  Classical metric and non-metric multidimensional scaling (MDS) variants are
widely known manifold learning (ML) methods which enable construction of low
dimensional representation (projections) of high dimensional data inputs.
However, their use is crucially limited to the cases when data are inherently
reducible to low dimensionality. In general, drawbacks and limitations of
these, as well as pure, MDS variants become more apparent when the exploration
(learning) is exposed to the structured data of high intrinsic dimension. As we
demonstrate on artificial and real-world datasets, the over-determination
problem can be solved by means of the hybrid and multi-component
discrete-continuous multi-modal optimization heuristics. Its remarkable feature
is, that projections onto 2D are constructed simultaneously with the data
categorization (classification) compensating in part for the loss of original
input information. We observed, that the optimization module integrated with ML
modeling, metric learning and categorization leads to a nontrivial mechanism
resulting in generation of patterns of categorical variables which can be
interpreted as a heuristic charting. The method provides visual information in
the form of non-convex clusters or separated regions. Furthermore, the ability
to categorize the surfaces into back and front parts of the analyzed 3D data
objects have been attained through self-organized structuring without
supervising.
