B0241
Title: Hierarchical variable clustering using singular value decomposition
Authors: Jan Bauer - Vrije Universiteit Amsterdam (Netherlands) [presenting]
Abstract: In multivariate analysis, finding latent variables serves as an initial step to interpret data. However, simplifying the underlying population by a reduced number of latent variables skims only the surface. Detecting nested structures among and within these factors are further steps to facilitate relations among variables and therefore to deepen the understanding of the underlying random vector. This can be accomplished using hierarchical variable clustering. A new concept is provided that detects the underlying hierarchical variable structure using singular value decomposition. Singular vectors can be exploited to detect the underlying block diagonal structure of a covariance matrix. This approach is extended to find the nested structure of the latent variables by divisive clustering. The hierarchical clustering structure that is easiest to interpret is not necessarily the one that fits the underlying sample. Therefore, a measure is provided that evaluates each cluster. The performance of the new concept is further illustrated for hierarchical variable clustering as well as the contributed evaluation measure with simulations and on real datasets.
