Projection under pairwise distance controls

8 Visualization of high dimensional and possibly complex data onto a low-dimensional 9 space is often difficult. Several projection methods have been already proposed to 10 display such high-dimensional structures on a lower-dimensional space, but the infor11 mation lost is not always considered. Here, a new projection paradigm is presented to 12 describe a non-linear projection method that takes into account the projection qual13 ity of each projected point in the reduced space, this quality being directly available 14 at the scale of this reduced space. More specifically, this novel method allows for a 15 straightforward visualization data in R with a simple reading of the approximation 16 quality and thus provides a novel variant of dimensionality reduction. 17