Can MDS rival with t-SNE by using the symmetric Kullback-Leibler divergence\\ across neighborhoods as a pseudo-distance?

Local methods of dimensionality reduction like neighborhood embedding (NE) and t-SNE in particular outperform older global approaches such as stress-based multi-dimensional scaling (MDS).Stochastic neighborhoods are less sensitive than distances to statistical variations between spaces with strongly different dimensionalities, making a match across them very difficult.Here, we take inspiration from those stochastic neighborhoods in order to devise a pseudo-distance that is less prone to concentration than the Euclidean distance.For two points in the high-dimensional data space, it is defined as the symmetrized Kullback-Leibler divergence across the (stochastic) neighborhoods of the two points (SKLAN).Plugging the SKLAN in a method of stress-based MDS, we compare quantitatively t-SNE, MDS with all Euclidean distances, and MDS with SKLAN & Euclidean distances on several data sets.The results show that SKLAN allows MDS to perform competitively with t-SNE.