Summarizing Finite Mixture Model with Overlapping Quantification

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 c...

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Autores principales:	Shunki Kyoya, Kenji Yamanishi
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	model-based clustering merging mixture components component overlap interpretability Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/0f3d687cacf84dcba36b1732b8a41ab5
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id	oai:doaj.org-article:0f3d687cacf84dcba36b1732b8a41ab5
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spelling	oai:doaj.org-article:0f3d687cacf84dcba36b1732b8a41ab52021-11-25T17:30:18ZSummarizing Finite Mixture Model with Overlapping Quantification10.3390/e231115031099-4300https://doaj.org/article/0f3d687cacf84dcba36b1732b8a41ab52021-11-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1503https://doaj.org/toc/1099-4300Finite 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.Shunki KyoyaKenji YamanishiMDPI AGarticlemodel-based clusteringmerging mixture componentscomponent overlapinterpretabilityScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1503, p 1503 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	model-based clustering merging mixture components component overlap interpretability Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	model-based clustering merging mixture components component overlap interpretability Science Q Astrophysics QB460-466 Physics QC1-999 Shunki Kyoya Kenji Yamanishi Summarizing Finite Mixture Model with Overlapping Quantification
description	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.
format	article
author	Shunki Kyoya Kenji Yamanishi
author_facet	Shunki Kyoya Kenji Yamanishi
author_sort	Shunki Kyoya
title	Summarizing Finite Mixture Model with Overlapping Quantification
title_short	Summarizing Finite Mixture Model with Overlapping Quantification
title_full	Summarizing Finite Mixture Model with Overlapping Quantification
title_fullStr	Summarizing Finite Mixture Model with Overlapping Quantification
title_full_unstemmed	Summarizing Finite Mixture Model with Overlapping Quantification
title_sort	summarizing finite mixture model with overlapping quantification
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/0f3d687cacf84dcba36b1732b8a41ab5
work_keys_str_mv	AT shunkikyoya summarizingfinitemixturemodelwithoverlappingquantification AT kenjiyamanishi summarizingfinitemixturemodelwithoverlappingquantification
_version_	1718412269232062464

Summarizing Finite Mixture Model with Overlapping Quantification

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