Hierarchical Clustering on the Torus
23 / 22
Authors
-
Ashis SenGupta
Department of Population Health Sciences, MCG, Augusta University, GA, USA and Indian Statistical Institute, Kolkata
-
Moumita Roy
Midnapore College (Autonomous), Midnapore
Keywords:
Akaike information criterion (AIC); Bayesian information criterion (BIC); Bivariate von-Mises distribution; Expectation-Maximization algorithm; Hierrachical; Clustering.Abstract
The aim of this paper is to introduce hierarchical clustering for bivariate circular or toroidal data. Here a mixture model approach is used as for model
based clustering. Here, the clustering is performed in two stages, the first stage being based on the marginal distribution of one of the circular variables
and the second stage being based on the conditional distribution of the other variable given the former. In particular, two types of such mixture models
are constructed. A real life application on gene data is made to illustrate the use of the proposed approach. Comparison of the two models is also done
based on this example.
Downloads
References
Dingxi, Q. and Tamhane, A. (2007). A Comparative Study of K-means
Algorithm and the Normal Mixture Model for Clustering:
Univariate Case, Journal of Statistical Planning and Inference.
137, 3722-3740.
Fisher, N.I., and Lee, A.J. (1992). Regression Models for an Angular
Response, Biometrics, 48(3), 665-677.
Jammalamadaka, S.R. and SenGupta, A. (2001). Topics in Circular
Statistics. World Scientific Publishers, New Jersey.
Johnson, R.A., and Wehrly, T.E. (1978). Some angular-linear
distributions and related regression models, Journal of the
American Statistical Association, 73, 602-606.
Johnson, R.A., and Wichern, D.W. (2007). Applied Multivariate
Statistical Analysis. Pearson Prentice Hall, New Jersey.
Kim, S. and SenGupta, A. (2017). Multivariate Multiple Circular
Regression. Journal of Statistical Computation and Simulation.
87, 1277-1291.
Liu, D., Peddada, S.D., Li, L. and Weinberg, C.R. (2006). Phase anal
ysis of circadian-related genes in two tissues. Bioinformatics
BMC, 7(87), https://doi.org/10.1186/1471-2105-7-87.
McLachlan, G.J., and Krishnan, T. (1997). The EM Algorithm and
Extensions. Wiley, NewYork.
Rao, C.R. (1973). Linear Statistical Inference and its Applications,
Second Edition. John Wiley & Sons, NewYork.
SenGupta, A. (2004). On the Construction of Probability Distributions
for Directional Data. Bul. Cal. Math. Soc., 96(2), 139-154.
SenGupta, A., Arnold, B. and CandKim, S. (2013). Inverse Circular
Circular Regression. Journal of Multivariate Analysis. 119,
200-208.
SenGupta, A., and Roy, M. (2021). Clustering on the Torus. Journal of
Statistical Theory and Practice, 58, 1-18.
SenGupta, A., and Ugwuowo, F. (2011). A Classification Method
for Directional Data with Application to the Human Skull.
Communication in Statistics, Theory and Methods, 40, 457-466,.
Singh H., Hnizdo V., and Demchuk E.(2002). Probabilistic model for
two dependent circular variables. Biometrika, 89(3), 719-723.
Wu, J.C.F. (1983). On the Convergence Properties of the EM Algorithm.
Annals of Statistics, 11(1), 95-103
Downloads
Submitted
Published
Issue
Section
How to Cite
