Abstract
Bu çalışmada çok değişkenli verideki homojenlik ve heterojenlik durumları incelenmiş ve heterojen değişkenler belirlenmiştir. Değişkenlerdeki parçalanmaların (heterojenlik) normal karma dağılımlardaki bileşenlere denk geldiği gösterilmiş ve alt grup sayıları belirlenmiştir. K-otalamalar (k-means) algoritmaları ile değişkenlerdeki parçalanmalara atanan gözlemler belirlenmiş ve veri gruplandırma yapılmıştır. Değişkenlerdeki her bir parçalanmanın Gauss Karma Modeldeki (GMM) bir kümelenmeye karşılık geldiği varsayımı altında muhtemel küme sayıları ve küme sayıları için aralık elde edilmiş ve küme sayılarına bağlı olarak model sayıları belirlenmiştir. Parçalanma (bileşen) sayısına bağlı model sayıları Genetik Algoritmalarla (GA) belirlenmiş ve En Çok Olabilirlik Kestirimi (MLE)algoritması ile parametreler tahmin edilmiştir. Modele dayalı kümeleme yöntemi ile Gauss Karma Modeller arasından veri yapısına uyan en iyi modelin seçimi log-likelihood, AIC ve BIC gibi bilgi kriterleri ile belirlenmiştir.
Keywords
Gauss Karma Model Değişken veri parçalama Genetik Algoritmalar Modele dayalı kümeleme Bilgi Kriteri
References
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Abstract
References
- 1. McLachlan, G. J. and Peel, D. (2000). Finite Mixture Models. Wiley, New York. 2. Fraley, C. and Raftery, A. E. (2002). Model-Based Clustering, Discriminant Analysis, and Density Estimation. Journal of the American Statistical Association, 97, 611-631. 3. McLachlan, G. J. and Chang, S. U. (2004). Mixture Modelling for Cluster Analysis. Statistical Methods in Medical Research 13, 347-361. 4. Fraley, C. and Raftery, A. E. (1998). How Many Clusters? Which Clustering Method? Answers via Model-Based Cluster Analysis. The Computer Journal, 41, 578-588. 5. Soffritti, G. (2003). Identifying multiple cluster structures in a data matrix. Communications in Statistics, Simulation & Computation, Vol. 32, Issue 4, pp. 1151-1181 6. Galimberti, G. and Soffritti, G. (2007). Model-based methods to identify multiple cluster structures in a data set. Computational Statistics and Data Analysis. doi 10.1016/j.csda.2007.02.019. 7. Seo, B. and Kim, D. (2012). Root selection in normal mixture models. Computational Statistics and Data Analysis. 56, 2454-2470. 8. Servi, T. and Erol, H. (2007). On Total Number Of Candidate Component Cluster Centers And Total Number of Candidate Mixture Models In Model Based Clustering. Selçuk Journal of Applied Mathematics Vol.8. No.2. pp. 57 – 69. 9. Gogebakan, M., & Erol, H. (2018). A New Semi-supervised Classification Method Based on Mixture Model Clustering for Classification of Multispectral Data. Journal of the Indian Society of Remote Sensing, 46(8), 1323-1331 10. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control 19 (6): 716–723. 11. Schwarz, G. (1978). Estimating the dimension of a model, Ann. Statist. 6 pp. 461–464. 12. Ranciati, S., Galimberti, G., & Soffritti, G. (2019). Bayesian variable selection in linear regression models with non-normal errors. Statistical Methods & Applications, 28(2), 323-358. 13. Erol, H. Gogebakan, M. Erol, R. (2017) Grid Structures and Orientations Of Clusters Using Discretization Of Variables In Big Data. Proceedings of International Conference on Engineering, Technology, and Applied Science ICETA 2017, ISSN 2411-9318, pp. 16-31. 14. Gogebakan, M., & Erol, H. (2019). Mixture Model Clustering Using Variable Data Segmentation and Model Selection: A Case Study of Genetic Algorithm, Mathematics Letters. Vol. 5, No. 2, 2019, pp. 23-32. doi: 10.11648/j.ml.20190502.12 15. Akogul, S., & Erisoglu, M. (2017). An Approach for Determining the Number of Clusters in a Model Based Cluster Analysis. Entropy, 19(9), 452–0 16. Cheballah, H., Giraudo, S., & Maurice, R., 2015. Hopf algebra structure on packed square matrices. Journal of Combinatorial Theory, Series A, 133, 139-182
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Araştırma Makalesi |
| Authors | |
| Publication Date | September 26, 2020 |
| Submission Date | November 29, 2019 |
| Acceptance Date | March 20, 2020 |
| Published in Issue | Year 2020 Volume: 9 Issue: 3 |
