[Paper Review] HyperTools: A Python toolbox for visualizing and manipulating high-dimensional data

Andrew C. Heusser, Kirsten Ziman+2 more|ArXiv.org|Jan 28, 2017

Computational Physics and Python Applications20 references3 citations

TL;DR

HyperTools is a Python toolbox that enables intuitive visualization and manipulation of high-dimensional data using dimensionality reduction and data alignment techniques. By projecting complex datasets into 2D or 3D spaces and aligning disparate datasets via Procrustean transformations, it reveals geometric structures and temporal trajectories, as demonstrated in neuroimaging, educational, and linguistic data, enabling deeper insights through interactive, publication-quality visualizations.

ABSTRACT

Data visualizations can reveal trends and patterns that are not otherwise obvious from the raw data or summary statistics. While visualizing low-dimensional data is relatively straightforward (for example, plotting the change in a variable over time as (x,y) coordinates on a graph), it is not always obvious how to visualize high-dimensional datasets in a similarly intuitive way. Here we present HypeTools, a Python toolbox for visualizing and manipulating large, high-dimensional datasets. Our primary approach is to use dimensionality reduction techniques (Pearson, 1901; Tipping & Bishop, 1999) to embed high-dimensional datasets in a lower-dimensional space, and plot the data using a simple (yet powerful) API with many options for data manipulation [e.g. hyperalignment (Haxby et al., 2011), clustering, normalizing, etc.] and plot styling. The toolbox is designed around the notion of data trajectories and point clouds. Just as the position of an object moving through space can be visualized as a 3D trajectory, HyperTools uses dimensionality reduction algorithms to create similar 2D and 3D trajectories for time series of high-dimensional observations. The trajectories may be plotted as interactive static plots or visualized as animations. These same dimensionality reduction and alignment algorithms can also reveal structure in static datasets (e.g. collections of observations or attributes). We present several examples showcasing how using our toolbox to explore data through trajectories and low-dimensional embeddings can reveal deep insights into datasets across a wide variety of domains.

Motivation & Objective

• To address the challenge of visualizing and interpreting high-dimensional datasets, where traditional 2D/3D plotting is infeasible.
• To provide a user-friendly, open-source toolbox that enables researchers to explore complex data through low-dimensional embeddings and data trajectories.
• To facilitate comparison and alignment of datasets with different coordinate systems, such as brain activity and video frames, using hyperalignment and Procrustean transformations.
• To support hypothesis generation and data exploration across diverse domains, including neuroscience, education, and social sciences, via intuitive, publication-ready visualizations.

Proposed method

• Employs dimensionality reduction algorithms such as PCA, t-SNE, and PPCA to project high-dimensional data into 2D or 3D spaces for visualization.
• Uses the hyperalignment algorithm and Procrustean transformation to align multiple high-dimensional datasets into a common coordinate system, even when their original dimensions differ.
• Applies piecewise cubic interpolation to resample time-series data to a common temporal resolution before alignment.
• Utilizes the `reduce` function to project data onto a shared lower-dimensional space (e.g., 6,641 dimensions matching brain voxel count) prior to alignment.
• Employs the `procrustes` function to compute optimal linear transformations that align one dataset (e.g., brain responses) to another (e.g., movie frames) by minimizing squared Euclidean distances.
• Supports interactive and animated visualizations of data trajectories, enabling dynamic exploration of temporal patterns in high-dimensional time series.

Experimental results

Research questions

• RQ1 How can high-dimensional data be effectively visualized in a way that preserves geometric and temporal structure?
• RQ2 To what extent can dimensionality reduction and alignment techniques reveal hidden patterns in diverse datasets such as brain activity, educational performance, and political discourse?
• RQ3 Can Procrustean alignment of datasets with different coordinate systems (e.g., brain responses and video frames) reveal meaningful correspondences?
• RQ4 How can a single-line API in a Python toolbox streamline complex data visualization and manipulation for non-expert users?

Key findings

• HyperTools successfully visualized the correspondence between brain responses and movie frames by aligning them into a shared 6,641-dimensional space, revealing structural similarities in their temporal trajectories.
• The toolbox enabled the visualization of brain responses 'through the lens' of the movie, where each brain pattern could be mapped back to a corresponding movie frame for direct interpretation.
• Using hyperalignment, the toolbox aligned brain data from 11 participants into a common space, allowing for the comparison of neural responses across individuals despite differences in original coordinate systems.
• The Procrustean transformation effectively realigned brain data to movie space, with the resulting aligned data enabling visual and quantitative comparison of geometric structures across modalities.
• The toolbox demonstrated utility across diverse domains, including neuroscience, education, politics, and biology, by revealing patterns not evident from summary statistics alone.
• The integration of dimensionality reduction and alignment into a single, accessible API allowed for complex visualizations and analyses with minimal code, often requiring only a single line of code.