Probabilistic principal component subspaces: a hierarchical finite mixture model for data visualization

Visual exploration has proven to be a powerful tool for multivariate data mining and knowledge discovery. 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 multimodal 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 subclusters of data points visualized at deeper levels. The methods involve hierarchical use of standard finite normal mixtures 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 several multimodal numerical data sets, and we then apply the method to the visual explanation in computer-aided diagnosis for breast cancer detection from digital mammograms.