Clustering Based on Nonparanormal Graphical Mixture Models

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Haji Aghabozorgi H.; ESKANDARI F.

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Journal Paper

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Journal: JOURNAL OF STATISTICAL SCIENCES Year:2022 | Volume:16 | Issue:1 Page(s): 63-89

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Information Journal Paper

Title

Clustering Based on Nonparanormal Graphical Mixture Models

Author(s)

Haji Aghabozorgi H. | ESKANDARI F. | Issue Writer Certificate

Keywords

Clustering

Graphical mixture models

Nonparanormal distribution

Penalized log-likelihood

Abstract

Introduction Graphical mixture models provide a powerful tool to visually depict the conditional independence relationships between high-dimensional heterogeneous data. In the study of Graphical mixture models, the distribution of the mixture components is mostly considered multivariate normal with different covariance matrices. The resulting model is the Gaussian graphical mixture model (GGMM). The nonparanormal graphical mixture model (NGMM) has been introduced by replacing the normal assumption with a semiparametric Gaussian copula, which extends the nonparanormal graphical model and mixture models. This study proposes Clustering based on NGMM under two forms of ℓ, 1 penalty functions. Its performance is compared with Clustering based on GGMM, in terms of cluster reconstruction and parameters estimation. Material and Methods The Clustering based on NGMM is performed via a penalized EM algorithm under conventional and unconventional forms of ℓ, 1 penalty functions (denoted by NGMM0 and NGMM1, respectively) and its performance over Gaussian and non-Gaussian simulated data sets are compared with the Gaussian ones (represented by GGMM0 and GGMM1, respectively). Along with the conventional ℓ, 1 penalty, an alternative, unconventional penalty term is considered, which depends on the mixture proportions. Thus, the choice of mixture model distribution (Gaussian or nonparanormal) along with the choice of penalty function has emerged as the primary key of comparison. To better compare the studied methods in terms of robustness against outliers, we considered deterministic and random contamination mechanisms. The proposed methodology is applied to Wisconsin diagnostic breast cancer data set to diagnose malignant or benign cancer patients. Results and Discussion The results of the simulation study on normal and nonparanormal datasets in ideal and noisy settings, as well as the application of breast cancer data set, showed that Clustering approaches based on NGMM (NGMM0 and NGMM1) are more efficient and robust in the recovery of true cluster assignments than the Clustering based on GGMM (GGMM0 and GGMM1), whereas, the unconventional PMLEs (GGMM1 and NGMM1) are more efficient in estimating the elements of precision matrices than the conventional PMLEs (GGMM0 and NGMM0). Conclusion The performance of Clustering methods depends on the choice of penalty function and model selection, such that the combination of the nonparanormal graphical mixture model and the penalty term depending on the mixing proportions (NGMM1) is more accurate than Gaussian ones in terms of cluster reconstruction and parameters estimation.

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APA: Copy

Haji Aghabozorgi, H., & ESKANDARI, F.. (2022). Clustering Based on Nonparanormal Graphical Mixture Models. JOURNAL OF STATISTICAL SCIENCES, 16(1 ), 63-89. SID. https://sid.ir/paper/1021438/en

Vancouver: Copy

Haji Aghabozorgi H., ESKANDARI F.. Clustering Based on Nonparanormal Graphical Mixture Models. JOURNAL OF STATISTICAL SCIENCES[Internet]. 2022;16(1 ):63-89. Available from: https://sid.ir/paper/1021438/en

IEEE: Copy

H. Haji Aghabozorgi, and F. ESKANDARI, “Clustering Based on Nonparanormal Graphical Mixture Models,” JOURNAL OF STATISTICAL SCIENCES, vol. 16, no. 1 , pp. 63–89, 2022, [Online]. Available: https://sid.ir/paper/1021438/en

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