# American Institute of Mathematical Sciences

February  2021, 4(1): 1-13. doi: 10.3934/mfc.2020022

## Word sense disambiguation based on stretchable matching of the semantic template

 1 School of Computer Science and Technology, Dalian University of Technology, No.2 Linggong Road, Ganjingzi District, Dalian City, Liaoning Province, China 2 Faculty of Library, Information and Media Science, University of Tsukuba, Tsukuba, Japan

* Corresponding author: Degen Huang

Received  January 2020 Revised  August 2020 Published  February 2021 Early access  September 2020

Fund Project: The second author is supported by the National Key Research and Development Program of China (2020AAA0108004) and the National Natural Science Foundation of China under (No. U1936109, 61672127)

It is evident that the traditional hard matching of a fixed-length template cannot satisfy the nearly indefinite variations in natural language. This issue mainly results from three major problems of the traditional matching mode: 1) in matching with a short template, the context of natural language cannot be effectively captured; 2) in matching with a long template, serious data sparsity will lead to a low success rate of template matching (i.e., low recall); and 3) due to a lack of flexible matching ability, traditional hard matching is more prone to failure. Therefore, this paper proposed a novel method of stretchable matching of the semantic template (SMOST) to deal with the above problems. We have applied this method to word sense disambiguation in the natural language processing field. In the same case of using only the SemCor corpus, the result of our system is very close to the best result of existing systems, which shows the effectiveness of new proposed method.

Citation: Wei Wang, Degen Huang, Haitao Yu. Word sense disambiguation based on stretchable matching of the semantic template. Mathematical Foundations of Computing, 2021, 4 (1) : 1-13. doi: 10.3934/mfc.2020022
##### References:
 [1] S. W. K. Chan, Generating context templates for word sense disambiguation, AI 2013: Advances in Artificial Intelligence, 8272 (2013), 466-477.  doi: 10.1007/978-3-319-03680-9_47. [2] D. S. Chaplot and R. Salakhutdinov, Knowledge-based word sense disambiguation using topic models, 32nd AAAI Conference on Artificial Intelligence (AAAI-18), (2018), 1-8. [3] X. X. Chen, Z. Y. Liu and M. S. Sun, A United Model for Word Sense Representation and Disambiguation, Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), 2014 (2014), 1025-1035. [4] J. P. Chen and W. Yu, Enriching semantic knowledge for WSD, IEICE Trans, E97-D (2014), 2212-2216.  doi: 10.1587/transinf.E97.D.2212. [5] Z. Hu, F. Luo and Y. Tan, WSD-GAN: Word sense disambiguation using generative adversarial networks, The Thirty-Third AAAI Conference on Artificial Intelligence (AAAI-19), 33 (2019), 9943-9944.  doi: 10.1609/aaai.v33i01.33019943. [6] M. Hwang and P. Kim, Adapted relation structure algorithm for word sense disambiguation, Proceedings of Third IEEE International Conference on Digital Information Management (ICDIM), 2008 (2008), 684-688.  doi: 10.1109/ICDIM.2008.4746825. [7] I. Iacobacci, M. T. Pilehvar and R. Navigli, Embeddings for Word Sense Disambiguation: An Evaluation Study, Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics, (2016), 897-907. [8] K. L. Jia, Research of word sense disambiguation based on soft pattern, Key Engineering Materials, 460/461 (2011), 130-135.  doi: 10.4028/www.scientific.net/KEM.460-461.130. [9] M. Kageback and H. Salomonsson, Word sense disambiguation using a bidirectional LSTM, Proceedings of the Workshop on Cognitive Aspects of the Lexicon, (2016), 51-56. [10] M. Le, M. Postma, J. Urbani and P. Vossen, A deep dive into word sense disambiguation with LSTM, Proceedings of the 27th International Conference on Computational Linguistics, (2018), 354-365. [11] L. Li and Q. Zhou, Chinese word sense disambiguation based on lexical semantic ontology, Journal of Chinese Language and Computing, 18 (2018), 13-23. [12] L. L. Li, B. Roth and C. Sporleder, Topic Models for Word Sense Disambiguation and Token-based Idiom Detection, Proceedings of the 48th Annual Meeting of the Association for Computational Linguistics, (2010), 1138-1147. [13] W. P Lu, H. Wu, P. Jian, Y. G. Huang and H. Y. Huang, An empirical study of classifier combination based word sense disambiguation, IEICE Trans, E101-D (2018), 225-233.  doi: 10.1587/transinf.2017EDP7090. [14] F. Luo, T. Liu, Q. Xia, B. Chang and et al., Incorporating glosses into neural word sense disambiguation, Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics, (2018), 2473-2482.  doi: 10.18653/v1/P18-1230. [15] F. Luo, T. Liu, Z. He and et al., Leveraging gloss knowledge in neural word sense disambiguation by hierarchical Co-attention, Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, (2018), 1402-1411.  doi: 10.18653/v1/D18-1170. [16] M. Maru, F. Scozzafava, F. Martelli and et al., SyntagNet: Challenging supervised word sense disambiguation with lexical-semantic combinations, Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP), (2019), 3532-3538. [17] S. Melacci, A. Globo and L. Rigutini, Enhancing modern supervised word sense disambiguation models by semantic lexical resources, 2018 LREC, (2018), 1012-1017. [18] O. Melamud, J. Goldberger and I. Dagan, context2vec: Learning generic context embedding with bidirectional lstm, Proceedings of the 20th SIGNLL onference on Computational Natural Language Learning (CoNLL), (2016), 51-61.  doi: 10.18653/v1/K16-1006. [19] A. Moro, A. Raganato and R. Navigli, Entity linking meets word sense disambiguation: A united approach, Transactions of the Association for Computational Linguistics, 2 (2014), 231-244.  doi: 10.1162/tacl_a_00179. [20] R. Navigli, Word sense disambiguation: A survey, ACM Computing Surveys, 41 (2009), 1-69.  doi: 10.1145/1459352.1459355. [21] R. Navigli and P. Velardi, Structural semantic interconnection: A knowledge-based approach to word sense disambiguation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 27 (2005), 1075-1086.  doi: 10.1109/TPAMI.2005.149. [22] A. R. Pal and D. Saha, Word sense disambiguation: A survey, International Journal of Control Theory and Computer Modeling (IJCTCM), 5 (2015), 1-16. [23] A. Panchenko, S. Faralli, S. P. Ponzetto and C. Biemann, Using linked disambiguated distributional networks for word sense disambiguation, Proceedings of the 1st Workshop on Sense, Concept and Entity Representations and their Applications, (2017), 72-78.  doi: 10.18653/v1/W17-1909. [24] S. Papandrea, A. Raganato and C. D. Bovi, SUPWSD: A flexible toolkit for supervised word sense disambiguation, Proceedings of the 2017 EMNLP System Demonstrations, Association for Computational Linguistics, (2017), 103-108. [25] T. Pasini and R. Navigli, Train-O-Matic: Large-Scale Supervised Word Sense Disambiguation in Multiple Languages without Manual Training Data, Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, Association for Computational Linguistics, (2017), 78-88.  doi: 10.18653/v1/D17-1008. [26] L.N. Pina and R. Johansson, Embedding Senses for Efficient Graph-based Word Sense Disambiguation, Proceedings of the 2016 Workshop on Graph-based Methods for Natural Language Processing, NAACL-HLT 2016, (2016), 1-5. [27] A. Popov, Word sense disambiguation with recurrent neural networks, Proceedings of the Student Research Workshop associated with RANLP 2017, (2017), 25-34.  doi: 10.26615/issn.1314-9156.2017_004. [28] A. Raganato, C. D. Bovi and R. Navigli, Neural sequence learning models for word sense disambiguation, Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, Association for Computational Linguistics, (2017), 1156-1167. [29] A. Raganato, J. Camacho-Collados and R. Navigli, Word sense disambiguation: A unified evaluation framework and empirical comparison, Proceedings of the 15th Conference of the European Chapter of the Association for Computational Linguistics, (2017), 99-110. [30] B. S. Rintyarna and R. Sarno, Topic models for word sense disambiguation and token-based idiom detection, 2016 Fourth International Conference on Information and Communication Technologies (ICoICT), (2016), 1-5. [31] F. Tacoa, D. Bollegala and M. Ishizuka, A context expansion method for supervised word sense disambiguation, 2012 IEEE Sixth International Conference on Semantic Computing, (2012), 339-341.  doi: 10.1109/ICSC.2012.27. [32] A. Trask, P. Michalak and J. Liu, SENSE2VEC - A fast and accurate method for word sense disambiguation in neural word embeddings, arXiv:1511.06388, Under Review as a Conference Paper at ICLR 2016, (2015), 1{9. [33] X. D. Wang, X. R. Tang, W. G. Qu and M. Gu, Word sense disambiguation by semantic inference, 2017 International Conference on Behavioral, Economic, Socio-cultural Computing, (2017), 1-6.  doi: 10.1109/BESC.2017.8256391. [34] D. Y. Yuan, J. Richardson, R. Doherty, C. Evans and E. Altendorf, Semi-supervised Word Sense Disambiguation with Neural Models, Proceedings of COLING 2016, the 26th International Conference on Computational Linguistics: Technical Papers, (2016), 1374-1385. [35] C. X. Zhang, L. R. Sun, X. Y. Gao, Z. M. Lu and Y. Yue, Integrate chinese semantic knowledge into word sense disambiguation, International Journal of Hybrid Information Technology, 8 (2015), 105-116. [36] C. X. Zhang, L. R. Sun and X. Y. Gao, Determine word sense based on semantic and syntax information, International Journal of Database and Theory and Application, 9 (2016), 17-22. [37] Z. Zhong and H. T. Ng, It makes sense: A wide-coverage word sense disambiguation system for free text, Proceedings of the ACL 2010 System Demonstrations, (2010), 78-83.

show all references

##### References:
 [1] S. W. K. Chan, Generating context templates for word sense disambiguation, AI 2013: Advances in Artificial Intelligence, 8272 (2013), 466-477.  doi: 10.1007/978-3-319-03680-9_47. [2] D. S. Chaplot and R. Salakhutdinov, Knowledge-based word sense disambiguation using topic models, 32nd AAAI Conference on Artificial Intelligence (AAAI-18), (2018), 1-8. [3] X. X. Chen, Z. Y. Liu and M. S. Sun, A United Model for Word Sense Representation and Disambiguation, Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), 2014 (2014), 1025-1035. [4] J. P. Chen and W. Yu, Enriching semantic knowledge for WSD, IEICE Trans, E97-D (2014), 2212-2216.  doi: 10.1587/transinf.E97.D.2212. [5] Z. Hu, F. Luo and Y. Tan, WSD-GAN: Word sense disambiguation using generative adversarial networks, The Thirty-Third AAAI Conference on Artificial Intelligence (AAAI-19), 33 (2019), 9943-9944.  doi: 10.1609/aaai.v33i01.33019943. [6] M. Hwang and P. Kim, Adapted relation structure algorithm for word sense disambiguation, Proceedings of Third IEEE International Conference on Digital Information Management (ICDIM), 2008 (2008), 684-688.  doi: 10.1109/ICDIM.2008.4746825. [7] I. Iacobacci, M. T. Pilehvar and R. Navigli, Embeddings for Word Sense Disambiguation: An Evaluation Study, Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics, (2016), 897-907. [8] K. L. Jia, Research of word sense disambiguation based on soft pattern, Key Engineering Materials, 460/461 (2011), 130-135.  doi: 10.4028/www.scientific.net/KEM.460-461.130. [9] M. Kageback and H. Salomonsson, Word sense disambiguation using a bidirectional LSTM, Proceedings of the Workshop on Cognitive Aspects of the Lexicon, (2016), 51-56. [10] M. Le, M. Postma, J. Urbani and P. Vossen, A deep dive into word sense disambiguation with LSTM, Proceedings of the 27th International Conference on Computational Linguistics, (2018), 354-365. [11] L. Li and Q. Zhou, Chinese word sense disambiguation based on lexical semantic ontology, Journal of Chinese Language and Computing, 18 (2018), 13-23. [12] L. L. Li, B. Roth and C. Sporleder, Topic Models for Word Sense Disambiguation and Token-based Idiom Detection, Proceedings of the 48th Annual Meeting of the Association for Computational Linguistics, (2010), 1138-1147. [13] W. P Lu, H. Wu, P. Jian, Y. G. Huang and H. Y. Huang, An empirical study of classifier combination based word sense disambiguation, IEICE Trans, E101-D (2018), 225-233.  doi: 10.1587/transinf.2017EDP7090. [14] F. Luo, T. Liu, Q. Xia, B. Chang and et al., Incorporating glosses into neural word sense disambiguation, Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics, (2018), 2473-2482.  doi: 10.18653/v1/P18-1230. [15] F. Luo, T. Liu, Z. He and et al., Leveraging gloss knowledge in neural word sense disambiguation by hierarchical Co-attention, Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, (2018), 1402-1411.  doi: 10.18653/v1/D18-1170. [16] M. Maru, F. Scozzafava, F. Martelli and et al., SyntagNet: Challenging supervised word sense disambiguation with lexical-semantic combinations, Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP), (2019), 3532-3538. [17] S. Melacci, A. Globo and L. Rigutini, Enhancing modern supervised word sense disambiguation models by semantic lexical resources, 2018 LREC, (2018), 1012-1017. [18] O. Melamud, J. Goldberger and I. Dagan, context2vec: Learning generic context embedding with bidirectional lstm, Proceedings of the 20th SIGNLL onference on Computational Natural Language Learning (CoNLL), (2016), 51-61.  doi: 10.18653/v1/K16-1006. [19] A. Moro, A. Raganato and R. Navigli, Entity linking meets word sense disambiguation: A united approach, Transactions of the Association for Computational Linguistics, 2 (2014), 231-244.  doi: 10.1162/tacl_a_00179. [20] R. Navigli, Word sense disambiguation: A survey, ACM Computing Surveys, 41 (2009), 1-69.  doi: 10.1145/1459352.1459355. [21] R. Navigli and P. Velardi, Structural semantic interconnection: A knowledge-based approach to word sense disambiguation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 27 (2005), 1075-1086.  doi: 10.1109/TPAMI.2005.149. [22] A. R. Pal and D. Saha, Word sense disambiguation: A survey, International Journal of Control Theory and Computer Modeling (IJCTCM), 5 (2015), 1-16. [23] A. Panchenko, S. Faralli, S. P. Ponzetto and C. Biemann, Using linked disambiguated distributional networks for word sense disambiguation, Proceedings of the 1st Workshop on Sense, Concept and Entity Representations and their Applications, (2017), 72-78.  doi: 10.18653/v1/W17-1909. [24] S. Papandrea, A. Raganato and C. D. Bovi, SUPWSD: A flexible toolkit for supervised word sense disambiguation, Proceedings of the 2017 EMNLP System Demonstrations, Association for Computational Linguistics, (2017), 103-108. [25] T. Pasini and R. Navigli, Train-O-Matic: Large-Scale Supervised Word Sense Disambiguation in Multiple Languages without Manual Training Data, Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, Association for Computational Linguistics, (2017), 78-88.  doi: 10.18653/v1/D17-1008. [26] L.N. Pina and R. Johansson, Embedding Senses for Efficient Graph-based Word Sense Disambiguation, Proceedings of the 2016 Workshop on Graph-based Methods for Natural Language Processing, NAACL-HLT 2016, (2016), 1-5. [27] A. Popov, Word sense disambiguation with recurrent neural networks, Proceedings of the Student Research Workshop associated with RANLP 2017, (2017), 25-34.  doi: 10.26615/issn.1314-9156.2017_004. [28] A. Raganato, C. D. Bovi and R. Navigli, Neural sequence learning models for word sense disambiguation, Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, Association for Computational Linguistics, (2017), 1156-1167. [29] A. Raganato, J. Camacho-Collados and R. Navigli, Word sense disambiguation: A unified evaluation framework and empirical comparison, Proceedings of the 15th Conference of the European Chapter of the Association for Computational Linguistics, (2017), 99-110. [30] B. S. Rintyarna and R. Sarno, Topic models for word sense disambiguation and token-based idiom detection, 2016 Fourth International Conference on Information and Communication Technologies (ICoICT), (2016), 1-5. [31] F. Tacoa, D. Bollegala and M. Ishizuka, A context expansion method for supervised word sense disambiguation, 2012 IEEE Sixth International Conference on Semantic Computing, (2012), 339-341.  doi: 10.1109/ICSC.2012.27. [32] A. Trask, P. Michalak and J. Liu, SENSE2VEC - A fast and accurate method for word sense disambiguation in neural word embeddings, arXiv:1511.06388, Under Review as a Conference Paper at ICLR 2016, (2015), 1{9. [33] X. D. Wang, X. R. Tang, W. G. Qu and M. Gu, Word sense disambiguation by semantic inference, 2017 International Conference on Behavioral, Economic, Socio-cultural Computing, (2017), 1-6.  doi: 10.1109/BESC.2017.8256391. [34] D. Y. Yuan, J. Richardson, R. Doherty, C. Evans and E. Altendorf, Semi-supervised Word Sense Disambiguation with Neural Models, Proceedings of COLING 2016, the 26th International Conference on Computational Linguistics: Technical Papers, (2016), 1374-1385. [35] C. X. Zhang, L. R. Sun, X. Y. Gao, Z. M. Lu and Y. Yue, Integrate chinese semantic knowledge into word sense disambiguation, International Journal of Hybrid Information Technology, 8 (2015), 105-116. [36] C. X. Zhang, L. R. Sun and X. Y. Gao, Determine word sense based on semantic and syntax information, International Journal of Database and Theory and Application, 9 (2016), 17-22. [37] Z. Zhong and H. T. Ng, It makes sense: A wide-coverage word sense disambiguation system for free text, Proceedings of the ACL 2010 System Demonstrations, (2010), 78-83.
One-to-one excellent matching
One-to-one poor matching
Good matching with stretched template (two random words in test sentence)
Good matching with stretched template (two random words in template)
Good matching with stretched template (two random words and one obstructing word in test sentence)
Words of a test sentence and their sense items
A template indexed by the word in a test sentence
Matching all word senses in a test sentence for all word senses in the template
Ordering of the node numbers of all matched word senses in a test sentence
Obtaining the word sense score by the matched node chain
Obtaining the final word sense score by the max score
Obtaining the template through word sense instead of word
Matching a Sense of Word (Algorithm 1)
Obtaining the Score of a Matched Node Chain (Algorithm 2)
Obtaining the Final Word Sense (Algorithm 3)
Comparison of F1 scores on our systems with different algorithms on five test sets
 Res. Different algorithms Sen2 Sen3 Sem07 Sem13 Sem15 SemCor 3.0 SMOST Max.score P1 65.8 63.9 57.6 62.0 65.6 SMOST Max.score P2 66.3 64.6 57.8 61.7 65.5 SMOST Max.vote P1 68.0 67.9 59.8 64.2 70.0 SMOST Max.vote P2 68.8 68.3 60.2 64.2 67.5 SMOST Max.vote*score P1 67.7 67.1 58.9 64.7 69.2 SMOST Max.vote*score P2 68.9 68.0 61.1 64.4 66.6
 Res. Different algorithms Sen2 Sen3 Sem07 Sem13 Sem15 SemCor 3.0 SMOST Max.score P1 65.8 63.9 57.6 62.0 65.6 SMOST Max.score P2 66.3 64.6 57.8 61.7 65.5 SMOST Max.vote P1 68.0 67.9 59.8 64.2 70.0 SMOST Max.vote P2 68.8 68.3 60.2 64.2 67.5 SMOST Max.vote*score P1 67.7 67.1 58.9 64.7 69.2 SMOST Max.vote*score P2 68.9 68.0 61.1 64.4 66.6
Comparison of F1 scores on several systems using supervised learning method on five test sets
 Res. System Sen2 Sen3 Sem07 Sem13 Sem15 SemCor 3.0 MFS 65.6 66.0 54.5 63.8 67.1 IMS baseline(Zhong2010) 70.9 69.3 61.3 65.3 69.5 BLSTM(Raganato2017) 71.4 68.8 61.8 65.6 69.2 Seq2Seq(Raganato2017) 68.5 67.9 60.9 64.3 67.3 SMOST (this paper) 68.9 68.3 61.1 64.7 70.0
 Res. System Sen2 Sen3 Sem07 Sem13 Sem15 SemCor 3.0 MFS 65.6 66.0 54.5 63.8 67.1 IMS baseline(Zhong2010) 70.9 69.3 61.3 65.3 69.5 BLSTM(Raganato2017) 71.4 68.8 61.8 65.6 69.2 Seq2Seq(Raganato2017) 68.5 67.9 60.9 64.3 67.3 SMOST (this paper) 68.9 68.3 61.1 64.7 70.0
Comparison of F1 scores on the systems using template matching method on Sen3 test set
 Resource System Recall Precision F1 multi-res. SSI (Navigli2004) 68.40 68.50 68.45 SSI-10words context (Hwang2008) 90.96 57.30 70.31 SemCor2.1 A-RS-10words context(Hwang2008) 56.80 75.53 64.84 +WordNet2.1 SMOST (this paper) 100.0 59.84 74.87
 Resource System Recall Precision F1 multi-res. SSI (Navigli2004) 68.40 68.50 68.45 SSI-10words context (Hwang2008) 90.96 57.30 70.31 SemCor2.1 A-RS-10words context(Hwang2008) 56.80 75.53 64.84 +WordNet2.1 SMOST (this paper) 100.0 59.84 74.87
 [1] Zhaohui Guo, Stanley Osher. Template matching via $l_1$ minimization and its application to hyperspectral data. Inverse Problems and Imaging, 2011, 5 (1) : 19-35. doi: 10.3934/ipi.2011.5.19 [2] A. Alamo, J. M. Sanz-Serna. Word combinatorics for stochastic differential equations: Splitting integrators. Communications on Pure and Applied Analysis, 2019, 18 (4) : 2163-2195. doi: 10.3934/cpaa.2019097 [3] Massimo Tarallo, Zhe Zhou. Limit periodic upper and lower solutions in a generic sense. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 293-309. doi: 10.3934/dcds.2018014 [4] Ronnie Pavlov, Pascal Vanier. The relationship between word complexity and computational complexity in subshifts. Discrete and Continuous Dynamical Systems, 2021, 41 (4) : 1627-1648. doi: 10.3934/dcds.2020334 [5] Boran Hu, Zehui Cheng, Zhangbing Zhou. Web services recommendation leveraging semantic similarity computing. Mathematical Foundations of Computing, 2018, 1 (2) : 101-119. doi: 10.3934/mfc.2018006 [6] Mingyuan Mao, Hewei Zhang, Simeng Li, Baochang Zhang. SEMANTIC-RTAB-MAP (SRM): A semantic SLAM system with CNNs on depth images. Mathematical Foundations of Computing, 2019, 2 (1) : 29-41. doi: 10.3934/mfc.2019003 [7] Christopher C. Tisdell, David Bee Olmedo. Beyond the compass: Exploring geometric constructions via a circle arc template and a straightedge. STEM Education, 2022, 2 (1) : 1-36. doi: 10.3934/steme.2022001 [8] Xiaoming Yan, Ping Cao, Minghui Zhang, Ke Liu. The optimal production and sales policy for a new product with negative word-of-mouth. Journal of Industrial and Management Optimization, 2011, 7 (1) : 117-137. doi: 10.3934/jimo.2011.7.117 [9] José Gómez-Torrecillas, F. J. Lobillo, Gabriel Navarro. Convolutional codes with a matrix-algebra word-ambient. Advances in Mathematics of Communications, 2016, 10 (1) : 29-43. doi: 10.3934/amc.2016.10.29 [10] Zhen Li, Jicheng Liu. Synchronization for stochastic differential equations with nonlinear multiplicative noise in the mean square sense. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5709-5736. doi: 10.3934/dcdsb.2019103 [11] Jian-Bing Zhang, Yi-Xin Sun, De-Chuan Zhan. Multiple-instance learning for text categorization based on semantic representation. Big Data & Information Analytics, 2017, 2 (1) : 69-75. doi: 10.3934/bdia.2017009 [12] Charlene Kalle, Niels Langeveld, Marta Maggioni, Sara Munday. Matching for a family of infinite measure continued fraction transformations. Discrete and Continuous Dynamical Systems, 2020, 40 (11) : 6309-6330. doi: 10.3934/dcds.2020281 [13] Luigi Ambrosio, Federico Glaudo, Dario Trevisan. On the optimal map in the $2$-dimensional random matching problem. Discrete and Continuous Dynamical Systems, 2019, 39 (12) : 7291-7308. doi: 10.3934/dcds.2019304 [14] Danilo Coelho, David Pérez-Castrillo. On Marilda Sotomayor's extraordinary contribution to matching theory. Journal of Dynamics and Games, 2015, 2 (3&4) : 201-206. doi: 10.3934/jdg.2015001 [15] Shichu Chen, Zhiqiang Wang, Yan Ren. A fast matching algorithm for the images with large scale disparity. Mathematical Foundations of Computing, 2020, 3 (3) : 141-155. doi: 10.3934/mfc.2020021 [16] J. M. Mazón, Julio D. Rossi, J. Toledo. Optimal matching problems with costs given by Finsler distances. Communications on Pure and Applied Analysis, 2015, 14 (1) : 229-244. doi: 10.3934/cpaa.2015.14.229 [17] Paola B. Manasero. Equivalences between two matching models: Stability. Journal of Dynamics and Games, 2018, 5 (3) : 203-221. doi: 10.3934/jdg.2018013 [18] Christian Licht, Thibaut Weller. Approximation of semi-groups in the sense of Trotter and asymptotic mathematical modeling in physics of continuous media. Discrete and Continuous Dynamical Systems - S, 2019, 12 (6) : 1709-1741. doi: 10.3934/dcdss.2019114 [19] Tatsuya Arai, Naotsugu Chinen. The construction of chaotic maps in the sense of Devaney on dendrites which commute to continuous maps on the unit interval. Discrete and Continuous Dynamical Systems, 2004, 11 (2&3) : 547-556. doi: 10.3934/dcds.2004.11.547 [20] Susu Zhang, Jiancheng Ni, Lijun Hou, Zili Zhou, Jie Hou, Feng Gao. Global-Affine and Local-Specific Generative Adversarial Network for semantic-guided image generation. Mathematical Foundations of Computing, 2021, 4 (3) : 145-165. doi: 10.3934/mfc.2021009

Impact Factor: