  Data visualisation helps understanding data represented by multiple
variables, also called features, stored in a large matrix where individuals are
stored in lines and variable values in columns. These data structures are
frequently called multidimensional spaces.In this paper, we illustrate ways of
employing the visual results of multidimensional projection algorithms to
understand and fine-tune the parameters of their mathematical framework. Some
of the common mathematical common to these approaches are Laplacian matrices,
Euclidian distance, Cosine distance, and statistical methods such as
Kullback-Leibler divergence, employed to fit probability distributions and
reduce dimensions. Two of the relevant algorithms in the data visualisation
field are t-distributed stochastic neighbourhood embedding (t-SNE) and
Least-Square Projection (LSP). These algorithms can be used to understand
several ranges of mathematical functions including their impact on datasets. In
this article, mathematical parameters of underlying techniques such as
Principal Component Analysis (PCA) behind t-SNE and mesh reconstruction methods
behind LSP are adjusted to reflect the properties afforded by the mathematical
formulation. The results, supported by illustrative methods of the processes of
LSP and t-SNE, are meant to inspire students in understanding the mathematics
behind such methods, in order to apply them in effective data analysis tasks in
multiple applications.
