Metric Properties of Structured Data Visualizations through Generative Probabilistic Modeling

Recently, generative probabilistic modeling princi-ples were extended to visualization of structured data types, such as sequences. The models are for-mulated as constrained mixtures of sequence mod-els- a generalization of density-based visualization methods previously developed for static data sets. In order to effectively explore visualization plots, one needs to understand local directional magni£-cation factors, i.e. the extend to which small posi-tional changes on visualization plot lead to changes in local noise models explaining the structured data. Magni£cation factors are useful for highlight-ing boundaries between data clusters. In this paper we present two techniques for estimating local met-ric induced on the sequence space by the model for-mulation. We £rst verify our approach in two con-trolled experiments involving arti£cially generated sequences. We then illustrate our methodology on sequences representing chorals by J.S. Bach.