Exploring Dimensionality Reductions with Forward and Backward Projections

Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data across domains. Dimensionality-reduction algorithms involve complex optimizations and the reduced dimensions computed by these algorithms generally lack clear relation to the initial data dimensions. Therefore, interpreting and reasoning about dimensionality reductions can be difficult. In this work, we introduce two interaction techniques, $\mathit{\text{forward}}\mathit{\text{projection}}$ and $\mathit{\text{backward}}\mathit{\text{projection}}$, for reasoning dynamically about scatter plots of dimensionally reduced data. We also contribute two related visualization techniques, $\mathit{\text{prolines}}$ and $\mathit{\text{feasibility}}\mathit{\text{map}}$ to facilitate and enrich the effective use of the proposed interactions, which we integrate in a new tool called $\mathit{\text{Praxis}}$. To evaluate our techniques, we first analyze their time and accuracy performance across varying sample and dimension sizes. We then conduct a user study in which twelve data scientists use $\mathit{\text{Praxis}}$ so as to assess the usefulness of the techniques in performing exploratory data analysis tasks. Results suggest that our visual interactions are intuitive and effective for exploring dimensionality reductions and generating hypotheses about the underlying data.