Power-law stochastic neighbor embedding

Abstract

Stochastic neighbor embedding (SNE) aims to transform the observations in high-dimensional space into a low-dimensional space which preserves neighbor identities by minimizing the Kullback-Leibler divergence of the pairwise distributions between two spaces where Gaussian distributions are assumed. Data visualization could be improved by adopting the t-SNE where Student t distribution is used in the low-dimensional space. However, data pairs in the latent space are forced to be squeezed due to the loss of dimensions. This study incorporates the power-law distribution into construction of the p-SNE. Such an unsupervised p-SNE increases the physical forces in neighbor embedding so that the neighbors in the low-dimensional space can be adjusted flexibly to reflect the neighboring in the high-dimensional space. The experiments on three learning tasks illustrate that the manifold or data structure using the proposed p-SNE is preserved in better shape than that using SNE and t-SNE.