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Stochastic Neighbor Embedding (SNE) methods minimize the divergence betweenthe similarity matrix of a high-dimensional data set and its counterpart from alow-dimensional embedding, leading to widely applied tools for datavisualization. Despite their popularity, the current SNE methods experience acrowding problem when the data include highly imbalanced similarities. Thisimplies that the data points with higher total similarity tend to get crowdedaround the display center. To solve this problem, we introduce a fastnormalization method and normalize the similarity matrix to be doublystochastic such that all the data points have equal total similarities.Furthermore, we show empirically and theoretically that the doublystochasticity constraint often leads to embeddings which are approximatelyspherical. This suggests replacing a flat space with spheres as the embeddingspace. The spherical embedding eliminates the discrepancy between the centerand the periphery in visualization, which efficiently resolves the crowdingproblem. We compared the proposed method (DOSNES) with the state-of-the-art SNEmethod on three real-world datasets and the results clearly indicate that ourmethod is more favorable in terms of visualization quality.

Doubly Stochastic Neighbor Embedding on Spheres