Self-organized manifold learning and heuristic charting via adaptive metrics

TL;DR

This paper introduces a hybrid optimization approach that enhances manifold learning by simultaneously constructing 2D projections and categorizing data, enabling better visualization and interpretation of high-dimensional structured data.

Contribution

It presents a novel hybrid heuristic method integrating metric learning, categorization, and manifold visualization for high-dimensional data analysis.

Findings

Effective in visualizing non-convex clusters

Enables categorization of 3D object surfaces

Improves manifold learning for high-dimensional data

Abstract

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.