Scale-independent quality criteria for dimensionality reduction

Dimensionality reduction aims at representing high-dimensional data in low-dimensional spaces, in order to facilitate their visual interpretation. Many techniques exist, ranging from simple linear projections to more complex nonlinear transformations. The large variety of methods emphasizes the need of quality criteria that allow for fair comparisons between them. This paper extends previous work about rank-based quality criteria and proposes to circumvent their scale dependency. Most dimensionality reduction techniques indeed rely on a scale parameter that distinguish between local and global data properties. Such a scale dependency can be similarly found in usual quality criteria: they assess the embedding quality on a certain scale. Experiments with various dimensionality reduction techniques eventually show the strengths and weaknesses of the proposed scale-independent criteria.