Two key properties of dimensionality reduction methods

Dimensionality reduction aims at providing faithful low-dimensional representations of high-dimensional data. Its general principle is to attempt to reproduce in a low-dimensional space the salient characteristics of data, such as proximities. A large variety of methods exist in the literature, ranging from principal component analysis to deep neural networks with a bottleneck layer. In this cornucopia, it is rather difficult to find out why a few methods clearly outperform others. This paper identifies two important properties that enable some recent methods like stochastic neighborhood embedding and its variants to produce improved visualizations of high-dimensional data. The first property is a low sensitivity to the phenomenon of distance concentration. The second one is plasticity, that is, the capability to forget about some data characteristics to better reproduce the other ones. In a manifold learning perspective, breaking some proximities typically allow for a better unfolding of data. Theoretical developments as well as experiments support our claim that both properties have a strong impact. In particular, we show that equipping classical methods with the missing properties significantly improves their results.