Making nonlinear manifold learning models interpretable: The manifold grand tour

Dimensionality reduction is required to produce visualizations of high dimensional data. In this framework, one of the most straightforward approaches to visualising high dimensional data is based on reducing complexity and applying linear projections while tumbling the projection axes in a defined sequence which generates a Grand Tour of the data. We propose using smooth nonlinear topographic maps of the data distribution to guide the Grand Tour, increasing the effectiveness of this approach by prioritising the linear views of the data that are most consistent with global data structure in these maps. A further consequence of this approach is to enable direct visualisation of the topographic map onto projective spaces that discern structure in the data. The experimental results on standard databases reported in this paper, using Self-Organising Maps and Generative Topographic Mapping, illustrate the practical value of the proposed approach. It must be remarked the novelty of the proposed method that improves some of the aspects of previous approaces based on the Grand Tour.