Araştırma Makalesi
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Yıl 2019, Cilt 14, Sayı 4, 139 - 146, 26.10.2019

Öz


Kaynakça

  • [1] McNicholas, P.D., (2016). Mixture Model-Based Classification: Chapman and Hall/CRC.
  • [2] McLachlan, G. and Peel, D., (2000). Finite Mixture Models, Willey Series in Probability and Statistics. In: John Wiley & Sons, New York.
  • [3] Erol, H., (2004). A Note on Non-identifibiality Problem of Finite Mixture Distribution Models in Model-based Classification. Selcuk Journal of Applied Mathematics, 5(1):3-10.
  • [4] Beran, R., (1977). Minimum Hellinger Distance Estimates for Parametric Models. The annals of Statistics, 5(3):445-463.
  • [5] Titterington, D.M., Smith, A.F., and Makov, U.E., (1985). Statistical Analysis of Finite Mixture Distributions: Wiley.
  • [6] Dempster, A.P., Laird, N.M., and Rubin, D.B., (1977). Maximum Likelihood from Incomplete Data Via the EM Algorithm. Journal of the Royal Statistical Society. Series B (methodological), pp:1-38.
  • [7] Thayasivam, U., Kuruwita, C., and Ramachandran, R.P., (2015). Robust L_2 E Parameter Estimation of Gaussian Mixture Models: Comparison with Expectation Maximization. 22nd International Conference, ICONIP 2015, Istanbul, Proceedings Books, pp:281-288.
  • [8] Scott, D.W., (2001). Parametric Statistical Modeling by Minimum Integrated Square Error. Technometrics, 43(3):274-285. doi: 10.1198/004017001316975880.
  • [9] Thayasivam, U., (2009). L_2 E Estimation of Mixture Complexity. UGA.
  • [10] Aitkin, M. and Rubin, D.B., (1985). Estimation and Hypothesis-Testing in Finite Mixture-Models. Journal of the Royal Statistical Society Series B-Methodological, 47(1):67-75.
  • [11] Teicher, H., (1963). Identifiability of Finite Mixtures. The Annals of Mathematical statistics, 34(4):1265-1269.
  • [12] Yakowitz, S.J. and Spragins, J.D., (1968). On the Identifiability of Finite Mixtures. The annals of Mathematical statistics, 39(1):209-214.
  • [13] Kadane, J.B., (1975). The Role of Identification in Bayesian Theory. Studies in Bayesian econometrics and statistics.
  • [14] Akdağ, S.A., (2018). Rüzgar Enerjisi Potansiyel Analizinde Karışım Dağılımları Temelli Tekniklerin Kullanılması, Doktora Tezi, İstanbul Teknik Üniversitesi, Enerji Enstitüsü.
  • [15] Toher, D., Downey, G., and Murphy, T., (2005). A Comparison of Model-based and Regression Classification Techniques Applied to Near-infrared Spectroscopic data in Food Authentication Studies. Technical Report 5/10, Department of Statistics, Trinity College Dublin.
  • [16] Mclachlan, G.J. and Basford, K.E., (1988). Mixture Models: Inference and Applications to Clustering. Marcel Dekker, New York.
  • [17] Fraley, C., Raftery, A.E., and Wehrens, R., (2005). Incremental Model Based Clustering for Large Data Sets with Small Clusters. Journal of Computational and Graphical Statistics, Vol:14, pp:1–18.
  • [18] Erol, H. and Akdeniz, F., (2005). A Per-field Classification Method Based on Mixture Distribution Models and an Application to Landsat Thematic Mapper data. International Journal of Remote Sensing Vol:26, No:6, pp:1229–1244.
  • [19] Dean, N., Murphy, T.B., and Downey, G., (2006). Updating Classification Rules with Unlabeled Data with Applications in Food Authenticity Studies. Journal of the Royal Statistical Society, Series C (Applied Statistics), Vol:55, pp:1–14.
  • [20] Wehrens, R., Buydens, L., Fraley, C., and Raftery, A.E., (2004). Model Based Clustering for Image Segmentation and Large Data Sets Via Sampling. Journal of Classification, Vol:21, pp:231–253.
  • [21] Yeung, K.Y., Fraley, C., Murua, A., Raftery, A.E. and Ruzzo, W.L., (2001). Model Based Clustering and Data Transformations for Gene Expression Data. Bioinformatics, 17(10):977-987.
  • [22] Servi, T., (2009). Çok Değişkenli Karma Dağılım Modeline Dayalı Kümeleme Analizi, Doktora Tezi, Çukurova Üniversitesi Fen Bilimleri Enstitüsü.
  • [23] Everitt, B.S. and David, J.H., (1981). Finite Mixture Distributions. Monographs on Applied Probability and Statistics. Chapman and Hall, London, New York.

A Remark on L2 Distance Function And Non-Identifiability Problem of Finite Mixture Distribution Models in Model-Based Classification

Yıl 2019, Cilt 14, Sayı 4, 139 - 146, 26.10.2019

Öz

          Finite mixture models provide flexible method of modeling data obtained from population consisting of finite number of homogeneous subpopulations. One of the main areas in which the finite mixture model structures is practically used in statistics is model based classification. However, the result of non identifiability problem arising from the structure of the finite mixture models may cause unreliable results on classification. In this paper we compare the probability density functions () of the finite mixture distribution models for two different populations by L2 distance. We propose the componentwise L2 distance function to compare the  of finite mixture distribution models for two different populations in the presence of non identifiability problem. Besides, a condition is proposed to control whether the L2 distance function gives similar results with the componentwise L2 distance function to compare the  of finite mixture distribution models for two different populations. 

Kaynakça

  • [1] McNicholas, P.D., (2016). Mixture Model-Based Classification: Chapman and Hall/CRC.
  • [2] McLachlan, G. and Peel, D., (2000). Finite Mixture Models, Willey Series in Probability and Statistics. In: John Wiley & Sons, New York.
  • [3] Erol, H., (2004). A Note on Non-identifibiality Problem of Finite Mixture Distribution Models in Model-based Classification. Selcuk Journal of Applied Mathematics, 5(1):3-10.
  • [4] Beran, R., (1977). Minimum Hellinger Distance Estimates for Parametric Models. The annals of Statistics, 5(3):445-463.
  • [5] Titterington, D.M., Smith, A.F., and Makov, U.E., (1985). Statistical Analysis of Finite Mixture Distributions: Wiley.
  • [6] Dempster, A.P., Laird, N.M., and Rubin, D.B., (1977). Maximum Likelihood from Incomplete Data Via the EM Algorithm. Journal of the Royal Statistical Society. Series B (methodological), pp:1-38.
  • [7] Thayasivam, U., Kuruwita, C., and Ramachandran, R.P., (2015). Robust L_2 E Parameter Estimation of Gaussian Mixture Models: Comparison with Expectation Maximization. 22nd International Conference, ICONIP 2015, Istanbul, Proceedings Books, pp:281-288.
  • [8] Scott, D.W., (2001). Parametric Statistical Modeling by Minimum Integrated Square Error. Technometrics, 43(3):274-285. doi: 10.1198/004017001316975880.
  • [9] Thayasivam, U., (2009). L_2 E Estimation of Mixture Complexity. UGA.
  • [10] Aitkin, M. and Rubin, D.B., (1985). Estimation and Hypothesis-Testing in Finite Mixture-Models. Journal of the Royal Statistical Society Series B-Methodological, 47(1):67-75.
  • [11] Teicher, H., (1963). Identifiability of Finite Mixtures. The Annals of Mathematical statistics, 34(4):1265-1269.
  • [12] Yakowitz, S.J. and Spragins, J.D., (1968). On the Identifiability of Finite Mixtures. The annals of Mathematical statistics, 39(1):209-214.
  • [13] Kadane, J.B., (1975). The Role of Identification in Bayesian Theory. Studies in Bayesian econometrics and statistics.
  • [14] Akdağ, S.A., (2018). Rüzgar Enerjisi Potansiyel Analizinde Karışım Dağılımları Temelli Tekniklerin Kullanılması, Doktora Tezi, İstanbul Teknik Üniversitesi, Enerji Enstitüsü.
  • [15] Toher, D., Downey, G., and Murphy, T., (2005). A Comparison of Model-based and Regression Classification Techniques Applied to Near-infrared Spectroscopic data in Food Authentication Studies. Technical Report 5/10, Department of Statistics, Trinity College Dublin.
  • [16] Mclachlan, G.J. and Basford, K.E., (1988). Mixture Models: Inference and Applications to Clustering. Marcel Dekker, New York.
  • [17] Fraley, C., Raftery, A.E., and Wehrens, R., (2005). Incremental Model Based Clustering for Large Data Sets with Small Clusters. Journal of Computational and Graphical Statistics, Vol:14, pp:1–18.
  • [18] Erol, H. and Akdeniz, F., (2005). A Per-field Classification Method Based on Mixture Distribution Models and an Application to Landsat Thematic Mapper data. International Journal of Remote Sensing Vol:26, No:6, pp:1229–1244.
  • [19] Dean, N., Murphy, T.B., and Downey, G., (2006). Updating Classification Rules with Unlabeled Data with Applications in Food Authenticity Studies. Journal of the Royal Statistical Society, Series C (Applied Statistics), Vol:55, pp:1–14.
  • [20] Wehrens, R., Buydens, L., Fraley, C., and Raftery, A.E., (2004). Model Based Clustering for Image Segmentation and Large Data Sets Via Sampling. Journal of Classification, Vol:21, pp:231–253.
  • [21] Yeung, K.Y., Fraley, C., Murua, A., Raftery, A.E. and Ruzzo, W.L., (2001). Model Based Clustering and Data Transformations for Gene Expression Data. Bioinformatics, 17(10):977-987.
  • [22] Servi, T., (2009). Çok Değişkenli Karma Dağılım Modeline Dayalı Kümeleme Analizi, Doktora Tezi, Çukurova Üniversitesi Fen Bilimleri Enstitüsü.
  • [23] Everitt, B.S. and David, J.H., (1981). Finite Mixture Distributions. Monographs on Applied Probability and Statistics. Chapman and Hall, London, New York.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Yüksel ÖNER (Sorumlu Yazar)
Ondokuz Mayis University
0000-0003-2433-3304
Türkiye


Fikriye KABAKCI Bu kişi benim
Recep Tayyip Erdogan University
0000-0001-6266-1902
Türkiye


Burçin ÖNER
0000-0001-9550-0435
Türkiye


Mehmet Gürcan
Firat University
0000-0002-3641-8113
Türkiye

Yayımlanma Tarihi 26 Ekim 2019
Yayınlandığı Sayı Yıl 2019, Cilt 14, Sayı 4

Kaynak Göster

Bibtex @araştırma makalesi { nwsatecapsci595546, journal = {Technological Applied Sciences}, issn = {}, eissn = {1308-7223}, address = {}, publisher = {E-Journal of New World Sciences Academy}, year = {2019}, volume = {14}, pages = {139 - 146}, doi = {}, title = {A Remark on L2 Distance Function And Non-Identifiability Problem of Finite Mixture Distribution Models in Model-Based Classification}, key = {cite}, author = {Öner, Yüksel and Kabakcı, Fikriye and Öner, Burçin and Gürcan, Mehmet} }
APA Öner, Y. , Kabakcı, F. , Öner, B. & Gürcan, M. (2019). A Remark on L2 Distance Function And Non-Identifiability Problem of Finite Mixture Distribution Models in Model-Based Classification . Technological Applied Sciences , 14 (4) , 139-146 . Retrieved from https://dergipark.org.tr/tr/pub/nwsatecapsci/issue/49784/595546
MLA Öner, Y. , Kabakcı, F. , Öner, B. , Gürcan, M. "A Remark on L2 Distance Function And Non-Identifiability Problem of Finite Mixture Distribution Models in Model-Based Classification" . Technological Applied Sciences 14 (2019 ): 139-146 <https://dergipark.org.tr/tr/pub/nwsatecapsci/issue/49784/595546>
Chicago Öner, Y. , Kabakcı, F. , Öner, B. , Gürcan, M. "A Remark on L2 Distance Function And Non-Identifiability Problem of Finite Mixture Distribution Models in Model-Based Classification". Technological Applied Sciences 14 (2019 ): 139-146
RIS TY - JOUR T1 - A Remark on L2 Distance Function And Non-Identifiability Problem of Finite Mixture Distribution Models in Model-Based Classification AU - Yüksel Öner , Fikriye Kabakcı , Burçin Öner , Mehmet Gürcan Y1 - 2019 PY - 2019 N1 - DO - T2 - Technological Applied Sciences JF - Journal JO - JOR SP - 139 EP - 146 VL - 14 IS - 4 SN - -1308-7223 M3 - UR - Y2 - 2019 ER -
EndNote %0 Technological Applied Sciences A Remark on L2 Distance Function And Non-Identifiability Problem of Finite Mixture Distribution Models in Model-Based Classification %A Yüksel Öner , Fikriye Kabakcı , Burçin Öner , Mehmet Gürcan %T A Remark on L2 Distance Function And Non-Identifiability Problem of Finite Mixture Distribution Models in Model-Based Classification %D 2019 %J Technological Applied Sciences %P -1308-7223 %V 14 %N 4 %R %U
ISNAD Öner, Yüksel , Kabakcı, Fikriye , Öner, Burçin , Gürcan, Mehmet . "A Remark on L2 Distance Function And Non-Identifiability Problem of Finite Mixture Distribution Models in Model-Based Classification". Technological Applied Sciences 14 / 4 (Ekim 2019): 139-146 .
AMA Öner Y. , Kabakcı F. , Öner B. , Gürcan M. A Remark on L2 Distance Function And Non-Identifiability Problem of Finite Mixture Distribution Models in Model-Based Classification. NWSA. 2019; 14(4): 139-146.
Vancouver Öner Y. , Kabakcı F. , Öner B. , Gürcan M. A Remark on L2 Distance Function And Non-Identifiability Problem of Finite Mixture Distribution Models in Model-Based Classification. Technological Applied Sciences. 2019; 14(4): 139-146.
IEEE Y. Öner , F. Kabakcı , B. Öner ve M. Gürcan , "A Remark on L2 Distance Function And Non-Identifiability Problem of Finite Mixture Distribution Models in Model-Based Classification", Technological Applied Sciences, c. 14, sayı. 4, ss. 139-146, Eki. 2019