Doubly Stochastic Neighbor Embedding on Spheres

Recently, Stochastic Neighbor Embedding (SNE) methods have widely been applied in data visualization. These methods minimize the divergence between the pairwise similarities of high- and low-dimensional data. Despite their popularity, the current SNE methods experience the "crowding problem" when the data include highly imbalanced similarities. This implies that the data points with higher total similarity tend to get crowded around the display center. To solve this problem, we normalize the similarity matrix to be doubly stochastic such that all the data points have equal total similarities. A fast normalization method is proposed. Furthermore, we show empirically and theoretically that the doubly stochasticity constraint often leads to approximately spherical embeddings. This suggests replacing a flat space with spheres as the embedding space. The spherical embedding eliminates the discrepancy between the center and the periphery in visualization and thus resolves the "crowding problem". We compared the proposed method with the state-of-the-art SNE method on three real-world datasets. The results indicate that our method is more favorable in terms of visualization quality.