Dimensionality reduction by rank preservation

Dimensionality reduction techniques aim at representing high-dimensional data in low-dimensional spaces. To be faithful and reliable, the representation is usually required to preserve proximity relationships. In practice, methods like multidimensional scaling try to fulfill this requirement by preserving pairwise distances in the low-dimensional representation. However, such a simplification does not easily allow for local scalings in the representation. It also makes these methods suboptimal with respect to recent quality criteria that are based on distance rankings. This paper addresses this issue by introducing a dimensionality reduction method that works with ranks. Appropriate hypotheses enable the minimization of a rank-based cost function. In particular, the scale indeterminacy that is inherent to ranks is circumvented by representing data on a space with a spherical topology.