Cm. Bishop et Me. Tipping, A HIERARCHICAL LATENT VARIABLE MODEL FOR DATA VISUALIZATION, IEEE transactions on pattern analysis and machine intelligence, 20(3), 1998, pp. 281-293
Visualization has proven to be a powerful and widely-applicable tool f
or the analysis and interpretation of multivariate data. Most visualiz
ation algorithms aim to find a projection from the data space down to
a two-dimensional visualization space. However, for complex data sets
living in a high-dimensional space, it is unlikely that a single two-d
imensional projection can reveal all of the interesting structure. We
therefore introduce a hierarchical visualization algorithm which allow
s the complete data set to be visualized at the top level, with cluste
rs and subclusters of data points visualized at deeper levels. The alg
orithm is based on a hierarchical mixture of latent variable models, w
hose parameters are estimated using the expectation-maximization algor
ithm. We demonstrate the principle of the approach on a toy data set,
and we then apply the algorithm to the visualization of a synthetic da
ta set in 12 dimensions obtained from a simulation of multiphase flows
in oil pipelines, and to data in 36 dimensions derived from satellite
images. A Matlab software implementation of the algorithm is publicly
available from the World Wide Web.