Signal and Data Processing Journal A scientific journal officially licensed by the Commission for Scientific Publications of the (MSRT). Publisher: Research Ceter for Developmen of Technologies
Volume 22, Issue 3 (12-2025)
JSDP 2025, 22(3): 77-90 |
Back to browse issues page
Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
Elyasi N, Hosseini Moghadam M. An application of the topological data analysis approach in Persian poetry classification. JSDP 2025; 22 (3) : 5
URL: http://jsdp.rcisp.ac.ir/article-1-1395-en.html
URL: http://jsdp.rcisp.ac.ir/article-1-1395-en.html
Assistant Professor, Faculty of Mathematical sciences and Computer, Kharazmi university, Tehran, Iran
Abstract: (496 Views)
This research delves into authorship attribution through an avant-garde lens, employing Topological Data Analysis (TDA) as a potent instrument to unravel intricate patterns within classical Persian poetry. The focal point of this study is the distinguished works of Ferdowsi and Hafez, two preeminent Persian poets, exploring the latent structures in their verses through the lenses of Persistent Homology and Mapper a pair of TDA methodologies. The discernment between Non-Semantic and Semantic authorship attribution methodologies lays the groundwork, elucidating the significance of capturing structural nuances in textual data. The main focus of this investigation revolves around the deployment of Persistent Homology a cutting-edge technique that transcends traditional text analysis methodologies. It operates in high-dimensional spaces, extracting topological features, and rendering them comprehensible through persistent diagrams. This paper meticulously unpacks the mathematical underpinnings of Persistent Homology, providing a stepwise exposition of its application, focusing on Homology, Simplicial Complex, and Group Theory. These foundational elements converge to empower extracting meaningful topological signatures from the poetic corpus. In tandem, Mapper, another TDA tool, unfolds as a pivotal player in this explorative journey. This algorithmic entity facilitates dimensionality reduction and simplicial complex construction to portray an accurate depiction of the intrinsic topological architecture residing in the dataset. The intricacies of Mapper's workflow from filter function selection to binning and clustering are meticulously detailed, forming a coherent narrative of its operational dynamics. Transitioning from theoretical discourse to practical implementation, this research adopts a case study approach, weaving Ferdowsi and Hafez's poetic masterpieces into the TDA tapestry. Beyond the mere application of algorithms, the study delves into the realm of accuracy assessments, subjecting the Mapper algorithm to rigorous tests, and gauging the precision of its poem classifications within identified clusters. An additional layer of complexity unfolds as the research embraces semantic clustering, elucidating thematic resonances embedded within the verses. The results borne out of this meticulous exploration not only underscore the efficacy of TDA methodologies in unveiling the intricate structures of Persian poetry but also offer a nuanced perspective on their interpretability and utility in the realm of authorship attribution. The poetic narrative, with its semantic richness and structural subtleties, emerges as a fertile ground for the application of TDA, pushing the boundaries of text classification methodologies. This research, therefore, contributes significantly to the evolving discourse on the intersection of literature and data science, offering a profound understanding of how TDA can be wielded as a transformative lens to decipher the profound threads of authorial expression.
Article number: 5
Type of Study: Applicable |
Subject:
Paper
Received: 2023/09/5 | Accepted: 2025/06/11 | Published: 2025/12/19 | ePublished: 2025/12/19
Received: 2023/09/5 | Accepted: 2025/06/11 | Published: 2025/12/19 | ePublished: 2025/12/19
References
1. الیاسی نیره، تیموری حسین، پاکنیت سروش، مقدمهای بر تحلیل توپولوژیکی داده: نظریه و رویکرد، انتشارات دانشگاه تفرش، 1400.
1. Eliasi, N., Teimouri, H., Pakniat, S., An Introduction to Topological Data Analysis: Theory and Approach, Tafresh University Press, 1400.
2. Holmes, D. "Authorship Attribution", Computers and the Humanities, 28:87-106. Kluwer Academic Publishers, 1995 [DOI:10.1007/BF01830689]
3. Malyutov, M.B. "Authorship Attribution of Texts: a Review", Proceedings of the program "Information transfer" held in ZIF. University of Bielefeld, Germany, 17 pages, 2004.
4. Chaski, C. "Who's at the Keyword? Authorship Attribution in Digital Evidence Investigations", International Journal of Digital Evidence, Volume 4, Issue 1 , 2005.
5. Diederich, J., Kindermann, J., Leopold, E., Paas, G. "Authorship Attribution with Support Vector Machines", Applied Intelligence, 19(1): pp.109-123, 2003. [DOI:10.1023/A:1023824908771]
6. Stamatatos, E., Fakotakis, N., Kokkinakis, G. "Computer-Based Authorship Attribution Without Lexical Measures", Computers and the Humanities, 35: pp. 193-214, Kluwer Academic Publishers, 2001. [DOI:10.1023/A:1002681919510]
7. Carlsson, G, Topology and data, Bull, Amer, Math, Soc, 46, pp. 255-308, 2009. [DOI:10.1090/S0273-0979-09-01249-X]
8. Emrani, S., Saponas, T., Morris, D., and Krim, H. A. "Novel Framework for Pulse Pressure Wave Analysis Using Persistent Homology", IEEE Signal Processing Letters, Vol. 22, No. 11, 2015. [DOI:10.1109/LSP.2015.2441068]
9. Günther, D., Reininghaus, J., Hotz, I., and Wagner, H. "Memory Efficient Computation of Persistent Homology for 3D Images using Discrete Morse Theory", 24th SIBGRAPI Conference on Graphics, Patterns and Images, 28-31, 2011. [DOI:10.1109/SIBGRAPI.2011.24]
10. Lum, P. Y., Singh. G, Lehman, A., Ishkanov. T., Vejdemo-Johansson, M., Alagappan, M., Carlsson, J., Carlsson, G. "Extracting insights from the shape of complex data using topology", Sci. Rep, 3, 1236 (2013). [DOI:10.1038/srep01236]
11. Lum, P. Y., Lehmann, L., Singh, G., Ishkhanov, T., Vejdemo- Johansson, M., Carlsson , G., "The topology of politics: voting connectivity in the US House of Representatives", KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP, 2012.
12. Lee, H., Ghung, M. K., Kang, H., Kim, B., Lee, D. "Discriminative persistent homology of Brain networks", IEEE International Symposium on Biomedical Imaging: From Nano to Macro, pp. 841-844, 2011. [DOI:10.1109/ISBI.2011.5872535]
13. Edelsbrunner, H. "Persistent Homology In Image processing", Lecture Notes in Computer Science book series, LNCS, vol. 7877, pp. 182-183, 2013. [DOI:10.1007/978-3-642-38221-5_19]
14. Bhattacharya, S., Ghrist, R., and Kumar, V. "Persistent Homology for Path Planning in Uncertain Environments", IEEE TRANSAC- TIONS ON ROBOTICS, VOL. 31, NO. 3, pp. 1-13, JUNE 2015. [DOI:10.1109/TRO.2015.2412051]
15. Nicolau, M., Levine, A. J., Carlsson, G. "Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival", Proc Natl Acad Sci U S A, 108 (17), pp.7265-70(2011). [DOI:10.1073/pnas.1102826108]
16. Zhu, X. "Persistent Homology: An Introduction and a New Text Representation for Natural Language Processing", Twenty-Third International Joint Conference on Artificial Intelligence, 2013.
17. Elyasi, N., Hosseini Moghadam, M. "An introduction to a new text classification and visualization for natural language processing using topological data analysis", arXiv preprint arXiv:1906.01726, (2019), https://arxiv.org/pdf/1906.01726 .
18. Gholizadeh, S., Seyeditabari, A., and Zadrozny, W. "Topological Signature of 19th Century Novelists: Persistent Homology in Text Mining", big data and cognitive computing, 2(4), 2018, doi:10.3390/bdcc2040033. [DOI:10.3390/bdcc2040033]
19. NILSSON, D., EKGREN, A., "Topology and Word Spaces", Bachelors Thesis at CSC.
20. Torres P., Hromic H., Heravi B. "Topic Detection in Twitter Using Topology Data Analysis", ICWE 2015 Workshops, LNCS 9396, pp. 186-197, 2015. [DOI:10.1007/978-3-319-24800-4_16]
21. Romano, D., Nicolau, M., Quintin, E. M., Mazaika, P. K., Light- body, A. A., Hazlett, H. C., Piven, J., Carlsson, G., Reiss, A. L. "Topological methods reveal high and low functioning neuro- phenotypes within fragile X syndrome", Human Brain Mapping, 35, 9, pp. 4904-4915, 2014. [DOI:10.1002/hbm.22521]
22. Rizvi, A., Camara, P., Kandror, E., Roberts, T., Schieren, I. et al. "Single-cell topological RNA-seq analysis reveals insights into cellular differentiation and development", Nature Biotechnology, 35(6), pp. 551-560, 2017. [DOI:10.1038/nbt.3854]
23. Mihaela, E., Sardiu, M. E., Joshua, M. Gilmore., Groppe, B., Florens, L., Michael, P. Washburn, "Identification of Topological Network Modules in Perturbed Protein Interaction Networks", Scientific Reports, 7(1), pp. 1-13, 2017. [DOI:10.1038/srep43845]
24. Jessica, L., Nielson, Jesse Paquette, Aiwen, W. Liu, Cristian F. Guandique, C., Amy. Tovar et al. "Topological data analysis for discovery in preclinical spinal cord injury and traumatic brain injury", Nature Communications, Oct 14, 2015. [DOI:10.1038/ncomms9581]
25. Saggar, M., Sporns, O., Gonzalez-Castillo, J., Bandettini, P., Carlsson, G. et al. "Towards a new approach to reveal dynamical organization of the brain using topological data analysis", Nature Communications, 9 (1), Apr 11, 2018. [DOI:10.1038/s41467-018-03664-4]
26. Bubenik, P., Dotko, P. "A persistence landscapes toolbox for topological statistics", J. Symbolic Computation, 78, pp. 91-114 (2016). [DOI:10.1016/j.jsc.2016.03.009]
27. Singh, G., Mémoli, F., Carlsson, G. "Topological methods for the analysis of high dimensional data sets and 3d object recognition", In Eurographics Symposium on Point-Based Graphics (eds Botsch, M., Pajarola, R.) (The Eurographics Association), 2007.
28. Chen, T., Guestrin, C., "Xgboost: A scalable tree boosting system", Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, ACM, San Francisco, CA, pp. 785-794, USA 2016. [DOI:10.1145/2939672.2939785]
Send email to the article author
| Rights and permissions | |
 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |