Projection under pairwise distance controls

Projection sous les contrôles de distance par paires

Alawieh Hiba (1) , Nicolas Wicker (1) , Christophe Biernacki (1, 2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 MODAL - MOdel for Data Analysis and Learning

Visualization of high-dimensional and possibly complex (non continuous for instance) data onto a low-dimensional space may be difficult. Several projection methods have been already proposed for displaying such high-dimensional structures on a lower-dimensional space, but the information lost is not always easy to use. Here, a new projection paradigm is presented to describe a non-linear projection method that takes into account the projection quality of each projected point in the reduced space, this quality being directly available in the same scale as this reduced space. More specifically, this novel method allows a straightforward visualization data in R 2 with a simple reading of the approximation quality, and provides then a novel variant of dimensionality reduction.

Mots clés: multidimensional scaling; Data visualization; dimension reduction; principal component analysis

Domaines: Méthodologie [stat.ME]

Alawieh Hiba, Nicolas Wicker, Christophe Biernacki. Projection under pairwise distance controls. 2018. ⟨hal-01420662v3⟩