Exploratory Observation Machine (XOM) with Kullback-Leibler Divergence for Dimensionality Reduction and Visualization

We present an extension of the Exploratory Observation Ma- chine (XOM) for structure-preserving dimensionality reduction. Based on minimizing the Kullback-Leibler divergence of neighborhood functions in data and image spaces, this Neighbor Embedding XOM (NE-XOM) cre- ates a link between fast sequential online learning known from topology- preserving mappings and principled direct divergence optimization ap- proaches. We quantitatively evaluate our method on real world data using multiple embedding quality measures. In this comparison, NE-XOM per- forms as a competitive trade-off between high embedding quality and low computational expense, which motivates its further use in real-world set- tings throughout science and engineering.