Toward the next generation of recommender systems: a survey of the state-of-the-art and possible extensions, IEEE Transactions on Knowledge and Data Engineering, vol.17, issue.6, pp.734-749, 2005. ,
DOI : 10.1109/TKDE.2005.99
Automatic subspace clustering of high dimensional data for data mining applications, ACM SIGMOD Record, vol.27, issue.2, pp.94-105, 1998. ,
DOI : 10.1145/276305.276314
WWW 2011 invited tutorial overview, Proceedings of the 20th international conference companion on World wide web, WWW '11, pp.281-282, 2011. ,
DOI : 10.1145/1963192.1963311
PIZZUTI : Fast outlier detection in high dimensional spaces, pp.15-26, 2002. ,
Optics : Ordering points to identify the clustering structure, SIGMOD 1999 Proceedings ACM SIGMOD International Conference on Management of Data, pp.49-60, 1999. ,
VASSILVITSKII : k-means++ : the advantages of careful seeding, Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp.1027-1035, 2007. ,
Fast aggregation of student mixture m els, European Signal Processing Conference, pp.312-216, 2009. ,
A Decentralized and Robust Approach to Estimating a Probabilistic Mixture Model for Structuring Distributed Data, 2011 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology, pp.372-379, 2011. ,
DOI : 10.1109/WI-IAT.2011.46
URL : https://hal.archives-ouvertes.fr/hal-00595300
A Decentralized Technique for Robust Probabilistic Mixture Modelling of a Distributed Data Set, Intelligent Distributed Computing V -Proceedings of the 5th International Symposium on Intelligent Distributed Computing, pp.271-276, 2011. ,
DOI : 10.1007/978-3-642-24013-3_29
A clustering technique for summarizing multivariate data, Behavioral Science, vol.27, issue.2, pp.153-155, 1967. ,
DOI : 10.1002/bs.3830120210
A Survey of Clustering Data Mining Techniques, Grouping Multidimensional Data, pp.25-71, 2006. ,
DOI : 10.1007/3-540-28349-8_2
SRIVASTAVA : A local scalable distributed expectation maximization algorithm for large peer-to-peer networks, The Ninth IEEE International Conference on Data Mining, pp.31-40, 2009. ,
Handling dynamics in gossip-based aggregation schemes, 2009 IEEE Symposium on Computers and Communications, pp.380-385, 2009. ,
DOI : 10.1109/ISCC.2009.5202291
In-Network Outlier Detection in Wireless Sensor Networks, 26th IEEE International Conference on Distributed Computing Systems (ICDCS'06), pp.51-59, 2006. ,
DOI : 10.1109/ICDCS.2006.49
Lof : Identifying density-based local outliers, Proceedings of the 2000 ACM SIGMOD International Conference on Management of Data, pp.93-104, 2000. ,
Aggregation of Probabilistic PCA Mixtures with a Variational-Bayes Technique Over Parameters, 2010 20th International Conference on Pattern Recognition, pp.702-705, 2010. ,
DOI : 10.1109/ICPR.2010.177
URL : https://hal.archives-ouvertes.fr/hal-00471313
Parsimonious reduction of Gaussian mixture models with a variational-Bayes approach, Pattern Recognition, vol.43, issue.3, pp.850-858, 2010. ,
DOI : 10.1016/j.patcog.2009.08.006
URL : https://hal.archives-ouvertes.fr/hal-00414325
Blobworld: image segmentation using expectation-maximization and its application to image querying, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, issue.8, pp.1026-1038, 1999. ,
DOI : 10.1109/TPAMI.2002.1023800
A classification EM algorithm for clustering and two stochastic versions, Computational Statistics & Data Analysis, vol.14, issue.3, pp.315-332, 1992. ,
DOI : 10.1016/0167-9473(92)90042-E
URL : https://hal.archives-ouvertes.fr/inria-00075196
Outlier detection : A survey, Rap. tech, 2007. ,
Approximate Distributed K-Means Clustering over a Peer-to-Peer Network, IEEE Transactions on Knowledge and Data Engineering, vol.21, issue.10, pp.1372-1388, 2009. ,
DOI : 10.1109/TKDE.2008.222
On generalizing the noise clustering algorithms, Proceedings of the 7th International Fuzzy Systems Association World Congress, pp.205-210, 1997. ,
Characterization and detection of noise in clustering, Pattern Recognition Letters, vol.12, issue.11, pp.657-664, 1991. ,
DOI : 10.1016/0167-8655(91)90002-4
Robust clustering methods: a unified view, IEEE Transactions on Fuzzy Systems, vol.5, issue.2, pp.270-293, 1997. ,
DOI : 10.1109/91.580801
ANGRYK : Distributed hierarchical document clustering, IASTED International Conference on Advances in Computer Science and Technology, pp.328-333, 2006. ,
RUBIN : Maximum likelihood from incomplete data via the em algorithm, Journal of the Royal Statistical Society. Series B (Methodological), vol.39, issue.1, pp.1-38, 1977. ,
MODHA : A data-clustering algorithm on distributed memory multiprocessors, Large-Scale Parallel Data Mining, pp.245-260, 2000. ,
Classifying documents by distributed p2p clustering, INFORMATIK 2003 -Innovative Informatikanwendungen Beiträge der 33. Jahrestagung der Gesellschaft für Informatik, pp.286-291, 2003. ,
A Geometric Framework for Unsupervised Anomaly Detection, Applications of Data Mining in Computer Security, pp.77-102, 2002. ,
DOI : 10.1007/978-1-4615-0953-0_4
A Density-Based algorithm for discovering clusters in large spatial databases with noise, Second International Conference on Knowledge Discovery and Data Mining, pp.226-231, 1996. ,
Fuzzy Shell Cluster Analysis, Learning, Networks and Statistics, pp.105-120, 1997. ,
DOI : 10.1007/978-3-7091-2668-4_7
A generic theoretical framework for modeling gossip-based algorithms, ACM SIGOPS Operating Systems Review, vol.41, issue.5, pp.19-27, 2007. ,
DOI : 10.1145/1317379.1317384
GIANNAKIS : Consensus-based distributed expectationmaximization algorithm for density estimation and classification using wireless sensor networks, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, pp.1989-1992, 2008. ,
Connaissances et clustering collaboratif d'objets complexes multisources, Thèse de doctorat, 2010. ,
Distributed data clustering can be efficient and exact, ACM SIGKDD Explorations Newsletter, vol.2, issue.2, pp.34-38, 2000. ,
DOI : 10.1145/380995.381010
How Many Clusters? Which Clustering Method? Answers Via Model-Based Cluster Analysis, The Computer Journal, vol.41, issue.8, pp.41578-588, 1998. ,
DOI : 10.1093/comjnl/41.8.578
Minimum volume ellipsoid, Wiley Interdisciplinary Reviews : Computational Statistics, vol.1, issue.1, pp.71-82, 2009. ,
Combining Multiple Clusterings Using Evidence Accumulation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.27, issue.6, pp.835-850, 2005. ,
DOI : 10.1109/TPAMI.2005.113
A general trimming approach to robust cluster analysis. The Annals of Statistics, pp.1324-1345, 2008. ,
Simplification and hierarchical representations of mixtures of exponential families, Signal Processing, vol.90, issue.12, pp.3197-3212, 2010. ,
DOI : 10.1016/j.sigpro.2010.05.024
Hierarchical Gaussian mixture model, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.4070-4073, 2010. ,
DOI : 10.1109/ICASSP.2010.5495750
A review of robust clustering methods, Advances in Data Analysis and Classification, vol.47, issue.Suppl 7, pp.89-109, 2010. ,
DOI : 10.1007/s11634-010-0064-5
An efficient image similarity measure based on approximations of KL-divergence between two gaussian mixtures, Proceedings Ninth IEEE International Conference on Computer Vision, pp.487-493, 2003. ,
DOI : 10.1109/ICCV.2003.1238387
Simplifying mixture models using the unscented transform. Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.30, issue.8, pp.1496-1502, 2008. ,
Hierarchical clustering of a mixture model, Advances in Neural Information Processing Systems 17, pp.505-512, 2005. ,
Unsupervised and semi-supervised clustering : a brief survey. A Review of Machine Learning Techniques for Processing Multimedia Content, 2004. ,
Distributed EM Algorithm for Gaussian Mixtures in Sensor Networks, IEEE Transactions on Neural Networks, vol.19, issue.7, pp.1154-1166, 2008. ,
DOI : 10.1109/TNN.2007.915110
Cure : An efficient clustering algorithm for large databases, SIGMOD 1998 Proceedings ACM SIGMOD International Conference on Management of Data, pp.73-84, 1998. ,
Rock: A robust clustering algorithm for categorical attributes, Information Systems, vol.25, issue.5, pp.345-366, 2000. ,
DOI : 10.1016/S0306-4379(00)00022-3
A New Efficient Hierarchical Distributed P2P Clustering Algorithm, 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery, pp.352-355, 2008. ,
DOI : 10.1109/FSKD.2008.280
Semantic Wiki Search, The Semantic Web : Research and Applications, 6th European Semantic Web Conference, pp.445-460, 2009. ,
DOI : 10.1007/978-3-642-02121-3_34
Collaborative Document Clustering, Proceedings of the Sixth SIAM International Conference on Data Mining, pp.453-463, 2006. ,
DOI : 10.1137/1.9781611972764.40
Hierarchically distributed peer-to-peer document clustering and cluster summarization. Knowledge and Data Engineering, IEEE Transactions on, vol.21, issue.5, pp.681-698, 2009. ,
Outlier detection in the multiple cluster setting using the minimum covariance determinant estimator, Computational Statistics & Data Analysis, vol.44, issue.4, pp.625-638, 2004. ,
DOI : 10.1016/S0167-9473(02)00280-3
Discovering cluster-based local outliers, Pattern Recognition Letters, vol.24, issue.9-10, pp.1641-1650, 2003. ,
DOI : 10.1016/S0167-8655(03)00003-5
Approximating the Kullback Leibler Divergence Between Gaussian Mixture Models, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07, pp.317-320, 2007. ,
DOI : 10.1109/ICASSP.2007.366913
An efficient approach to clustering in large multimedia databases with noise, Proceedings of 4th International Conference in Knowledge Discovery and Data Mining, pp.58-65, 1998. ,
A Survey of Outlier Detection Methodologies, Artificial Intelligence Review, vol.22, issue.2, pp.85-126, 2004. ,
DOI : 10.1023/B:AIRE.0000045502.10941.a9
Extensions to the k-means algorithm for clustering large data sets with categorical values, Data Mining and Knowledge Discovery, vol.2, issue.3, pp.283-304, 1998. ,
DOI : 10.1023/A:1009769707641
Data clustering: 50 years beyond K-means, Pattern Recognition Letters, vol.31, issue.8, pp.31651-666, 2010. ,
DOI : 10.1016/j.patrec.2009.09.011
Data clustering: a review, ACM Computing Surveys, vol.31, issue.3, pp.31264-323, 1999. ,
DOI : 10.1145/331499.331504
DBDC: Density Based Distributed Clustering, Advances in Database Technology EDBT, pp.88-105, 2004. ,
DOI : 10.1007/978-3-540-24741-8_7
BABAOGLU : T-man : Gossip-based overlay topology management, Engineering Self-Organising Systems, Third International Workshop, pp.1-15, 2005. ,
Gossip-based aggregation in large dynamic networks, ACM Transactions on Computer Systems, vol.23, issue.3, pp.219-2521, 2005. ,
DOI : 10.1145/1082469.1082470
KARGUPTA : Collective, hierarchical clustering from distributed, heterogeneous data, Large-Scale Parallel Data Mining, Workshop on Large-Scale Parallel KDD Systems, pp.221-244, 2000. ,
UHLMANN : A general method for approximating nonlinear transformations of probability distributions, Rap. tech, 1996. ,
Distributed Clustering Using Collective Principal Component Analysis, Knowledge and Information Systems, vol.3, issue.4, pp.422-448, 2001. ,
DOI : 10.1007/PL00011677
Chameleon: hierarchical clustering using dynamic modeling, Computer, vol.32, issue.8, pp.68-75, 1999. ,
DOI : 10.1109/2.781637
Cooperative Clustering Model and Its Applications, Thèse de doctorat, 2008. ,
Efficient gossipbased aggregate computation, Proceedings of the Twenty-Fifth ACM SIGACT-SIGMOD- SIGART Symposium on Principles of Database Systems, pp.308-317, 2006. ,
Gossiping in distributed systems, ACM SIGOPS Operating Systems Review, vol.41, issue.5, pp.2-7, 2007. ,
DOI : 10.1145/1317379.1317381
TUCAKOV : Distance-Based outliers : Algorithms and applications, VLDB Journal : Very Large Data Bases, pp.237-253, 2000. ,
VLASSIS : Newscast em, Advances in Neural Information Processing Systems 17, pp.713-720, 2005. ,
Ml estimation of the t distribution using em and its extensions, ecm and ecme, Statistica Sinica, vol.5, issue.1, pp.19-39, 1995. ,
Minimum covariance determinant, Wiley Interdisciplinary Reviews: Computational Statistics, vol.20, issue.1, pp.36-43, 2010. ,
DOI : 10.1002/wics.61
Privacy-preserving distributed clustering using generative models, Third IEEE International Conference on Data Mining, pp.211-218, 2003. ,
DOI : 10.1109/ICDM.2003.1250922
De-ransac : Robust distributed consensus in sensor networks, IEEE Transactions on Systems, Man, and Cybernetics : part B, 2010. ,
Intelligent Gossip, Intelligent Distributed Computing, Systems and Applications , Proceedings of the 2nd International Symposium on Intelligent Distributed Computing, pp.3-10, 2008. ,
DOI : 10.1007/978-3-540-85257-5_1
A View of the Em Algorithm that Justifies Incremental, Sparse, and other Variants, Proceedings of the NATO Advanced Study Institute on Learning in graphical models, pp.355-368, 1998. ,
DOI : 10.1007/978-94-011-5014-9_12
Clarans : A method for clustering objects for spatial data mining. Knowledge and Data Engineering, IEEE Transactions on, vol.14, issue.5, pp.1003-1016, 2002. ,
Robust estimation in gaussian mixtures using multiresolution kd-trees, Proceedings of the Seventh International Conference on Digital Image Computing : Techniques and Applications, pp.145-154, 2003. ,
Gaussian mixture models via entropic quantization, European Signal Processing Conference, pp.2012-2016, 2009. ,
Sided and symmetrized bregman centroids. Information Theory, IEEE Transactions on, vol.55, issue.6, pp.2882-2904, 2009. ,
Distributed EM algorithms for density estimation and clustering in sensor networks, IEEE Transactions on Signal Processing, vol.51, issue.8, pp.2245-2253, 2003. ,
DOI : 10.1109/TSP.2003.814623
A kernel-based approach for detecting outliers of high-dimensional biological data, BMC Bioinformatics, vol.10, issue.Suppl 4, 2009. ,
DOI : 10.1186/1471-2105-10-S4-S7
An efficient integrated gender detection scheme and time mediated averaging of gender dependent acoustic models, 8th European Conference on Speech Communication and Technology, pp.2509-2512, 2003. ,
Distributed deviation detection in sensor networks, ACM SIGMOD Record, vol.32, issue.4, pp.77-82, 2003. ,
DOI : 10.1145/959060.959074
ABBADI : Distributed average consensus with stochastic communication failures, Proceedings of the 46th IEEE Conference on Decision and Control, pp.490-495, 2007. ,
Robust mixture modelling using the t distribution, Statistics and Computing, vol.10, issue.4, pp.339-348, 2000. ,
DOI : 10.1023/A:1008981510081
Structuration géo-temporelle de données multimédia personnelles en vue de la navigation sur un appareil mobile, Thèse de doctorat, 2005. ,
Quarter Sphere Based Distributed Anomaly Detection in Wireless Sensor Networks, 2007 IEEE International Conference on Communications, pp.3864-3869, 2007. ,
DOI : 10.1109/ICC.2007.637
A survey on clustering current status and challenging issues, International Journal on Computer Science and Engineering, vol.2, issue.9, pp.2976-2980 ,
Efficient algorithms for mining outliers from large data sets, Proceedings of the ACM SIGMOD International Conference on Management of Data, pp.427-438, 2000. ,
Speaker Verification Using Adapted Gaussian Mixture Models, Digital Signal Processing, vol.10, issue.1-3, pp.19-41, 2000. ,
DOI : 10.1006/dspr.1999.0361
Using Finite Mixtures to Robustify Statistical Models, Thèse de doctorat, 2011. ,
A Fast Algorithm for the Minimum Covariance Determinant Estimator, Technometrics, vol.35, issue.3, pp.212-223, 1999. ,
DOI : 10.1080/01621459.1994.10476821
Robust statistics for outlier detection, Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, vol.75, issue.1, pp.73-79, 2011. ,
DOI : 10.1002/widm.2
Kullback-Leibler Approach to Gaussian Mixture Reduction, IEEE Transactions on Aerospace and Electronic Systems, vol.43, issue.3, pp.989-999, 2007. ,
DOI : 10.1109/TAES.2007.4383588
Rachet : An efficient cover-based merging of clustering hierarchies from distributed datasets. Distributed and Parallel Databases NAKAMORI : An alternative extension of the k-means algorithm for clustering categorical data, International Journal of Applied Mathematics and Computer Science, vol.11, issue.142, pp.157-180241, 2002. ,
Density-based clustering in spatial databases : The algorithm gdbscan and its applications, Data Mining and Knowledge Discovery, vol.2, issue.2, pp.169-194, 1998. ,
DOI : 10.1023/A:1009745219419
Estimating the Dimension of a Model, The Annals of Statistics, vol.6, issue.2, pp.461-464, 1978. ,
DOI : 10.1214/aos/1176344136
A Robust and Secure Aggregation Protocol for Wireless Sensor Networks, 2011 Sixth IEEE International Symposium on Electronic Design, Test and Application, pp.222-227, 2011. ,
DOI : 10.1109/DELTA.2011.59
Cluster ensembles ? a knowledge reuse framework for combining multiple partitions, Journal of Machine Learning Research, vol.3, issue.3, pp.583-617, 2002. ,
HADJICOSTIS : Distributed function calculation via linear iterations in the presence of malicious agents -part ii : Overcoming malicious behavior, American Control Conference, pp.1357-1362, 2008. ,
Enhancing Effectiveness of Outlier Detections for Low Density Patterns, Advances in Knowledge Discovery and Data Mining, pp.535-548, 2002. ,
DOI : 10.1007/3-540-47887-6_53
Split and merge EM algorithm for improving Gaussian mixture density estimates, Neural Networks for Signal Processing VIII. Proceedings of the 1998 IEEE Signal Processing Society Workshop (Cat. No.98TH8378), pp.133-140, 2000. ,
DOI : 10.1109/NNSP.1998.710657
-means clustering over vertically partitioned data, Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining , KDD '03, pp.206-215, 2003. ,
DOI : 10.1145/956750.956776
URL : https://hal.archives-ouvertes.fr/hal-01056666
A new partitioning around medoids algorithm, Journal of Statistical Computation and Simulation, vol.73, issue.8, pp.575-584, 2003. ,
DOI : 10.1080/0094965031000136012
Image indexing with mixture hierarchies, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001, pp.3-10, 2001. ,
DOI : 10.1109/CVPR.2001.990449
Gossip-Based Greedy Gaussian Mixture Learning, Proceedings of the 10th Panhellenic conference on Advances in Informatics, pp.349-359, 2005. ,
DOI : 10.1007/11573036_33
CYCLON: Inexpensive Membership Management for Unstructured P2P Overlays, Journal of Network and Systems Management, vol.21, issue.6, pp.197-217, 2005. ,
DOI : 10.1007/s10922-005-4441-x
A Robust and Scalable Peer-to-Peer Gossiping Protocol, 2nd International Workshop Agents and Peer-toPeer Computing, pp.47-58, 2003. ,
DOI : 10.1007/978-3-540-25840-7_6
Proactive gossip-based management of semantic overlay networks, Concurrency and Computation: Practice and Experience, vol.13, issue.17, pp.2299-2311, 2007. ,
DOI : 10.1002/cpe.1225
Fully distributed EM for very large datasets, Proceedings of the 25th international conference on Machine learning, ICML '08, pp.1184-1191, 2008. ,
DOI : 10.1145/1390156.1390305
Distributed average consensus with least-mean-square deviation, Journal of Parallel and Distributed Computing, vol.67, issue.1, pp.33-46, 2007. ,
DOI : 10.1016/j.jpdc.2006.08.010
Survey of Clustering Algorithms, IEEE Transactions on Neural Networks, vol.16, issue.3, pp.645-678, 2005. ,
DOI : 10.1109/TNN.2005.845141
A distribution-based clustering algorithm for mining in large spatial databases, Proceedings of the Fourteenth International Conference on Data Engineering, pp.324-331, 1998. ,
KRIEGEL : A fast parallel clustering algorithm for large spatial databases, Data Mining and Knowledge Discovery, vol.3, issue.3, pp.263-290, 1999. ,
DOI : 10.1023/A:1009884809343
Diffusion-Based EM Algorithm for Distributed Estimation of Gaussian Mixtures in Wireless Sensor Networks, Sensors, vol.11, issue.12, pp.6297-6316, 2011. ,
DOI : 10.3390/s110606297
Accurate Recasting of Parameter Estimation Algorithms Using Sufficient Statistics for Efficient Parallel Speed-Up, 4th European Conference on Principles and Practices of Knowledge Discovery in Databases, pp.243-254, 2000. ,
DOI : 10.1007/3-540-45372-5_24
Unsupervised Outlier Detection in Sensor Networks Using Aggregation Tree, Advanced Data Mining and Applications, Third International Conference, pp.158-169, 2007. ,
DOI : 10.1007/978-3-540-73871-8_16
Birch : An efficient data clustering method for very large databases, Proceedings of the ACM SIGMOD International Conference on Management of Data, pp.103-114, 1996. ,
Outlier Detection Techniques for Wireless Sensor Networks: A Survey, IEEE Communications Surveys & Tutorials, vol.12, issue.2, pp.159-170, 2010. ,
DOI : 10.1109/SURV.2010.021510.00088
HAVINGA : A taxonomy framework for unsupervised outlier detection techniques for multi-type data sets, Rap. tech, 2007. ,
EM algorithms for Gaussian mixtures with split-and-merge operation, Pattern Recognition, vol.36, issue.9, pp.1973-1983, 2003. ,
DOI : 10.1016/S0031-3203(03)00059-1
A Novel Outlier Detection Algorithm for Distributed Databases, 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery, pp.293-297, 2008. ,
DOI : 10.1109/FSKD.2008.422
A decentralized and robust approach to estimating a probabilistic mixture model for structuring distributed data. (soumis à la revue internationale Web Intelligence and Agent Systems, sur invitation, version étendue d'une sélection d'articles du congrès IEEE, Liste des publications Revues internationales, pp.22-27, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00595300
Fast aggregation of student mixture models, European Signal Processing Conference, pp.312-216, 2009. ,
A Decentralized and Robust Approach to Estimating a Probabilistic Mixture Model for Structuring Distributed Data, 2011 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology, pp.22-27, 2011. ,
DOI : 10.1109/WI-IAT.2011.46
URL : https://hal.archives-ouvertes.fr/hal-00595300
A Decentralized Technique for Robust Probabilistic Mixture Modelling of a Distributed Data Set, Intelligent Distributed Computing V -Proceedings of the 5th International Symposium on Intelligent Distributed Computing, 2011. ,
DOI : 10.1007/978-3-642-24013-3_29
Les ellipses continues et pointillées représentent respectivement les modèles de f et g La figure (a) montre la première étape de l'algorithme où les divergences entre les composantes de f et g sont calculées. La meilleure correspondance obtenue m, consiste à associer, par exemple, l'ensemble {f 1 , f 2 , f 3 } à g 1 et les composantes restantes à g 2 . La figure (b) présente les mises à jour des paramètres de modèle réduit g en se basant sur la fonction de correspondance m, et en, p.50 ,
Les ellipses continues et pointillées représentent respectivement les modèles de f et g. La figure (a) contient les composantes originales de distribution de Student Dans la figure (b), chaque composante Student est approximée par un mélange de gaussiennes de P = 3 composantes. L'optimisation du critère de match bound consiste à chercher la meilleure fonction de correspondance m entre les composantes de f et g, d'une façon à minimiser la sommation de la divergence de KL, Ici, les flèches montrent la fonction de correspondance m obtenue implicitement par la méthode match bound entre les ,
après avoir lié les composantes f i avec les composantes g i selon m. La figure (c) représente la mise à jour de composantes du modèle réduit g. Les paramètres du modèle g sont calculés à partir de ceux du modèle f selon la fonction m, p.54 ,
Elle illustre aussi les données générées à partir de chaque composante f i de f . Les ellipses uniques sont les composantes f i de f , et les ellipses multiples sont les composantes g j de g, p.58 ,
Elle montre bien le changement de topologie après l'application du protocole de cyclon (une implémentation de PSS) sur le noeud 2. Le noeud 2 après avoir choisi aléatoirement son voisin 9, il lui envoie la liste {2, 0, 6} et il reçoit également un autre ensemble {0, 5, 7}. Puis les deux noeuds mettent à jour leurs listes de voisins, p.79 ,
abord, des modèles de mélange sont estimés localement sur chaque site. Puis, ces modèles sont échangés et agrégés avec les modèles voisins, en utilisant un protocole de communication gossip. Notre méthode inclut une étape de détection et d'élimination des modèles non fiables dans le processus d'agrégation ,
Les ellipses en pointillé sur chaque noeud représentent les modèles correspondants Le noeud (1) possède ici une liste de 6 voisins. Nous allons voir après, comment est obtenu le modèle global sur cet exemple, p.86 ,
Pour chaque échantillon, un algorithme itératif est appliqué pour améliorer sa qualité, en éliminant les modèles non fiables. Cet algorithme consiste à comparer la similarité entre les modèles M j ? M voisin et ceux dans S t . Puis les modèles M j les plus proches sont sélectionnés pour former à nouveau l'échantillon S t . La convergence est réalisée lorsque tous les échantillons deviennent stables, p.91 ,