An advancement in clustering via nonparametric density estimation
- 852 Downloads
Density-based clustering methods hinge on the idea of associating groups to the connected components of the level sets of the density underlying the data, to be estimated by a nonparametric method. These methods claim some desirable properties and generally good performance, but they involve a non-trivial computational effort, required for the identification of the connected regions. In a previous work, the use of spatial tessellation such as the Delaunay triangulation has been proposed, because it suitably generalizes the univariate procedure for detecting the connected components. However, its computational complexity grows exponentially with the dimensionality of data, thus making the triangulation unfeasible for high dimensions. Our aim is to overcome the limitations of Delaunay triangulation. We discuss the use of an alternative procedure for identifying the connected regions associated to the level sets of the density. By measuring the extent of possible valleys of the density along the segment connecting pairs of observations, the proposed procedure shifts the formulation from a space with arbitrary dimension to a univariate one, thus leading benefits both in computation and visualization.
KeywordsCluster analysis Connected sets Nonparametric density estimation Kernel method
We wish to thank the two anonymous referees and an Associate editor for their valuable comments which have stimulated a clearer exposition of the original formulation and helped to improve the overall outcome.
- Azzalini, A., Menardi, G., Rosolin, T.: R package pdfCluster: cluster analysis via nonparametric density estimation (version 1.0-0) (2012). http://cran.r-project.org/package=pdfCluster
- Forina, M., Armanino, C., Lanteri, S., Tiscornia, E.: Classication of olive oils from their fatty acid composition. In: Food Research and Data Analysis, pp. 189–214. Applied Sc. Publishers, London (1983) Google Scholar
- Forina, M., Armanino, C., Castino, M., Ubigli, M.: Multivariate data analysis as a discriminating method of the origin of wines. Vitis 25, 189–201 (1986) Google Scholar
- Fraley, C., Raftery, A.E.: MCLUST vers. 3 for R: normal mixture modeling and model-based clustering. Tech. Rep. 504, Univ. Washington, Dep. Stat. (2006), rev. 2009 Google Scholar
- Prates, M., Lachos, V., Cabral, C.: R package mixsmsn: fitting finite mixture of scale mixture of skew-normal distributions (version 1.0-3) (2012). http://cran.r-project.org/web/packages/mixsmsn/index.html
- R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2013). http://www.R-project.org/. ISBN 3-900051-07-3-900051-0
- Scott, D.W., Sain, S.: Multidimensional Density Estimation. Handbook of Statistics, vol. 24, pp. 229–261 (2005) Google Scholar
- Wishart, D.: Mode analysis: a generalization of nearest neighbor which reduces chaining effects. In: Cole, A.J. (ed.) Numerical Taxonomy, pp. 282–308. Academic Press, London (1969) Google Scholar