Yu, Y. Chen, W. Slamu, and X. Luo, "Multi-modal knowledge graphs representa- tion learning via multi-headed self-attention," IEEE Access, vol. 10, pp. 3467–3476, 2022. doi: 10.1109/ACCESS.2021.3054909
[93] Q. Feng, Z. Liu, and C. L. P. Chen, "Broad and deep neural network for high-dimensional data representation learning," IEEE Access, vol. 10, pp. 17736–17750, 2022. doi: 10.1109/AC- CESS.2022.3074505
