HyperTools: a Python Toolbox for Gaining Geometric Insights into High-Dimensional Data

Andrew C. Heusser, Kirsten Ziman, Lucy L. W. Owen, Jeremy R. Manning

Abstract: Dimensionality reduction algorithms have played a foundational role in facilitating the deep understanding of complex high- dimensional data. One particularly useful application of dimensionality reduction techniques is in data visualization. Low-dimensional visualizations can help practitioners understand where machine learning algorithms might leverage the geometric properties of a dataset to improve performance. Another challenge is to generalize insights across datasets [e.g. data from multiple modalities describing the same system (Haxby et al., 2011), artwork or photographs of similar content in different styles (Zhu et al., 2017), etc.]. Several recently developed techniques(e.g. Haxby et al., 2011; Chen et al., 2015) use the procrustean transformation (Schonemann, 1966) to align the geometries of two or more spaces so that data with different axes may be plotted in a common space. We propose that each of these techniques (dimensionality reduction, alignment, and visualization) applied in sequence should be cast as a single conceptual hyperplot operation for gaining geometric insights into high-dimensional data. Our Python toolbox enables this operation in a single (highly flexible) function call.