Hypertrix: An indicatrix for high-dimensional visualizations

Visualizing high dimensional data is challenging, since any dimensionality reduction technique will distort distances. A classic method in cartography–Tissot’s Indicatrix, specific to sphere-to-plane maps– visualizes distortion using ellipses. Inspired by this idea, we describe the hypertrix: a method for representing distortions that occur when data is projected from arbitrarily high dimensions onto a 2D plane. We demonstrate our technique through synthetic and real-world datasets, and describe how this indicatrix can guide interpretations of nonlinear dimensionality reduction.