Hybrid Gaussian and von Mises Model-Based Clustering

Data collected about a phenomenon often measures its magnitude and direction. The most common approach to clustering this data assumes that directional data can be modeled as Gaussian. However, directional data has special properties that conventional statistics cannot handle. To deal with them, other approaches like the von Mises distribution must be applied. In this paper we present a new model based on mixtures of Bayesian networks to simultaneously cluster both linear and directional data.

[1]  김경민,et al.  Finite mixture models and model-based clustering , 2017 .

[2]  Paul D. McNicholas,et al.  Model-Based Clustering , 2016, Journal of Classification.

[3]  Kurt Hornik,et al.  movMF: An R Package for Fitting Mixtures of von Mises-Fisher Distributions , 2014 .

[4]  Concha Bielza,et al.  Directional naive Bayes classifiers , 2015, Pattern Analysis and Applications.

[5]  Mohd Talib Latif,et al.  Fitting a mixture of von Mises distributions in order to model data on wind direction in Peninsular Malaysia , 2013 .

[6]  Rafael Yuste,et al.  Age-based comparison of human dendritic spine structure using complete three-dimensional reconstructions. , 2013, Cerebral cortex.

[7]  Jeffrey J. Love,et al.  Insignificant solar‐terrestrial triggering of earthquakes , 2013 .

[8]  Kanti V. Mardia,et al.  Mixtures of concentrated multivariate sine distributions with applications to bioinformatics , 2012 .

[9]  M. Butala,et al.  On the reported ionospheric precursor of the 1999 Hector Mine, California earthquake , 2012 .

[10]  S. R. Jammalamadaka,et al.  Directional Statistics, I , 2011 .

[11]  Simone Calderara,et al.  Mixtures of von Mises Distributions for People Trajectory Shape Analysis , 2011, IEEE Transactions on Circuits and Systems for Video Technology.

[12]  Xu Qin,et al.  A New Circular Distribution and Its Application to Wind Data , 2010 .

[13]  On the reported magnetic precursor of the 1993 Guam earthquake , 2009 .

[14]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[15]  J. A. Carta,et al.  A review of wind speed probability distributions used in wind energy analysis: Case studies in the Canary Islands , 2009 .

[16]  M. Johnston,et al.  On the reported magnetic precursor of the 1989 Loma Prieta earthquake , 2009 .

[17]  Kanti V. Mardia,et al.  A multivariate von mises distribution with applications to bioinformatics , 2008 .

[18]  N. Spruston Pyramidal neurons: dendritic structure and synaptic integration , 2008, Nature Reviews Neuroscience.

[19]  Simone Calderara,et al.  Detection of abnormal behaviors using a mixture of Von Mises distributions , 2007, 2007 IEEE Conference on Advanced Video and Signal Based Surveillance.

[20]  S. R. Jammalamadaka,et al.  The generalized von Mises distribution , 2007 .

[21]  K. Mardia,et al.  Protein Bioinformatics and Mixtures of Bivariate von Mises Distributions for Angular Data , 2007, Biometrics.

[22]  A. Zamilpa,et al.  Clinical effects produced by a standardized herbal medicinal product of Hibiscus sabdariffa on patients with hypertension. A randomized, double-blind, lisinopril-controlled clinical trial. , 2006, Planta medica.

[23]  Inderjit S. Dhillon,et al.  Clustering on the Unit Hypersphere using von Mises-Fisher Distributions , 2005, J. Mach. Learn. Res..

[24]  David Maxwell Chickering,et al.  Learning Bayesian Networks: The Combination of Knowledge and Statistical Data , 1994, Machine Learning.

[25]  G. Cooper,et al.  A Bayesian Method for the Induction of Probabilistic Networks from Data , 2004, Machine-mediated learning.

[26]  Alan Peters,et al.  THE SMALL PYRAMIDAL NEURON OF THE RAT CEREBRAL CORTEX , 1968, Zeitschrift für Zellforschung und Mikroskopische Anatomie.

[27]  Ian T. Jolliffe,et al.  Fitting mixtures of von Mises distributions: a case study involving sudden infant death syndrome , 2003, Comput. Stat. Data Anal..

[28]  Shi Zhong,et al.  A Comparative Study of Generative Models for Document Clustering , 2003 .

[29]  K. Svoboda,et al.  Structure and function of dendritic spines. , 2002, Annual review of physiology.

[30]  Taku Komura,et al.  Topology matching for fully automatic similarity estimation of 3D shapes , 2001, SIGGRAPH.

[31]  Pedro Larrañaga,et al.  An improved Bayesian structural EM algorithm for learning Bayesian networks for clustering , 2000, Pattern Recognit. Lett..

[32]  David G. Stork,et al.  Pattern Classification (2nd ed.) , 1999 .

[33]  B. Jacobs,et al.  Life‐span dendritic and spine changes in areas 10 and 18 of human cortex: A quantitative golgi study , 1997, The Journal of comparative neurology.

[34]  Nir Friedman,et al.  Learning Belief Networks in the Presence of Missing Values and Hidden Variables , 1997, ICML.

[35]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[36]  D. N. Geary Mixture Models: Inference and Applications to Clustering , 1989 .

[37]  A. F. Smith,et al.  Statistical analysis of finite mixture distributions , 1986 .

[38]  E. Batschelet Circular statistics in biology , 1981 .

[39]  N. Fisher,et al.  The BIAS of the maximum likelihood estimators of the von mises-fisher concentration parameters , 1981 .

[40]  G. Schwarz Estimating the Dimension of a Model , 1978 .

[41]  Kanti V. Mardia,et al.  A Model for Cylindrical Variables with Applications , 1978 .

[42]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[43]  H. Akaike A new look at the statistical model identification , 1974 .

[44]  E. Batschelet,et al.  Angular-linear correlation coefficient for rhythmometry and circannually changing human birth rates at different geographic latitudes. , 1973, International journal of chronobiology.

[45]  A. Peters,et al.  The small pyramidal neuron of the rat cerebral cortex. The perikaryon, dendrites and spines. , 1970, The American journal of anatomy.