Self-organised manifold learning and heuristic charting via adaptive metrics

Classical metric and non-metric multidimensional scaling MDS variants represent the well-known manifold learning ML methods which enable construction of low-dimensional representation projections of high-dimensional data inputs. However, their use is 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 as well as real-world datasets, the over-determination problem can be solved by means of the hybrid and multi-component discrete-continuous multi-modal optimisation heuristics. A remarkable feature of the approach is that projections onto 2D are constructed simultaneously with the data categorisation compensating in part for the loss of original input information. We observed that the optimisation module integrated with ML modelling, metric learning and categorisation leads to a nontrivial mechanism resulting in heuristic charting of data.