DR-SNE: Density-Regularized Stochastic Neighbor Embedding

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.