Model interpretability is a problem for multivariate data in general and, very
specifically, for dimensionality reduction techniques as applied to data visualization. The
problem is even bigger for nonlinear dimensionality reduction (NLDR) methods, to which
interpretability limitations are consubstantial.
Data visualization is a key process for knowledge extraction from data that helps us to
gain insights into the observed data structure through graphical representations and metaphors.
NLDR techniques provide flexible visual insight, but the locally varying representation distor-
tion they generate makes interpretation far from intuitive.
For some NLDR models, indirect quantitative measures of this mapping distortion can
be calculated explicitly and used as part of an interpretative post-processing of the results.
In this Master Thesis, we apply a cartogram method, inspired on techniques of geographic
representation, to the purpose of data visualization using NLDR models. In particular, we
show how this method allows reintroducing the distortion, measured in the visual maps of
several self-organizing clustering methods.
The main capabilities and limitations of the cartogram visualization of multivariate data
using standard and hierarchical self-organizing models were investigated in some detail with
artificial data as well as with real information stemming from a neuro-oncology problem that
involves the discrimination of human brain tumor types, a problem for which knowledge dis-
covery techniques in general, and data visualization in particular should be useful tools.
