A hierarchical latent variable model for data visualization

Visualization has proven to be a powerful and widely-applicable tool the analysis and interpretation of data. Most visualization 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-dimensional projection can reveal all of the interesting structure. We therefore introduce a hierarchical visualization algorithm 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 algorithm is based on a hierarchical mixture of latent variable models, whose parameters are estimated using the expectation-maximization algorithm. We demonstrate the principle of the approach first on a toy data set, and then apply the algorithm to the visualization of a synthetic data set in 12 dimensions obtained from a simulation of multi-phase flows in oil pipelines and to data in 36 dimensions derived from satellite images.

Visualization of molecular fingerprints

A visualization plot of a data set of molecular data is a useful tool for gaining insight into a set of molecules. In chemoinformatics, most visualization plots are of molecular descriptors, and the statistical model most often used to produce a visualization is principal component analysis (PCA). This paper takes PCA, together with four other statistical models (NeuroScale, GTM, LTM, and LTM-LIN), and evaluates their ability to produce clustering in visualizations not of molecular descriptors but of molecular fingerprints. Two different tasks are addressed: understanding structural information (particularly combinatorial libraries) and relating structure to activity. The quality of the visualizations is compared both subjectively (by visual inspection) and objectively (with global distance comparisons and local k-nearest-neighbor predictors). On the data sets used to evaluate clustering by structure, LTM is found to perform significantly better than the other models. In particular, the clusters in LTM visualization space are consistent with the relationships between the core scaffolds that define the combinatorial sublibraries. On the data sets used to evaluate clustering by activity, LTM again gives the best performance but by a smaller margin. The results of this paper demonstrate the value of using both a nonlinear projection map and a Bernoulli noise model for modeling binary data.