A genetic algorithm for mixture model clustering using variable data segmentation and model selection is proposed in this study. Principle of the method is demonstrated on mixture model clustering of Ruspini data set. The segment numbers of the variables in the data set were determined and the variables were converted into categorical variables. It is shown that variable data segmentation forms the number and structure of cluster centers in data. Genetic Algorithms were used to determine the number of finite mixture models. The number of total mixture models and possible candidate mixture models among them are calculated using cluster centers formed by variable data segmentation in data set. Mixture of normal distributions is used in mixture model clustering. Maximum likelihood, AIC and BIC values were obtained by using the parameters in the data for each candidate mixture model. Candidate mixture models are established, to determine the number and structure of clusters, using sample means and variance-covariance matrices for data set. The best mixture model for model based clustering of data is selected according to information criteria among possible candidate mixture models. The number of components in the best mixture model corresponds to the number of clusters, and the components of the best mixture model correspond to the structure of clusters in data set.
Published in | Mathematics Letters (Volume 5, Issue 2) |
DOI | 10.11648/j.ml.20190502.12 |
Page(s) | 23-32 |
Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2019. Published by Science Publishing Group |
Cluster Centers, Data Clustering, Data Mining, Genetic Algorithm, Information Criteria, Mixture Model Clustering, Model Selection, Variable Data Segmentation
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APA Style
Maruf Gogebakan, Hamza Erol. (2019). Mixture Model Clustering Using Variable Data Segmentation and Model Selection: A Case Study of Genetic Algorithm. Mathematics Letters, 5(2), 23-32. https://doi.org/10.11648/j.ml.20190502.12
ACS Style
Maruf Gogebakan; Hamza Erol. Mixture Model Clustering Using Variable Data Segmentation and Model Selection: A Case Study of Genetic Algorithm. Math. Lett. 2019, 5(2), 23-32. doi: 10.11648/j.ml.20190502.12
AMA Style
Maruf Gogebakan, Hamza Erol. Mixture Model Clustering Using Variable Data Segmentation and Model Selection: A Case Study of Genetic Algorithm. Math Lett. 2019;5(2):23-32. doi: 10.11648/j.ml.20190502.12
@article{10.11648/j.ml.20190502.12, author = {Maruf Gogebakan and Hamza Erol}, title = {Mixture Model Clustering Using Variable Data Segmentation and Model Selection: A Case Study of Genetic Algorithm}, journal = {Mathematics Letters}, volume = {5}, number = {2}, pages = {23-32}, doi = {10.11648/j.ml.20190502.12}, url = {https://doi.org/10.11648/j.ml.20190502.12}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20190502.12}, abstract = {A genetic algorithm for mixture model clustering using variable data segmentation and model selection is proposed in this study. Principle of the method is demonstrated on mixture model clustering of Ruspini data set. The segment numbers of the variables in the data set were determined and the variables were converted into categorical variables. It is shown that variable data segmentation forms the number and structure of cluster centers in data. Genetic Algorithms were used to determine the number of finite mixture models. The number of total mixture models and possible candidate mixture models among them are calculated using cluster centers formed by variable data segmentation in data set. Mixture of normal distributions is used in mixture model clustering. Maximum likelihood, AIC and BIC values were obtained by using the parameters in the data for each candidate mixture model. Candidate mixture models are established, to determine the number and structure of clusters, using sample means and variance-covariance matrices for data set. The best mixture model for model based clustering of data is selected according to information criteria among possible candidate mixture models. The number of components in the best mixture model corresponds to the number of clusters, and the components of the best mixture model correspond to the structure of clusters in data set.}, year = {2019} }
TY - JOUR T1 - Mixture Model Clustering Using Variable Data Segmentation and Model Selection: A Case Study of Genetic Algorithm AU - Maruf Gogebakan AU - Hamza Erol Y1 - 2019/09/23 PY - 2019 N1 - https://doi.org/10.11648/j.ml.20190502.12 DO - 10.11648/j.ml.20190502.12 T2 - Mathematics Letters JF - Mathematics Letters JO - Mathematics Letters SP - 23 EP - 32 PB - Science Publishing Group SN - 2575-5056 UR - https://doi.org/10.11648/j.ml.20190502.12 AB - A genetic algorithm for mixture model clustering using variable data segmentation and model selection is proposed in this study. Principle of the method is demonstrated on mixture model clustering of Ruspini data set. The segment numbers of the variables in the data set were determined and the variables were converted into categorical variables. It is shown that variable data segmentation forms the number and structure of cluster centers in data. Genetic Algorithms were used to determine the number of finite mixture models. The number of total mixture models and possible candidate mixture models among them are calculated using cluster centers formed by variable data segmentation in data set. Mixture of normal distributions is used in mixture model clustering. Maximum likelihood, AIC and BIC values were obtained by using the parameters in the data for each candidate mixture model. Candidate mixture models are established, to determine the number and structure of clusters, using sample means and variance-covariance matrices for data set. The best mixture model for model based clustering of data is selected according to information criteria among possible candidate mixture models. The number of components in the best mixture model corresponds to the number of clusters, and the components of the best mixture model correspond to the structure of clusters in data set. VL - 5 IS - 2 ER -