Abstract
Feed-forward neural networks are algorithms with supervised learning. It means that we have to a priori identify the most relevant variables and to know the desired outputs for combinations of these variables. For example, forecasting the frequency of car accidents with a perceptron requires an a priori segmentation of some explanatory variables like the driver’s age into categories, in a similar manner to Generalized Linear Models. The misspecification of these categories can induce a large bias in the forecast. On the other hand, the presence of collinearity between covariates affects the accuracy of the prediction. In this situation, the coefficient estimates of the multiple regression may change erratically in response to small changes in the model or the data. Self-organizing maps offer an elegant solution to segment explanatory variables and to detect dependence among covariates.
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Notes
- 1.
In our approach, codebooks are randomly chosen. An alternative consists to use the initialization procedure of the k-means algorithm, presented in Sect. 5.2.
- 2.
A variant of this algorithm consists to recompute immediately the new position of centroids after assignment of each records of the dataset.
- 3.
This should not be confused with the number of neurons on edges of the map.
References
Arthur D, Vassilvitskii S (2007) K-means++: the advantages of careful seeding. In: SODA ‘07: proceedings of the eighteenth annual ACM-SIAM symposium on discrete algorithms, pp 1027–1035
Benzecri JP (1973) L’Analyse des données. Tome 2 : l’analyse des correspondances, Dunod, p. 619
Brockett P, Xia X, Derrig R (1998) Using Kohonen’s self-organizing feature map to uncover automobile bodily injury claims fraud. J Risk Insur 65(2):245–274
Burt C (1950) The factorial analysis of qualitative data. Br J Psychol 3:166–185
Cottrell M, Ibbou S, Letrémy P (2004) SOM-based algorithms for qualitative variables. Neural Netw 17:1149–1167
Greenacre MJ (1984) Theory and applications of correspondence analysis. Academic, London
Hainaut D (2019) A self-organizing predictive map for non-life insurance. Eur Actuar J 9(1):173–207
Huysmans J, Baesens B, Vanthienen J, Van Gestel T (2006) Failure prediction with self organizing maps. Expert Syst Appl 30(3):479–487
Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biol Cybern 43(1):59–69
Kohonen T (2013) Essentials of the self-organizing map. Neural Netw 37:52–65
Lebart L, Morineau A, Warwick KM (1984) Multivariate descriptive statistical analysis: correspondence analysis and related techniques for large matrices. Wiley, Chichester
Wütrich M, Buser C (2017) Data analytics for non-life insurance pricing. Lectures notes. Available on https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2870308
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Denuit, M., Hainaut, D., Trufin, J. (2019). Self-organizing Maps and k-Means Clustering in Non Life Insurance. In: Effective Statistical Learning Methods for Actuaries III. Springer Actuarial(). Springer, Cham. https://doi.org/10.1007/978-3-030-25827-6_5
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