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Classical metric and non-metric multidimensional scaling (MDS) variants arewidely known manifold learning (ML) methods which enable construction of lowdimensional representation (projections) of high dimensional data inputs.However, their use is crucially limited to the cases when data are inherentlyreducible to low dimensionality. In general, drawbacks and limitations ofthese, as well as pure, MDS variants become more apparent when the exploration(learning) is exposed to the structured data of high intrinsic dimension. As wedemonstrate on artificial and real-world datasets, the over-determinationproblem can be solved by means of the hybrid and multi-componentdiscrete-continuous multi-modal optimization heuristics. Its remarkable featureis, that projections onto 2D are constructed simultaneously with the datacategorization (classification) compensating in part for the loss of originalinput information. We observed, that the optimization module integrated with MLmodeling, metric learning and categorization leads to a nontrivial mechanismresulting in generation of patterns of categorical variables which can beinterpreted as a heuristic charting. The method provides visual information inthe form of non-convex clusters or separated regions. Furthermore, the abilityto categorize the surfaces into back and front parts of the analyzed 3D dataobjects have been attained through self-organized structuring withoutsupervising.

Self-organized manifold learning and heuristic charting via adaptive metrics