Optimized bi-dimensional data projection for clustering visualization

We propose a new method to project n-dimensional data onto two dimensions, for visualization purposes. Our goal is to produce a bi-dimensional representation that better separate existing clusters. Accordingly, to generate this projection we apply Differential Evolution as a meta-heuristic to optimize a divergence measure of the projected data. This divergence measure is based on the Cauchy–Schwartz divergence, extended for multiple classes. It accounts for the separability of the clusters in the projected space using the Renyi entropy and Information Theoretical Clustering analysis. We test the proposed method on two synthetic and five real world data sets, obtaining well separated projected clusters in two dimensions. These results were compared with results generated by PCA and a recent likelihood based visualization method.

► Cauchy–Schwartz divergence can be used to evaluate clustering of data projections.
► Differential Evolution can generate projections with optimal divergence values.
► Differential Evolution is more robust to noise than compared methods.
► Results show improvement over PCA on flow citometry visualization.