A new approach to cluster analysis: the clustering-function-based method
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2006 · Volume 68 · Issue 3
DOI: 10.1111/j.1467-9868.2006.00549.x
Abstract
Summary.The purpose of the paper is to present a new statistical approach to hierarchical cluster analysis withnobjects measured onpvariables. Motivated by the model of multivariate analysis of variance and the method of maximum likelihood, a clustering problem is formulated as a least squares optimization problem, simultaneously solving for both ann-vector ofunknowngroup membership of objects and a linear clustering function. This formulation is shown to be linked to linear regression analysis and Fisher linear discriminant analysis and includes principal component regression for tackling multicollinearity or rank deficiency, polynomial orB-splines regression for handling non-linearity and various variable selection methods to eliminate irrelevant variables from data analysis. Algorithmic issues are investigated by using sign eigenanalysis.
Keywords
Discriminant analysis, Gene expression data, Regression analysis, Sign eigenanalysis, Unsupervised learning
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