Self-organized manifold learning and heuristic charting via adaptive   metrics
  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. 
Denis Horvath, Jozef Ulicny and Branislav Brutovsky
physics.data-an