A Comparison of Information Criteria in Clustering Based on Mixture of Multivariate Normal Distributions

Akogul, Serkan; Erişoğlu, Murat

doi:10.3390/mca21030034

Cited by 23 publications

(23 citation statements)

References 19 publications

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“…The complexity reflects the fact that for each of the K groups, ( P − J ) independent allele frequencies are estimated, so that the total number of free parameters of the model is ( K ( P − J )). We also implemented the variant of the AIC for small sample sizes, defined as (Akogul & Erisoglu, ):

{AIC}_{normalc} = - 2 L^{'} + 2 false(K (P - J) N false) / false(N - K P + K J - 1 false) false) false)

A popular alternative to AIC and AICc is the BIC (Schwarz, ), which also relies on a penalised deviance, albeit putting a stronger cost on complexity:

BIC = - 2 L^{'} + l n false(N false) false(K (P - J) false)

Finally, we also implemented the Kullback Information Criterion (KIC, Cavanaugh, ), which gave the best overall results for detecting the number of clusters from mixtures of multivariate normal distributions (Akogul & Erisoglu, ):

KIC = - 2 L^{'} + 3 false(K (P - J) + 1 false)

All these statistics have similar behaviours in that the lower values typically indicate better fits. In practice, a sharp decrease in the statistics values with increasing numbers of clusters is most likely to reveal the optimal numbers of clusters (Jombart et al., ).…”

Section: Methodsmentioning

confidence: 99%

A fast likelihood solution to the genetic clustering problem

et al. 2018

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The investigation of genetic clusters in natural populations is an ubiquitous problem in a range of fields relying on the analysis of genetic data, such as molecular ecology, conservation biology and microbiology. Typically, genetic clusters are defined as distinct panmictic populations, or parental groups in the context of hybridisation. Two types of methods have been developed for identifying such clusters: model‐based methods, which are usually computer‐intensive but yield results which can be interpreted in the light of an explicit population genetic model, and geometric approaches, which are less interpretable but remarkably faster.Here, we introduce snapclust, a fast maximum‐likelihood solution to the genetic clustering problem, which allies the advantages of both model‐based and geometric approaches. Our method relies on maximising the likelihood of a fixed number of panmictic populations, using a combination of geometric approach and fast likelihood optimisation, using the Expectation‐Maximisation (EM) algorithm. It can be used for assigning genotypes to populations and optionally identify various types of hybrids between two parental populations. Several goodness‐of‐fit statistics can also be used to guide the choice of the retained number of clusters.Using extensive simulations, we show that snapclust performs comparably to current gold standards for genetic clustering as well as hybrid detection, with some advantages for identifying hybrids after several backcrosses, while being orders of magnitude faster than other model‐based methods. We also illustrate how snapclust can be used for identifying the optimal number of clusters, and subsequently assign individuals to various hybrid classes simulated from an empirical microsatellite dataset. snapclust is implemented in the package adegenet for the free software R, and is therefore easily integrated into existing pipelines for genetic data analysis. It can be applied to any kind of co‐dominant markers, and can easily be extended to more complex models including, for instance, varying ploidy levels. Given its flexibility and computer‐efficiency, it provides a useful complement to the existing toolbox for the study of genetic diversity in natural populations.

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{AIC}_{normalc} = - 2 L^{'} + 2 false(K (P - J) N false) / false(N - K P + K J - 1 false) false) false)

A popular alternative to AIC and AICc is the BIC (Schwarz, ), which also relies on a penalised deviance, albeit putting a stronger cost on complexity:

BIC = - 2 L^{'} + l n false(N false) false(K (P - J) false)

KIC = - 2 L^{'} + 3 false(K (P - J) + 1 false)

Section: Methodsmentioning

confidence: 99%

A fast likelihood solution to the genetic clustering problem

et al. 2018

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“…The alternative having the highest C-RIV value is the optimal number of clusters for the dataset. To form the pairwise comparison matrix of the criteria, the study of Akogul and Erisoglu [53] has been used. In their study [53], the efficiency of the information criteria was examined.…”

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confidence: 99%

“…To form the pairwise comparison matrix of the criteria, the study of Akogul and Erisoglu [53] has been used. In their study [53], the efficiency of the information criteria was examined. They also analyzed real datasets that are commonly used in clustering analysis.…”

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confidence: 99%

“…Thus, the success of finding the right number of clusters in the dataset was computed for each information criterion. For all the synthetic datasets, in the corresponding study, the average of successes of the information criteria was given [53] as 43.6, 21.2, 47.4, 17.3, and 58.2 for AIC, AWE, BIC, CLC, and KIC, respectively.…”

mentioning

confidence: 99%

“…In the work of Akogul and Erisoglu [53], the effectiveness of the information criteria was determined according to the success of finding right number of clusters. In the current study, those successes have been used to determine the importance level of the criteria in the AHP model.…”

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An Approach for Determining the Number of Clusters in a Model-Based Cluster Analysis

Akogul

Erişoğlu

2017

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154

105

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Abstract:To determine the number of clusters in the clustering analysis that has a broad range of applied sciences, such as physics, chemistry, biology, engineering, economics etc., many methods have been proposed in the literature. The aim of this paper is to determine the number of clusters of a dataset in a model-based clustering by using an Analytic Hierarchy Process (AHP). In this study, the AHP model has been created by using the information criteria Akaike's Information Criterion (AIC), Approximate Weight of Evidence (AWE), Bayesian Information Criterion (BIC), Classification Likelihood Criterion (CLC), and Kullback Information Criterion (KIC). The achievement of the proposed approach has been tested on common real and synthetic datasets. The proposed approach based on the corresponding information criteria has produced accurate results. The currently produced results have been seen to be more accurate than those corresponding to the information criteria.

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Physical activity-related health competence and symptom burden for exercise prescription in patients with multiple myeloma: a latent profile analysis

et al. 2023

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The purpose of this study is to ensure best possible supply of exercise therapy to patients with multiple myeloma (MM); it is helpful to identify patient groups with similar symptom burden and physical activity–related health competences (PAHCO). Latent profile analyses (LPA) of MM patients were used to identify profiles of patients with similar PAHCO and symptom burden. Analysis of variance was applied to investigate group differences in important covariates. N = 98 MM patients (57% male, age 64 ± 9 years) could be assigned to three distinct PAHCO profiles: 46% were patients with high PAHCO, 48% patients with moderate, and 5% were patients with low PAHCO. The mean probability to be assigned to a certain profile was over 99%. The first group showed significant higher physical activity (PA) and lower comorbidities. Regarding symptom burden, three different profiles exist, including group one (32% of patients) with very low symptom burden, profile two (40%) with medium symptom burden, and group three (15%) with very high symptom burden (mean probability ≥ 98%). Patients in profile one had a lower number of treatment lines compared to the other profiles. Patients who were assigned to the high PAHCO profile were more likely to display a milder symptoms profile. In this exploratory analysis, we identified different patient profiles for PAHCO and symptom burden that may be used to individualize exercise recommendations and supervision modalities in MM patients. PAHCO and symptom burden level may be used to stratify MM patients in order to provide more personalized and effective exercise counseling. The profiles require individualized exercise recommendations and different supervision modalities, including educational instructions tailored particularly to every patient’s needs, according to their PAHCO and symptom profile. Trial registration number NCT04328038.

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A Comparison of Information Criteria in Clustering Based on Mixture of Multivariate Normal Distributions

Cited by 23 publications

References 19 publications

A fast likelihood solution to the genetic clustering problem

A fast likelihood solution to the genetic clustering problem

An Approach for Determining the Number of Clusters in a Model-Based Cluster Analysis

Physical activity-related health competence and symptom burden for exercise prescription in patients with multiple myeloma: a latent profile analysis

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