iHELP: interactive hierarchical linear projections for interpreting non-linear projections

We propose an interactive analytical system for exploring and interpreting non-linear projections. Although non-linear projections are widely used in disclosing complex structures in high-dimensional analysis, there is a strong need to interpret them due to their inherent complexity and weak interpretability. In the machine learning and visualization communities, it is inspiring to use local linear models to fit and interpret non-linear models. Regarding non-linear projections, there are research gaps in both generation and exploration of linear fitting segments. To fill this gap, we propose an optimization algorithm to partition a non-linear projection into linear segments according to the feature of local affine transformations. We then construct a hierarchy of linear segments and conjunct hierarchical visualizations to support a coarse-to-fine exploration. After that, we design and implement a visual interface that integrates the proposed algorithms and a suite of visual tools. Three case studies demonstrate that the proposed approach facilitates the interpretation of non-linear projections. Graphical abstract