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Data visualization is one of the major applications of nonlineardimensionality reduction. From the information retrieval perspective, thequality of a visualization can be evaluated by considering the extent that theneighborhood relation of each data point is maintained while the number ofunrelated points that are retrieved is minimized. This property can bequantified as a trade-off between the mean precision and mean recall of thevisualization. While there have been some approaches to formulate thevisualization objective directly as a weighted sum of the precision and recall,there is no systematic way to determine the optimal trade-off between these twonor a clear interpretation of the optimal value. In this paper, we investigatethe properties of $\alpha$-divergence for information visualization, focusingour attention on a particular range of $\alpha$ values. We show that theminimization of the new cost function corresponds to maximizing a geometricmean between precision and recall, parameterized by $\alpha$. Contrary to someearlier methods, no hand-tuning is needed, but we can rigorously estimate theoptimal value of $\alpha$ for a given input data. For this, we provide astatistical framework using a novel distribution called Exponential Divergencewith Augmentation (EDA). By the extensive set of experiments, we show that theoptimal value of $\alpha$, obtained by EDA corresponds to the optimal trade-offbetween the precision and recall for a given data distribution.

Optimizing the Information Retrieval Trade-off in Data Visualization Using $\alpha$-Divergence