521 lines
29 KiB
Text
521 lines
29 KiB
Text
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\field{abstract}{Although many clustering procedures aim to construct an optimal partition of objects or, sometimes, of variables, there are other methods, called block clustering methods, which consider simultaneously the two sets and organize the data into homogeneous blocks. Recently, we have proposed a new mixture model called block mixture model which takes into account this situation. This model allows one to embed simultaneous clustering of objects and variables in a mixture approach. We have studied this probabilistic model under the classification likelihood approach and developed a new algorithm for simultaneous partitioning based on the classification EM algorithm. In this paper, we consider the block clustering problem under the maximum likelihood approach and the goal of our contribution is to estimate the parameters of this model. Unfortunately, the application of the EM algorithm for the block mixture model cannot be made directly; difficulties arise due to the dependence structure in the model and approximations are required. Using a variational approximation, we propose a generalized EM algorithm to estimate the parameters of the block mixture model and, to illustrate our approach, we study the case of binary data by using a Bernoulli block mixture.}
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\field{eventtitle}{{{IEEE Transactions}} on {{Pattern Analysis}} and {{Machine Intelligence}}}
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\field{journaltitle}{IEEE Transactions on Pattern Analysis and Machine Intelligence}
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\field{month}{4}
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\field{title}{An {{EM}} Algorithm for the Block Mixture Model}
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\field{year}{2005}
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\keyw{Approximation algorithms,Classification algorithms,Clustering algorithms,Clustering methods,Data mining,EM algorithm,Index Terms- Block mixture model,Maximum likelihood estimation,Parameter estimation,Partitioning algorithms,Self organizing feature maps,Sparse matrices,variational approximation.}
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\field{abstract}{Let a collection of networks represent interactions within several (social or ecological) systems. We pursue two objectives: identifying similarities in the topological structures that are held in common between the networks and clustering the collection into sub-collections of structurally homogeneous networks. We tackle these two questions with a probabilistic model based approach. We propose an extension of the Stochastic Block Model (SBM) adapted to the joint modeling of a collection of networks. The networks in the collection are assumed to be independent realizations of SBMs. The common connectivity structure is imposed through the equality of some parameters. The model parameters are estimated with a variational Expectation-Maximization (EM) algorithm. We derive an ad-hoc penalized likelihood criterion to select the number of blocks and to assess the adequacy of the consensus found between the structures of the different networks. This same criterion can also be used to cluster networks on the basis of their connectivity structure. It thus provides a partition of the collection into subsets of structurally homogeneous networks. The relevance of our proposition is assessed on two collections of ecological networks. First, an application to three stream food webs reveals the homogeneity of their structures and the correspondence between groups of species in different ecosystems playing equivalent ecological roles. Moreover, the joint analysis allows a finer analysis of the structure of smaller networks. Second, we cluster 67 food webs according to their connectivity structures and demonstrate that five mesoscale structures are sufficient to describe this collection.}
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\field{abstract}{The structure of a bipartite interaction network can be described by providing a clustering for each of the two types of nodes. Such clusterings are outputted by fitting a Latent Block Model (LBM) on an observed network that comes from a sampling of species interactions in the field. However, the sampling is limited and possibly uneven. This may jeopardize the fit of the LBM and then the description of the structure of the network by detecting structures which result from the sampling and not from actual underlying ecological phenomena. If the observed interaction network consists of a weighted bipartite network where the number of observed interactions between two species is available, the sampling efforts for all species can be estimated and used to correct the LBM fit. We propose to combine an observation model that accounts for sampling and an LBM for describing the structure of underlying possible ecological interactions. We develop an original inference procedure for this model, the efficiency of which is demonstrated in simulation studies. The practical interest in ecology of our model is highlighted on a large dataset of plant-pollinator network.}
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\strng{bibnamehash}{cf148152bf4f33b329bfd7d07cf74c02}
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\field{abstract}{Although many clustering procedures aim to construct an optimal partition of objects or, sometimes, of variables, there are other methods, called block clustering methods, which consider simultaneously the two sets and organize the data into homogeneous blocks. Recently, we have proposed a new mixture model called block mixture model which takes into account this situation. This model allows one to embed simultaneous clustering of objects and variables in a mixture approach. We have studied this probabilistic model under the classification likelihood approach and developed a new algorithm for simultaneous partitioning based on the classification EM algorithm. In this paper, we consider the block clustering problem under the maximum likelihood approach and the goal of our contribution is to estimate the parameters of this model. Unfortunately, the application of the EM algorithm for the block mixture model cannot be made directly; difficulties arise due to the dependence structure in the model and approximations are required. Using a variational approximation, we propose a generalized EM algorithm to estimate the parameters of the block mixture model and, to illustrate our approach, we study the case of binary data by using a Bernoulli block mixture.}
|
|
\field{eventtitle}{{{IEEE Transactions}} on {{Pattern Analysis}} and {{Machine Intelligence}}}
|
|
\field{issn}{1939-3539}
|
|
\field{journaltitle}{IEEE Transactions on Pattern Analysis and Machine Intelligence}
|
|
\field{month}{4}
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|
\field{number}{4}
|
|
\field{title}{An {{EM}} Algorithm for the Block Mixture Model}
|
|
\field{volume}{27}
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|
\field{year}{2005}
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|
\field{dateera}{ce}
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\field{pages}{643\bibrangedash 647}
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|
\range{pages}{5}
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|
\verb{doi}
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|
\verb 10.1109/TPAMI.2005.69
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|
\endverb
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\verb{file}
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\verb /home/polarolouis/Zotero/storage/6IG45HH2/govaert2005.pdf.pdf;/home/polarolouis/Zotero/storage/TL8M3XRF/Govaert et Nadif - 2005 - An EM algorithm for the block mixture model.pdf;/home/polarolouis/Zotero/storage/2Y48IB26/1401917.html
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|
\endverb
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|
\keyw{Approximation algorithms,Classification algorithms,Clustering algorithms,Clustering methods,Data mining,EM algorithm,Index Terms- Block mixture model,Maximum likelihood estimation,Parameter estimation,Partitioning algorithms,Self organizing feature maps,Sparse matrices,variational approximation.}
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|
\endentry
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\entry{chabert-liddellLearningCommonStructures2023}{online}{}{}
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\name{author}{3}{}{%
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family={Chabert-Liddell},
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family={Barbillon},
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given={Pierre},
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givenun=0}}%
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\field{abstract}{Let a collection of networks represent interactions within several (social or ecological) systems. We pursue two objectives: identifying similarities in the topological structures that are held in common between the networks and clustering the collection into sub-collections of structurally homogeneous networks. We tackle these two questions with a probabilistic model based approach. We propose an extension of the Stochastic Block Model (SBM) adapted to the joint modeling of a collection of networks. The networks in the collection are assumed to be independent realizations of SBMs. The common connectivity structure is imposed through the equality of some parameters. The model parameters are estimated with a variational Expectation-Maximization (EM) algorithm. We derive an ad-hoc penalized likelihood criterion to select the number of blocks and to assess the adequacy of the consensus found between the structures of the different networks. This same criterion can also be used to cluster networks on the basis of their connectivity structure. It thus provides a partition of the collection into subsets of structurally homogeneous networks. The relevance of our proposition is assessed on two collections of ecological networks. First, an application to three stream food webs reveals the homogeneity of their structures and the correspondence between groups of species in different ecosystems playing equivalent ecological roles. Moreover, the joint analysis allows a finer analysis of the structure of smaller networks. Second, we cluster 67 food webs according to their connectivity structures and demonstrate that five mesoscale structures are sufficient to describe this collection.}
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\field{title}{Learning Common Structures in a Collection of Networks. {{An}} Application to Food Webs}
|
|
\field{type}{article}
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\field{urlday}{22}
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\field{urlyear}{2023}
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\field{year}{2023}
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\verb{doi}
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|
\verb 10.48550/arXiv.2206.00560
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\verb{eprint}
|
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\verb 2206.00560
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\endverb
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\verb /home/polarolouis/Zotero/storage/M74TXGCF/Chabert-Liddell et al. - 2023 - Learning common structures in a collection of netw.pdf;/home/polarolouis/Zotero/storage/A35M8KNP/2206.html
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\keyw{Statistics - Applications,Statistics - Methodology}
|
|
\endentry
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|
\entry{anakokDisentanglingStructureEcological2022}{online}{}{}
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\name{author}{4}{}{%
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family={Barbillon},
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familyi={B\bibinitperiod},
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given={Pierre},
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family={Fontaine},
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family={Thebault},
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given={Elisa},
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giveni={E\bibinitperiod},
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givenun=0}}%
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\strng{namehash}{91ac6a753125108a3ce0782cad59a3d8}
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\strng{fullhash}{1f785414b676cf3eff4e0a7230f1c933}
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\strng{authorbibnamehash}{1f785414b676cf3eff4e0a7230f1c933}
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|
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|
\field{abstract}{The structure of a bipartite interaction network can be described by providing a clustering for each of the two types of nodes. Such clusterings are outputted by fitting a Latent Block Model (LBM) on an observed network that comes from a sampling of species interactions in the field. However, the sampling is limited and possibly uneven. This may jeopardize the fit of the LBM and then the description of the structure of the network by detecting structures which result from the sampling and not from actual underlying ecological phenomena. If the observed interaction network consists of a weighted bipartite network where the number of observed interactions between two species is available, the sampling efforts for all species can be estimated and used to correct the LBM fit. We propose to combine an observation model that accounts for sampling and an LBM for describing the structure of underlying possible ecological interactions. We develop an original inference procedure for this model, the efficiency of which is demonstrated in simulation studies. The practical interest in ecology of our model is highlighted on a large dataset of plant-pollinator network.}
|
|
\field{day}{29}
|
|
\field{eprintclass}{stat}
|
|
\field{eprinttype}{arxiv}
|
|
\field{langid}{english}
|
|
\field{month}{11}
|
|
\field{title}{Disentangling the Structure of Ecological Bipartite Networks from Observation Processes}
|
|
\field{urlday}{14}
|
|
\field{urlmonth}{6}
|
|
\field{urlyear}{2023}
|
|
\field{year}{2022}
|
|
\field{dateera}{ce}
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|
\field{urldateera}{ce}
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|
\verb{eprint}
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|
\verb 2211.16364
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|
\endverb
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\verb{file}
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\verb /home/polarolouis/Zotero/storage/LQ3FINZG/Anakok et al. - 2022 - Disentangling the structure of ecological bipartit.pdf
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\endverb
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\verb{urlraw}
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|
\verb{url}
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|
\verb http://arxiv.org/abs/2211.16364
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|
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|
|
\keyw{Statistics - Methodology}
|
|
\endentry
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|
\enddatalist
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\endrefsection
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|
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|
|