Interpreting Dimension Reductions through Gradient Visualization

Dimension reduction (DRs) are significant in data analysis to reduce the complexity of high dimensional data while preserving information to the greatest extent. However, the complex processes involved in DRs attribute to their inability to reason the relationship between the projection and the original data features (dimensions). "Why points are clustered?" and "What feature/s caused the points to scatter?" are some of the common questions. As a solution, we use gradients of the projection to generate visual explanations of the DRs. Utilizing these gradients, we show the point-wise sensitivities of the projection with respect to the original data features to explain the reasoning of DR. The combination of the gra- dients with various visualization techniques contribute to the exploration of the impact of dimensions on the projection. To overcome the curse of dimensionality, we propose inter- active techniques that facilitate the combination and comparison of features impact on the projection through gradients. Encapsulating the gradients and the visualization techniques, we present a web-based framework that facilitates an overview of impacts of all features and allows users to selectively explore notable features.