scholarly journals On determining efficient finite mixture models with compact and essential components for clustering data

2013 ◽  
Vol 14 (1) ◽  
pp. 79-88 ◽  
Author(s):  
Ahmed R. Abas
Keyword(s):  
Mixture Models ◽  
Finite Mixture Models ◽  
Finite Mixture ◽  
Essential Components ◽  
Clustering Data

scholarly journals Summarizing Finite Mixture Model with Overlapping Quantification

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1503
Author(s):  
Shunki Kyoya ◽  
Kenji Yamanishi
Keyword(s):  
Mutual Information ◽  
Mixture Models ◽  
Mixture Model ◽  
Finite Mixture Models ◽  
Finite Mixture Model ◽  
Finite Mixture ◽  
Model Based Clustering ◽  
Multiple Components ◽  
Clustering Data ◽  
Novel Concept

Finite mixture models are widely used for modeling and clustering data. When they are used for clustering, they are often interpreted by regarding each component as one cluster. However, this assumption may be invalid when the components overlap. It leads to the issue of analyzing such overlaps to correctly understand the models. The primary purpose of this paper is to establish a theoretical framework for interpreting the overlapping mixture models by estimating how they overlap, using measures of information such as entropy and mutual information. This is achieved by merging components to regard multiple components as one cluster and summarizing the merging results. First, we propose three conditions that any merging criterion should satisfy. Then, we investigate whether several existing merging criteria satisfy the conditions and modify them to fulfill more conditions. Second, we propose a novel concept named clustering summarization to evaluate the merging results. In it, we can quantify how overlapped and biased the clusters are, using mutual information-based criteria. Using artificial and real datasets, we empirically demonstrate that our methods of modifying criteria and summarizing results are effective for understanding the cluster structures. We therefore give a new view of interpretability/explainability for model-based clustering.

scholarly journals A Finite Mixture Modelling Perspective for Combining Experts’ Opinions with an Application to Quantile-Based Risk Measures

Risks ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 115
Author(s):  
Despoina Makariou ◽  
Pauline Barrieu ◽  
George Tzougas
Keyword(s):  
Decision Making ◽  
Mixture Models ◽  
Finite Mixture Models ◽  
Risk Measures ◽  
Finite Mixture ◽  
Parametric Family ◽  
Collective Decision Making ◽  
Multiple Sources ◽  
Mixture Modelling ◽  
Expert Opinions

The key purpose of this paper is to present an alternative viewpoint for combining expert opinions based on finite mixture models. Moreover, we consider that the components of the mixture are not necessarily assumed to be from the same parametric family. This approach can enable the agent to make informed decisions about the uncertain quantity of interest in a flexible manner that accounts for multiple sources of heterogeneity involved in the opinions expressed by the experts in terms of the parametric family, the parameters of each component density, and also the mixing weights. Finally, the proposed models are employed for numerically computing quantile-based risk measures in a collective decision-making context.

scholarly journals Non-local spatially varying finite mixture models for image segmentation

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Javier Juan-Albarracín ◽  
Elies Fuster-Garcia ◽  
Alfons Juan ◽  
Juan M. García-Gómez
Keyword(s):  
Image Segmentation ◽  
Mixture Models ◽  
Finite Mixture Models ◽  
Finite Mixture ◽  
Non Local ◽  
Spatially Varying

Finite Mixture Models

2013 ◽  
pp. 1296-1296
Author(s):  
Tracey Ward ◽  
Raphael Bernier ◽  
Cora Mukerji ◽  
Danielle Perszyk ◽  
James C. McPartland ◽  
...  
Keyword(s):  
Mixture Models ◽  
Finite Mixture Models ◽  
Finite Mixture
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