W. P. Bouberima, M. Nadif, and Y. K. Bencheikh, Clustering Using EM and CEM , Cluster Number Selection Via the Von Mises-Fisher Mixture Models, International Journal of Open Problems in Computer Science and Mathematics, vol.6, issue.1, 2013.
DOI : 10.12816/0006153

W. P. Bouberima, Y. K. Bencheikh, and M. Nadif, Different variants of Normalized EM Algorithm for Gene Expression Data. The 2nd International Workshop on Biological Knowledge Discovery and Data Mining -DEXA '11, pp.1-2
URL : https://hal.archives-ouvertes.fr/hal-00740344

W. P. Bouberima, M. Nadif, and Y. K. Bencheikh, Choice of the model and the number of components in von Mises-Fisher mixtures, The 3 rd International Conference of the ERCIM (European Research Consortium for Informatics and Mathematics)

W. P. Bouberima, M. Nadif, and Y. K. Bencheikh, Assessing the Number of Clusters From a Mixture of Von Mises-Fisher Volume : 2185 ; Issue : 1, p, Journal : Lecture Notes in Engineering and Computer Science, pp.30-32, 2006.

W. P. Bouberima, M. Nadif, and Y. K. Bencheikh, Classification de données directionnelles .Seizì emes rencontres de la Société francophone de classification (poster), pp.2-4, 2009.

W. Bouberima, M. Nadif, and Y. K. Bencheikh, Etude Comparative entre les k-means axiales et le k-means sphérique sur des données textuelles, Journées de statistique M. Abramowitz et I. A. Stegun : Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 1972.

H. Akaike, Information theory and an extension of maximum likelihood principle, Second International Symposium on Information Theory, pp.267-281, 1973.

K. J. Arnold, On spherical probability distributions, dissertation. Rapport technique, Massachusetts Institute of technology, 1941.

F. Ball and P. Blackwell, A finite form for the wrapped poisson distribution Adv

G. H. Ball and D. J. Hall, Isodata a novel method of data analysis and pattern classification . Rapport technique, standford research institute, menbo park calif, 1965.

G. H. Ball and D. J. Hall, A clustering technique for summarizing multivariate data, Behavioral Science, vol.27, issue.2, pp.153-155, 1967.
DOI : 10.1002/bs.3830120210

A. Banerjee, I. S. Dhillon, J. Ghosh, and S. Sra, Clustering on the unit hypersphere using von mises-fisher distributions, The Journal of Machine Learning Research, vol.6, pp.1345-1382, 2005.

J. D. Banfield and A. E. Raftery, Model-Based Gaussian and Non-Gaussian Clustering, Biometrics, vol.49, issue.3, pp.803-821, 1993.
DOI : 10.2307/2532201

E. Batschelet, Circular statistics in biology, 1981.

R. J. Beran, Exponential Models for Directional Data, The Annals of Statistics, vol.7, issue.6, pp.1162-1178, 1979.
DOI : 10.1214/aos/1176344838

A. Berlinet and . Ch, Parabolic acceleration of the EM algorithm, Statistics and Computing, vol.11, issue.442, pp.35-47, 2009.
DOI : 10.1007/s11222-008-9067-x

D. T. Best and N. I. Fisher, Efficient Simulation of the von Mises Distribution, Applied Statistics, vol.28, issue.2, pp.152-157, 1979.
DOI : 10.2307/2346732

C. Biernacki, Choix de modèles en classification, Thése de doctorat, 1997.

C. Biernacki, G. Celeux, and G. Govaert, Assessing a mixture model for clustering with the integrated completed likelihood, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.22, issue.7, pp.719-725, 2000.
DOI : 10.1109/34.865189

C. Bingham and K. V. Mardia, A small circle distribution on the sphere, Biometrika, vol.65, issue.2, pp.379-389, 1978.
DOI : 10.1093/biomet/65.2.379

A. Blake and C. Marinos, Shape from texture, Artificial Intelligence, vol.45, issue.3, pp.323-380, 1990.
DOI : 10.1016/0004-3702(90)90011-N

W. P. Bouberima, Y. K. Bencheikh, and M. Nadif, Different Variants of Normalized EM Algorithm for Gene Expression Data, 2011 22nd International Workshop on Database and Expert Systems Applications, pp.418-422, 2011.
DOI : 10.1109/DEXA.2011.26
URL : https://hal.archives-ouvertes.fr/hal-00740344

B. Boulerice and G. R. Ducharme, Decentred directional data, Ann. Inst. Statist. Math, vol.46, pp.573-586, 1994.

H. Bozdogan, Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions, Psychometrika, vol.10, issue.2, pp.345-370, 1987.
DOI : 10.1007/BF02294361

H. Bozdogan, Mixture-model cluster analysis using model selection criteria and a new information measure of complexity, Proceedings of the first US/Japan conference on the Frontiers of Statistical Modeling : An Informational Approach, pp.69-113, 1994.

M. Broniatowski, G. Celeux, and J. Diebolt, Reconnaissance de mélanges de densités par un algorithme d'apprentissage probabiliste, Diday E. et al., Data analysis and Informatics, 1983.

K. Bubna and C. V. Stewart, Model Selection Techniques and Merging Rules for Range Data Segmentation Algorithms, Computer Vision and Image Understanding, vol.80, issue.2, pp.215-245, 2000.
DOI : 10.1006/cviu.2000.0871

K. P. Burnham and D. R. , Anderson : Model Selection and Multimodel Inference : A Practical Information-Theoretic Approach, 2002.

G. Celeux, Classification et modéles, pp.43-58, 1988.

G. Celeux and D. Chauveau, Diebolt : A stochastic approximation type em algorithm for the mixture problem, Research report, 1991.

G. Celeux, D. Chauveau, and J. Diebolt, On stochastique version of th em algorithm, Research report, 1995.

G. Celeux, Diebolt : A probabilistic teacher algorithm for iterative maximum likelihood estimation. In Classification and Related Methods of Data Analysis, 1987.

G. Celeux and J. , Diebolt : L'algorithme sem : un algorithme d'apprentissage probabiliste pour la reconnaissance de mélange de densités, pp.35-52, 1986.

G. Celeux and J. Diebolt, A simulated annealing type em algorithm, Research report, 1989.

G. Celeux and J. Diebolt, A stochastic approximation type em algorithme for the mixture problem, Computational Statistics & Data Analysis -Special issue on optimization, vol.41, issue.12, pp.119-134, 1992.

G. Celeux and G. Govaert, 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

Y. Chikuse, Statistics on Special Manifolds, 2003.
DOI : 10.1007/978-0-387-21540-2

N. E. Day, Estimating the components of a mixture of normal distributions, Biometrika, vol.56, issue.3, pp.464-474, 1969.
DOI : 10.1093/biomet/56.3.463

S. Dégerine, Lois de von mises et lois liées, Ann. Inst. Henri Poincaré-Probab. Stat, vol.15, pp.63-77, 1979.

B. Delyon, M. Lavielle, and E. Moulines, Convergence of a stochastic approximation version of the em algorithm. The Annals of Statistics, pp.94-122, 1999.

A. P. Dempster, N. M. Laird, and D. B. , Rubin : Maximum likelihood from incomplete data via the em algorithm, Journal of the Royal Statistical Society, Series B, vol.39, pp.1-38, 1977.

I. Dhillon, I. S. Dhillon, Y. Guan, and J. Kogan, Iterative clustering of high dimensional text data augmented by local search, 2002 IEEE International Conference on Data Mining, 2002. Proceedings., pp.131-138, 2002.
DOI : 10.1109/ICDM.2002.1183895

I. S. Dhillon and D. S. Modha, Concept decompositions for large sparse text data using clustering, Machine Learning, pp.143-175, 2001.

I. S. Dhillon and S. , Sra : Modeling data using directional distributions, Utcs technical report, 2003.

I. S. Dhillon and J. Fan, Guan : Data mining for scientific and engineering applications, 2001.

E. Diday, Nouvelles méthodes et nouveaux concepts en classification automatique et reconnaissance des formes, Thèse d'´ etat université Paris 6, 1972.

E. Diday, Optimisation en classification automatique, INRIA, 1979.

J. L. Dortet-bernadet and N. , Model-based clustering on the unit sphere with an illustration using gene expression profiles, Biostatistics, vol.9, issue.1, pp.66-80, 2007.
DOI : 10.1093/biostatistics/kxm012
URL : https://hal.archives-ouvertes.fr/hal-00264414

T. D. Downs and J. Liebman, Statistical Methods for Vectorcardiographic Directions, IEEE Transactions on Biomedical Engineering, vol.16, issue.1
DOI : 10.1109/TBME.1969.4502609

S. T. Dumais and H. Chen, Hierarchical classification of Web content, Proceedings of the 23rd annual international ACM SIGIR conference on Research and development in information retrieval , SIGIR '00, p.0
DOI : 10.1145/345508.345593

J. Dunn, Well-Separated Clusters and Optimal Fuzzy Partitions, Journal of Cybernetics, vol.4, issue.1, pp.95-104, 1974.
DOI : 10.1080/01969727408546059

M. B. Eisen, P. T. Spellman, and P. O. Brown, Botstein : Cluster analysis and display of genome-wide expression patterns, Proceedings of the National Academy of Sciences of the United States of America, 1998.

M. A. Figueiredo and A. K. Jain, Unsupervised learning of finite mixture models, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, issue.3, pp.381-396, 2002.
DOI : 10.1109/34.990138

N. I. Fisher, T. Fisher, B. J. Lewis, and . Embleton, Statistical analysis of circular data, 1995.
DOI : 10.1017/CBO9780511564345

R. A. Fisher, Dispersion on a Sphere, Proc. Roy. Soc, A217, pp.295-305, 1953.
DOI : 10.1098/rspa.1953.0064

J. Ghosh and A. M. Chinnaiyan, Mixture modelling of gene expression data from microarray experiments, Bioinformatics, vol.18, issue.2, pp.275-286, 2002.
DOI : 10.1093/bioinformatics/18.2.275

A. D. Gordon, P. E. Jupp, and R. W. Byrne, The construction and assessment of mental maps, British Journal of Mathematical and Statistical Psychology, vol.42, issue.2, pp.169-182, 1989.
DOI : 10.1111/j.2044-8317.1989.tb00906.x

A. L. Gould, A Regression Technique for Angular Variates, Biometrics, vol.25, issue.4, pp.683-700, 1969.
DOI : 10.2307/2528567

G. Govaert, Classification avec distance adaptative, Thèse de doctorat de 3 ` eme cycle, 1975.

G. Govaert, Classification croisée. Thése d'´ etat, 1983.

G. Govaert, Analyse des données. Traitement du signal et de l'image. Hermes science, 2003.

G. Govaert and M. Nadif, Classification binaire et modèles, Rev.Statistique Appliquées, vol.38, issue.1, pp.67-81, 1990.

I. Gradshteyn, Ryzhik : Table of Integrals, 2007.

R. J. Hathaway, Another interpretation of the EM algorithm for mixture distributions, Statistics & Probability Letters, vol.4, issue.2, pp.53-56, 1986.
DOI : 10.1016/0167-7152(86)90016-7

C. M. Hurvich and C. L. Tsai, Regression and time series model selection in small samples, Biometrika, vol.76, issue.2, pp.297-307, 1989.
DOI : 10.1093/biomet/76.2.297

S. R. Jammalamadaka and A. Sengupta, Topics in Circular Statistics, World Scientific, vol.5, 2001.
DOI : 10.1142/4031

R. E. Jensen, A dynamical programming algorithm for cluster data analysis, J Oper Res Soc Amer, vol.7, pp.1034-1057, 1969.

F. X. Jollois and M. Nadif, Speed-up for the expectation-maximization algorithm for clustering categorical data, Journal of Global Optimization, vol.45, issue.1, pp.513-525, 2007.
DOI : 10.1007/s10898-006-9059-3

P. E. Jupp, Some applications of directional statistics to astronomy, the 5th Conference on Multivariate Statistics and Matrices in Statistics, pp.123-133, 1995.

M. Kearns, Y. Mansour, and A. Ng, An Information-Theoretic Analysis of Hard and Soft Assignment Methods for Clustering, the Thirteenth Conference on Uncertainty in Artificial Intelligence, pp.282-293, 1997.
DOI : 10.1007/978-94-011-5014-9_18

J. T. Kent, The fisher-bingham distribution on the sphere, J. Royal. Stat. Soc, vol.44, issue.1, pp.71-80, 1982.

J. T. Kent and K. V. Mardia, Consistency of Procrustes Estimators, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.59, issue.1, pp.281-290, 1997.
DOI : 10.1111/1467-9868.00069

W. Kuhn and F. Grün, Beziehungen zwischen elastischen Konstanten und Dehnungsdoppelbrechung hochelastischer Stoffe, Kolloid-Zeitschrift, vol.101, issue.3, pp.248-271, 1942.
DOI : 10.1007/BF01793684

A. Kume and S. G. Walker, On the Fisher???Bingham distribution, Statistics and Computing, vol.92, issue.2, pp.167-172, 2009.
DOI : 10.1007/s11222-008-9081-z

F. Lagona and . Picone, Maximum likelihood estimation of bivariate circular hidden Markov models from incomplete data, Journal of Statistical Computation and Simulation, vol.9, issue.7, pp.1-15, 2012.
DOI : 10.1348/000711000159240

F. Lagona and . Picone, Model-based clustering of multivariate skew data with circular components and missing values, Journal of Applied Statistics, vol.9, issue.5, pp.927-945, 2012.
DOI : 10.1214/aos/1176346060

G. N. Lance and W. T. Williams, A General Theory of Classificatory Sorting Strategies: 1. Hierarchical Systems, The Computer Journal, vol.9, issue.4, pp.373-380, 1967.
DOI : 10.1093/comjnl/9.4.373

A. Lelu, Modéles neuronaux pour l'analyse de données documentaires et textuelles

C. Liu, D. B. Rubin, and Y. N. Wu, Parameter expansion to accelerate EM: the PX-EM algorithm, Biometrika, vol.85, issue.4, pp.755-770, 1998.
DOI : 10.1093/biomet/85.4.755

K. Mardia, C. Taylor, and G. Subramaniam, Protein Bioinformatics and Mixtures of Bivariate von Mises Distributions for Angular Data, Biometrics, vol.89, issue.2, pp.505-512, 2007.
DOI : 10.1111/j.1541-0420.2006.00682.x

K. V. Mardia, Statistics of Directional Data, 1972.

K. V. Mardia, Characterization of directional distributions. Statistical Distributions in Scientific Work (Characterizations and Applications, pp.365-386, 1974.

K. V. Mardia, Statistics of directional data, J. Roy. Statist. Soc. Ser. B, vol.37, issue.3, pp.349-393, 1975.

K. V. Mardia, A. Baczkowski, X. Feng, and T. J. , Statistical methods for automatic interpretation of digitally scanned finger prints, Pattern Recognition Letters, vol.18, issue.11-13, pp.1197-1203, 1997.
DOI : 10.1016/S0167-8655(97)00103-7

K. V. Mardia and P. E. , Jupp : Directional Statistics, 2009.

K. V. Mardia, J. T. Kent, C. R. Goodall, and J. A. , Kriging and splines with derivative information, Biometrika, vol.83, issue.1, pp.207-221, 1996.
DOI : 10.1093/biomet/83.1.207

K. V. Mardia, K. V. Hughes, C. C. Taylor, and H. Singh, A multivariate von mises distribution with applications to bioinformatics, Canadian Journal of Statistics, vol.89, issue.1, pp.99-109, 2008.
DOI : 10.1002/cjs.5550360110

G. Mclachlan, R. Bean, and D. Peel, A mixture model-based approach to the clustering of microarray expression data, Bioinformatics, vol.18, issue.3, pp.413-422, 2002.
DOI : 10.1093/bioinformatics/18.3.413

G. Mclachlan and T. Krishnan, The EM algorithm and extensions, 1997.

G. J. Mclachlan and D. , Peel : Finite mixture models, 2000.

A. Mcquarrie, R. Shumway, and C. L. Tsai, The model selection criterion AICu, Statistics & Probability Letters, vol.34, issue.3, pp.285-292, 1997.
DOI : 10.1016/S0167-7152(96)00192-7

J. B. Mcqueen, Some methods for classification and analysis of multivariate observations In the 5th Berkeley symposium on math. Statistics and probability, pp.281-297, 1967.

M. Nadif and G. Govaert, Clustering for binary data and mixture models???choice of the model, Applied Stochastic Models and Data Analysis, vol.13, issue.3-4, pp.269-278, 1998.
DOI : 10.1002/(SICI)1099-0747(199709/12)13:3/4<269::AID-ASM321>3.0.CO;2-7

R. Neal and G. Hinton, A View of the Em Algorithm that Justifies Incremental, Sparse, and other Variants, 1998.
DOI : 10.1007/978-94-011-5014-9_12

M. Phuong and N. X. , Vinh : Normalized em algorithm for tumor clustering using gene expression data, the 8th IEEE International conference on Bioinformatics and BioEngineering, pp.315-320, 2008.

G. Pólya, Zur Statistik der sph??rischen Verteilung der Fixsterne, Astronomische Nachrichten, vol.208, issue.12, pp.175-180, 1919.
DOI : 10.1002/asna.19182081205

T. M. Pukkila and C. R. Rao, Pattern recognition based on scale invariant discriminant functions, Information Sciences, vol.45, issue.3, pp.379-389, 1988.
DOI : 10.1016/0020-0255(88)90012-6

C. R. Rao, Linear Statistical Inference and its Applications, 1973.
DOI : 10.1002/9780470316436

S. Régnier, Sur quelques aspects mathématiques desprobì emes de classification automatique, ICC bulletin, vol.4, pp.175-191, 1965.

J. Rissanen, Modeling by shortest data description, Automatica, vol.14, issue.5, pp.465-471, 1978.
DOI : 10.1016/0005-1098(78)90005-5

E. Ronchetti, Robust model selection in regression, Statistics & Probability Letters, vol.3, issue.1, pp.21-23, 1985.
DOI : 10.1016/0167-7152(85)90006-9

G. Salton and C. Buckley, Term-weighting approaches in automatic text retrieval, Information Processing & Management, vol.24, issue.5, pp.513-532, 1988.
DOI : 10.1016/0306-4573(88)90021-0

G. Salton and M. J. , McGil : Introduction to Modern Retrieval, 1983.

A. Schwarz, Reconnaissance des composants d'un mélange, Thèse de doctorat de 3 ` eme cycle, 1974.

G. Schwarz, Estimating the Dimension of a Model, The Annals of Statistics, vol.6, issue.2, pp.461-464, 1978.
DOI : 10.1214/aos/1176344136

R. Sharan and R. Shamir, Click : a clustering algorithm with applications to gene expression analysis, Proceedings of 8th International Conference on Intelligent Systems for Molecular Biology(ISMB), pp.307-316, 2000.

P. Shi and C. L. Tsai, Random walk on a circle, Biometrika, vol.50, pp.385-390, 1963.

P. Shi and C. L. Tsai, A note on the unification of the Akaike information criterion, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.60, issue.3, pp.551-558, 1998.
DOI : 10.1111/1467-9868.00139

P. H. Sneath, Computers in taxonomyl, J. gen. Microbiol, vol.17, issue.1, pp.201-226, 1957.

R. R. Sokal and P. H. , Sneath : principales of numerical taxonomy, 1963.

N. Stergiou, Innovative Analyses of Human Movement, Human Kinetics, 2004.

N. Sugiura, Further analysts of the data by akaike' s information criterion and the finite corrections, Communications in Statistics - Theory and Methods, vol.3, issue.10, pp.13-26, 1978.
DOI : 10.1080/03610927808827599

P. Tamayo, D. Slonim, J. Mesirov, Q. Zhu, S. Kitareewan et al., Interpreting patterns of gene expression with self-organizing maps: Methods and application to hematopoietic differentiation, Proceedings of the National Academy of Sciences of the United States of America, pp.2097-2912, 1999.
DOI : 10.1073/pnas.96.6.2907

B. Thiesson, C. Meek, and E. D. Heckerman, Accelerating em for large databases. Msr- tr-99-31, microsoft researcht, 2001.

G. Tseng, Penalized and weighted K-means for clustering with scattered objects and prior information in high-throughput biological data, Bioinformatics, vol.23, issue.17, pp.2247-2255, 2007.
DOI : 10.1093/bioinformatics/btm320

G. Ulrich, Computer Generation of Distributions on the m-Sphere, Applied Statistics, vol.33, issue.2, pp.158-163, 1984.
DOI : 10.2307/2347441

G. J. Upton, Fingleton : Spatial Data Analysis by Example Categorical and Directional Data, 1989.

R. Mises, Ueber die " ganzzaligkeit " der atomgewicht und verwandte fragen, Physikal, vol.19, pp.490-500, 1918.

T. H. Waterman, The Analysis of Spatial Orientation, Ergeb. Biol, vol.26, pp.97-117, 1963.
DOI : 10.1007/978-3-642-99872-0_11

G. S. Watson, Orientation statistics in the earth sciences, Bul. Geol. Inst. Univ. Uppsale, vol.2, pp.73-89, 1970.

G. S. Watson, Statistics on Spheres, The University of Arkansas lecture notes in the mathematical sciences, 1983.

A. Wintner, On the Shape of the Angular Case of Cauchy's Distribution Curves, The Annals of Mathematical Statistics, vol.18, issue.4, pp.589-593, 1947.
DOI : 10.1214/aoms/1177730351

J. H. Wolf, PATTERN CLUSTERING BY MULTIVARIATE MIXTURE ANALYSIS, Multivariate Behavioral Research, vol.5, issue.3, pp.329-350, 1970.
DOI : 10.1207/s15327906mbr0503_6

A. T. Wood, Some notes on the fisher???bingham family on the sphere, Communications in Statistics - Theory and Methods, vol.51, issue.11, pp.3881-3897, 1988.
DOI : 10.1214/aos/1176345690

C. F. Wu, On the Convergence Properties of the EM Algorithm, The Annals of Statistics, vol.11, issue.1, pp.95-103, 1983.
DOI : 10.1214/aos/1176346060

Y. Xu, V. Olman, and D. Xu, Clustering gene expression data using a graphtheoretic approach : an application of minimum spanning trees, Bioinformatics, vol.17, issue.4, pp.309-318, 2001.

S. Zhong, Efficient online spherical k-means clustering, IEEE Int. Joint Conf. Neural Networks (IJCNN 2005), pp.3180-3185, 2005.