
تعداد نشریات | 26 |
تعداد شمارهها | 447 |
تعداد مقالات | 4,557 |
تعداد مشاهده مقاله | 5,379,997 |
تعداد دریافت فایل اصل مقاله | 3,580,061 |
Parsimonious mixture of mean-mixture of normal distributions with missing data | ||
Journal of Mahani Mathematical Research | ||
دوره 13، شماره 3 - شماره پیاپی 28، آبان 2024، صفحه 33-54 اصل مقاله (1.18 M) | ||
نوع مقاله: Special Issue Dedicated to memory of Prof. Mahbanoo Tata | ||
شناسه دیجیتال (DOI): 10.22103/jmmr.2024.22642.1549 | ||
نویسندگان | ||
Farzane Hashemi* 1؛ Saeed Darijani2 | ||
1Department of Statistics, University of Kashan, Kashan, Iran | ||
2Farhangian University Of Kerman, Kerman, Iran | ||
چکیده | ||
Clustering multivariate data based on mixture distributions is a usual method to characterize groups and label data sets. Mixture models have recently been received considerable attention to accommodate asymmetric and missing data via exploiting skewed and heavy-tailed distributions. In this paper, a mixture of multivariate mean-mixture of normal distributions is considered for handling missing data. The EM-type algorithms are carried out to determine maximum likelihood of parameters estimations. We analyzed the real data sets and conducted simulation studies to demonstrate the superiority of the proposed methodology. | ||
کلیدواژهها | ||
EM-type algorithms؛ Finite mixture model؛ MMN distribution؛ Missing data؛ Skew distribution | ||
مراجع | ||
[1] Arellano-Valle, RB., Azzalini, A., Ferreira, CS., & Santoro, K. (2020). A two-piece normal measurement error model, Computational Statistics and Data Analysis, 144, 106863. https://doi.org/10.1016/j.csda.2019.106863
[2] Aitken, A. (1925). On Bernoulli's numerical solution of algebraic equations. Proceedings of the Royal Society of Edinburgh, 46, 289 305. https://doi.org/10.1017/S0370164600022070
[3] Akaike, H. (1998). Information theory and an extension of the maximum likelihood principle. In Selected papers of hirotugu akaike, New York, NY: Springer New York, 199 213. https://doi.org/10.1007/978-1-4612-1694-0 15
[4] Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian journal of statistics, 171 178. https://www.jstor.org/stable/4615982
[5] Bai, X., Chen, K., & Yao, W. (2016). Mixture of linear mixed models using multivariate t distribution. Journal of Statistical Computation and Simulation, 86(4), 771 787. https://doi.org/10.1080/00949655.2015.1036431
[6] Ban eld, JD., & Raftery, AE. (1993). Model-based Gaussian and non-Gaussian clustering. Biometrics, 803 821. https://doi.org/10.2307/2532201
[7] Biernacki, C., Celeux, G., & Govaert, G. (2000). Assessing a mixture model for clustering with the integrated completed likelihood. IEEE transactions on pattern analysis and machine intelligence, 22(7), 719 725. https://doi.org/10.1109/34.865189
[8] Clark, KM., & McNicholas, PD. (2023). Clustering Three-Way Data with Outliers. arXiv preprint arXiv:2310.05288.
[9] Celeux, G., & Govaert, G. (1995). Gaussian parsimonious clustering models. Pattern recognition, 28(5), 781 793. https://doi.org/10.1016/0031-3203(94)00125-6
[10] Diaconis, P., & Efron, B. (1983). Computer-intensive methods in statistics. Scienti c American, 248(5), 116-131. https://www.jstor.org/stable/24968902
[11] Dempster, AP., Laird, NM., & Rubin, DB. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the royal statistical society: series B (methodological), 39(1), 1 22. https://doi.org/10.1111/j.2517-6161.1977.tb01600.x
[12] Hashemi, F., Naderi, M., & Mashinchi, M. (2019). Clustering right-skewed data stream via Birnbaum{Saunders mixture models: A exible approach based on fuzzy clustering algorithm. Applied Soft Computing, 82, 105539. https://doi.org/10.1016/j.asoc.2019.105539
[13] Hashemi, F., Naderi, M., Jamalizadeh, A., & Bekker, A. (2021). A exible factor analysis based on the class of mean-mixture of normal distributions. Computational statistics & data analysis, 157, 107162. https://doi.org/10.1016/j.csda.2020.107162
[14] Hubert, L., & Arabie, P. (1985). Comparing partitions. Journal of classi cation, 2, 193-218. https://doi.org/10.1007/BF01908075
[15] Lin, TI. (2014). Learning from incomplete data via parameterized t mixture models through eigenvalue decomposition. Computational statistics & data analysis, 71, 183-195. https://doi.org/10.1016/j.csda.2013.02.020
[16] Lin, TC., & Lin, TI. (2010). Supervised learning of multivariate skew normal mixture models with missing information. Computational Statistics, 25, 183 201. https://doi.org/10.1007/s00180-009-0169-5
[17] Little, R. J., & Rubin, D. B. (2019). Statistical analysis with missing data (Vol. 793). John Wiley & Sons.
[18] Liu, C., & Rubin, DB. (1994). The ECME algorithm: a simple extension of EM and ECM with faster monotone convergence. Biometrika, 81(4), 633 648. https://doi.org/10.1093/biomet/81.4.633
[19] McNicholas, PD., & Murphy, TB. (2008). Parsimonious Gaussian mixture models. Statistics and Computing, 18, 285 296. https://doi.org/10.1007/s11222-008-9056-0
[20] Meng, XL., & Rubin, DB. (1993). Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika, 80(2), 267 278. https://doi.org/10.1093/biomet/80.2.267
[21] Naderi, M., Hung, WL., Lin, TI., & Jamalizadeh, A. (2019). A novel mixture model using the multivariate normal mean{variance mixture of Birnbaum{Saunders distributions and its application to extrasolar planets. Journal of Multivariate Analysis, 171, 126 138. https://doi.org/10.1016/j.jmva.2018.11.015
[22] Naderi, M., Hashemi, F., Bekker, A., & Jamalizadeh, A. (2020). Modeling right-skewed nancial data streams: A likelihood inference based on the generalized Birnbaum-Saunders mixture model. Applied Mathematics and Computation, 376, 125109. https://doi.org/10.1016/j.amc.2020.125109
[23] Naderi, M., Bekker, A., Arashi, M., & Jamalizadeh, A. (2020). A theoretical framework for Landsat data modeling based on the matrix variate mean-mixture of normal model. Plos one, 15(4), e0230773. https://doi.org/10.1371/journal.pone.0230773
[24] Naderi, M., & Nooghabi, MJ. (2024). Clustering asymmetrical data with out-liers: Parsimonious mixtures of contaminated mean-mixture of normal distributions. Journal of Computational and Applied Mathematics, 437, 115433. https://doi.org/10.1016/j.cam.2023.115433 [25] Negarestani, H., Jamalizadeh, A., Sha ei, S., & Balakrishnan, N. (2019). Mean mixtures of normal distributions: properties, inference and application. Metrika, 82, 501 528. https://doi.org/10.1007/s00184-018-0692-x
[26] Rand, WM. (1971). Objective criteria for the evaluation of clustering methods. Journal of the American Statistical association, 66(336), 846 850. https://doi.org/10.1080/01621459.1971.10482356
[27] Punzo, A., & McNicholas, PD. (2016). Parsimonious mixtures of multivariate contaminated normal distributions. Biometrical Journal, 58(6), 1506 1537. https://doi.org/10.1002/bimj.201500144
[28] Schwarz, G. (1978). Estimating the dimension of a model. The annals of statistics, 461 464. https://www.jstor.org/stable/2958889
[29] Sepahdar, A., Madadi, M., Balakrishnan, N., & Jamalizadeh, A. (2022). Parsimonious mixture-of-experts based on mean mixture of multivariate normal distributions. Stat, 11(1), e421. https://doi.org/10.1002/sta4.421
[30] Wang, WL., & Lin, TI. (2015). Robust model-based clustering via mixtures of skew-t distributions with missing information. Advances in Data Analysis and Classi cation, 9, 423 445. https://doi.org/10.1007/s11634-015-0221-y | ||
آمار تعداد مشاهده مقاله: 141 تعداد دریافت فایل اصل مقاله: 128 |