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Annals of Data Science

10-08-2024

Non-negative Sparse Matrix Factorization for Soft Clustering of Territory Risk Analysis

Authors: Shengkun Xie, Chong Gan, Anna T. Lawniczak

Published in: Annals of Data Science

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Abstract

Developing effective methodologies for territory design and relativity estimation is crucial in auto insurance rate filings and reviews. This study introduces a novel approach utilizing fuzzy clustering to enhance the design process of territories for auto insurance rate-making and regulation. By adopting a soft clustering method, we aim to overcome the limitations of traditional hard clustering techniques and improve the assessment of territory risk. Furthermore, we employ non-negative sparse matrix approximation techniques to refine the estimates of risk relativities for basic rating units. This method promotes sparsity in the fuzzy membership matrix by eliminating small membership values, leading to more robust and interpretable results. We also compare the outcomes with those obtained using non-negative sparse principal component analysis, a technique explored in our previous research. Integrating fuzzy clustering with non-negative sparse matrix decomposition offers a promising approach for auto insurance rate filings. The combined methodology enhances decision-making and provides sparse estimates, which can be advantageous in various data science applications where fuzzy clustering is relevant.

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Kauhl B, König J, Wolf S (2023) Spatial distribution of COVID-19 hospitalizations and associated risk factors in health insurance data using Bayesian spatial modelling. Int J Environ Res Public Health 20(5):4375. https://doi.org/10.3390/ijerph20054375CrossRef

Fernandez A (2017) Prisoners of the zip code: how single zip code rate-making hurts the public interest. Thomas L. Rev. 30:117

Butler P (2006) Driver negligence vs. Odometer miles: rival theories to explain 12 predictors of auto insurance claims. In: American risk & insurance association annual meeting. Washington, DC, vol 9

Xie S, Gan C, Chua-Chow C (2021) Estimating territory risk relativity for auto insurance rate regulation using generalized linear mixed models. In: DATA, pp 329–334. https://doi.org/10.5220/0010601003290334

Boudreault M, Ojeda A (2022) Ratemaking territories and adverse selection for flood insurance. Insur Math Econ 107:349–360. https://doi.org/10.1016/j.insmatheco.2022.09.005CrossRef

Yeo AC, Smith KA, Willis RJ, Brooks M (2001) Clustering technique for risk classification and prediction of claim costs in the automobile insurance industry. Intell Syst Account Finance Manag 10(1):39–50. https://doi.org/10.1002/isaf.196CrossRef

Grubesic TH (2008) Zip codes and spatial analysis: problems and prospects. Socioecon Plann Sci 42(2):129–149. https://doi.org/10.1016/j.seps.2006.09.001CrossRef

Clark DR (2011) Credibility for a tower of excess layers. Variance 5(1):32–44

Duong TD, Duong VN (2008) Non-negative sparse principal component analysis for multidimensional constrained optimization. In: PRICAI 2008: trends in artificial intelligence: 10th Pacific rim international conference on artificial intelligence, Hanoi, Vietnam, December 15–19, 2008. Proceedings 10. Springer, Berlin, pp 103–114. https://doi.org/10.1007/978-3-540-89197-01_3

10.

Duong TD (2009) Non-negative sparse principal component analysis. J Tech Educ Sci 4(3):31–38

11.

Hoyer PO (2004) Non-negative matrix factorization with sparseness constraints. J Mach Learn Res 5(9):1457–1469

12.

Xie S, Gan C (2022) Fuzzy clustering and non-negative sparse matrix approximation on estimating territory risk relativities. In: 2022 IEEE international conference on fuzzy systems (FUZZ-IEEE). IEEE, pp 1–8. https://doi.org/10.1109/FUZZ-IEEE55066.2022.9882750

13.

Meister C, Lazov S, Augenstein I, Cotterell R (2021) Is sparse attention more interpretable? arXiv preprint arXiv:2106.01087. https://doi.org/10.48550/arXiv.2106.01087

14.

Campos D, Marques A, Nguyen T, Kurtz M, Zhai C (2022) Sparse* BERT: sparse models generalize to new tasks and domains. arXiv preprint arXiv:2205.12452. https://doi.org/10.48550/arXiv.2205.12452

15.

Asteris M, Papailiopoulos D, Dimakis A (2014) Nonnegative sparse PCA with provable guarantees. In: International conference on machine learning. PMLR, pp 1728–1736

16.

Shi Y (2022) Big data and big data analytics. In: Advances in big data analytics. Springer, Singapore. https://doi.org/10.1007/978-981-16-3607-3_1

17.

Olson DL, Shi Y (2007) Introduction to business data mining, vol 10. McGraw-Hill/Irwin, New York, pp 2250–2254

18.

Shi Y, Tian Y, Kou G, Peng Y, Li J (2011) Optimization based data mining: theory and applications. Springer, BerlinCrossRef

19.

Tien JM (2017) Internet of things, real-time decision making, and artificial intelligence. Ann Data Sci 4:149–178. https://doi.org/10.1007/s40745-017-0112-5CrossRef

20.

Majhi SK (2021) Fuzzy clustering algorithm based on modified whale optimization algorithm for automobile insurance fraud detection. Evol Intel 14(1):35–46. https://doi.org/10.1007/s12065-019-00260-3CrossRef

21.

Majhi SK, Bhatachharya S, Pradhan R, Biswal S (2019) Fuzzy clustering using salp swarm algorithm for automobile insurance fraud detection. J Intell Fuzzy Syst 36(3):2333–2344. https://doi.org/10.3233/JIFS-169944CrossRef

22.

Subudhi S, Panigrahi S (2020) Use of optimized Fuzzy C-means clustering and supervised classifiers for automobile insurance fraud detection. J King Saud Univ Comput Inf Sci 32(5):568–575. https://doi.org/10.1016/j.jksuci.2017.09.010CrossRef

23.

Seyedali M, Andrew L (2016) The whale optimization algorithm advances in engineering software. Elsevier Ltd., Amsterdam. https://doi.org/10.1016/j.advengsoft.2016.01.008CrossRef

24.

Viaene S, Ayuso M, Guillen M, Van Gheel D, Dedene G (2007) Strategies for detecting fraudulent claims in the automobile insurance industry. Eur J Oper Res 176(1):565–583. https://doi.org/10.1016/j.ejor.2005.08.005CrossRef

25.

Wang X, Wang H, Wang Y (2020) A density weighted fuzzy outlier clustering approach for class imbalanced learning. Neural Comput Appl 32:13035–13049. https://doi.org/10.1007/s00521-020-04747-4CrossRef

26.

Liu H, Li R (2021) Research into military family risk based on ANP and fuzzy clustering. Oper Res Manag Sci 30(3):7. https://doi.org/10.12005/orms.2021.0068CrossRef

27.

Jandaghi G, Moradpour Z (2015) Segmentation of life insurance customers based on their profile using fuzzy clustering. Int Lett Soc Human Sci 61:17–24. https://doi.org/10.18052/www.scipress.com/ILSHS.61.17CrossRef

28.

Jandaghi G, Moazzez H, Moradpour Z (2015) Life insurance customers segmentation using fuzzy clustering. World Sci News 21:24–35

29.

Devriendt S, Antonio K, Reynkens T, Verbelen R (2021) Sparse regression with multi-type regularized feature modeling. Insur Math Econ 96:248–261. https://doi.org/10.1016/j.insmatheco.2020.11.010CrossRef

30.

Shi P, Shi K (2021) A sparse deep two-part model for nonlife insurance claims with dependent frequency and severity. Available at SSRN 3824359. https://doi.org/10.2139/ssrn.3824359

31.

Fontaine S, Yang Y, Qian W, Gu Y, Fan B (2020) A unified approach to sparse Tweedie modeling of multisource insurance claim data. Technometrics 62(3):339–356. https://doi.org/10.1080/00401706.2019.1647881CrossRef

32.

Seo H, Shin J, Kim KH, Lim C, Bae J (2022) Driving risk assessment using non-negative matrix factorization with driving behavior records. IEEE Trans Intell Transp Syst 23(11):20398–20412. https://doi.org/10.1109/TITS.2022.3193125CrossRef

33.

Das KP, Hapuwitharana JC, Fowler J, Young SS (2021) Non-negative matrix factorization: a useful method for two-way life tables. J Stat Manag Syst 24(3):481–498. https://doi.org/10.1080/09720510.2020.1756048CrossRef

34.

Zhu S, Wang Y, Wu Y (2011) Health care fraud detection using nonnegative matrix factorization. In: 2011 6th international conference on computer science & education (ICCSE). IEEE, pp 499–503. https://doi.org/10.1109/ICCSE.2011.6028688

35.

Kim H, Park H (2007) Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis. Bioinformatics 23(12):1495–1502. https://doi.org/10.1093/bioinformatics/btm134CrossRef

36.

Monga V, Mihçak MK (2007) Robust and Secure Image Hashing via Non-Negative Matrix Factorizations. IEEE Trans Inf Forensics Secur 2(3–1):376–390. https://doi.org/10.1109/TIFS.2007.902670CrossRef

37.

Huff SD, McGaha PK, Reed M, Kratz M, Peters JA, Atkinson V (2012) All-terrain vehicle injuries in Texas, mapping the path to intervention with a geographic information system. J Agromed 17(1):51–62. https://doi.org/10.1080/1059924X.2012.632206CrossRef

38.

Ruugia S, Moturi C (2017) Application of GIS spatial interpolation methods in auto insurance risk territory segmentation and rating. ORSEA J 4:1. https://doi.org/10.12005/orms.2021.0068CrossRef

39.

Bezdek JC, Ehrlich R, Full W (1984) FCM: the fuzzy c-means clustering algorithm. Comput Geosci 10(2–3):191–203. https://doi.org/10.1016/0098-3004(84)90020-7CrossRef

40.

Steinley D (2006) K-means clustering: a half-century synthesis. Br J Math Stat Psychol 59(1):1–34. https://doi.org/10.1348/000711005X48266CrossRef

41.

Shapiro A. F (2004) Fuzzy logic in insurance. Insur Math Econ 35(2):399–424. https://doi.org/10.1016/j.insmatheco.2004.07.010CrossRef

42.

Tsingalis I, Kotropoulos C, Drosou A, Tzovaras D (2020) Non-negative sparse pca: an intelligible exact approach. IEEE Trans Emerg Top Comput Intell 6(1):192–204. https://doi.org/10.1109/TETCI.2020.3042268CrossRef

43.

Tsingalis I, Kotropoulos C (2019) A simple algorithm for non-negative sparse principal component analysis. In: 2019 IEEE international conference on image processing (ICIP). IEEE, pp 2075–2079. https://doi.org/10.1109/ICIP.2019.8804397

44.

Seddik MEA, Tamaazousti M, Couillet R (2019) A kernel random matrix-based approach for sparse PCA. In: ICLR 2019-international conference on learning representations

45.

Lee D, Seung HS (2000) Algorithms for non-negative matrix factorization. Adv Neural Inf Process Syst 13

46.

Cavanaugh JE (1997) Unifying the derivations for the Akaike and corrected Akaike information criteria. Stat Probab Lett 33(2):201–208. https://doi.org/10.1016/S0167-7152(96)00128-9CrossRef

Title: Non-negative Sparse Matrix Factorization for Soft Clustering of Territory Risk Analysis
Authors: Shengkun Xie
Chong Gan
Anna T. Lawniczak
Publication date: 10-08-2024
Publisher: Springer Berlin Heidelberg
Published in: Annals of Data Science
Print ISSN: 2198-5804
Electronic ISSN: 2198-5812
DOI: https://doi.org/10.1007/s40745-024-00570-z

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