DR-SNE改进t-SNE，让降维后局部密度分布更真实。
DR-SNE: Density-Regularized Stochastic Neighbor Embedding
- 引入密度正则项，直接对齐原始与嵌入空间的邻域尺度分布。
- 在真实和合成数据上，显著提升局部浓度保留效果。
- 适合关注局部密度差异的可视化场景，如生物数据、社交网络。
t-SNE等降维方法虽能保留局部邻域结构，但会严重扭曲数据的局部分布。本文提出密度正则化随机邻域嵌入（DR-SNE），在随机邻域嵌入基础上加入正则项，直接对齐原始空间与嵌入空间中归一化的逆邻域尺度分布。该目标在保持嵌入全局缩放不变性的同时，有效保留相对局部密度。在真实与合成数据集上，DR-SNE普遍提升了目标浓度分布的保真度，同时维持可控的邻域保真水平。实验揭示浓度保留与邻域保真之间存在稳定的权衡关系，随正则化强度变化而改变。这些结果表明，DR-SNE是SNE的一种简洁扩展，适用于局部浓度相对变化重要的表示任务。
原文摘要 · Abstract (English)
Dimensionality-reduction methods such as t-SNE preserve local neighborhood structure but can substantially distort the local distribution of data. We introduce Density-Regularized Stochastic Neighbor Embedding (DR-SNE), which augments stochastic neighbor embedding with a regularizer that directly aligns normalized inverse-neighborhood-scale profiles between the original and embedding spaces. The resulting objective preserves relative local concentration while remaining invariant to global rescaling of the embedding. Across real and synthetic datasets, DR-SNE generally improves preservation of the targeted concentration profile while maintaining controlled levels of neighborhood fidelity. Experiments reveal a consistent empirical trade-off between concentration preservation and neighborhood fidelity as the regularization strength varies. These results position DR-SNE as a simple extension of SNE for settings in which relative variation in local concentration is an important property of the representation.
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