Hierarchy of probabilistic principal component subspaces for data mining

Visual exploration has proven to be a powerful tool for multivariate data mining. Most visualization algorithms aim to find a projection from the data space down to a visually perceivable rendering space. To reveal all of the interesting aspects of complex data sets living in a high-dimensional space, a hierarchical visualization algorithm is introduced which allows the complete data set to be visualized at the top level, with clusters and sub-clusters of data points visualized at deeper levels. The methods involve multiple use of standard finite normal mixture models and probabilistic principal component projections, whose parameters are estimated using the expectation-maximization and principal component neural networks under the information theoretic criteria. We demonstrate the principle of the approach on two three-dimensional synthetic data sets.