Projection under pairwise distance control

Abstract

Visualization of high dimensional and possibly complex data onto a low-dimensional space is often difficult. Several projection methods have been already proposed to display such high-dimensional structures on a lower-dimensional space, but the information lost is not always considered. 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 at the scale of this reduced space. More specifically, this novel method allows for a straightforward visualization of data in ${\mathbb{R}}^2$ with a simple reading of the approximation quality, and thus provides a novel variant of dimensionality reduction.

Keywords:

• Data visualization
• dimensionality reduction
• multidimensional scaling
• principal component analysis
• kernel principal component analysis