Squintability and Other Metrics for Assessing Projection Pursuit Indexes, and Guiding Optimization Choices

TL;DR

This paper introduces measures for smoothness and squintability of projection pursuit indexes, evaluates a swarm-based optimizer's effectiveness in high-dimensional data visualization, and provides tools in R packages for these metrics.

Contribution

It defines new metrics for assessing PP index properties and evaluates the JSO optimizer's performance, enhancing high-dimensional data visualization techniques.

Findings

Higher squintability increases optimization success rate.

Smoothness has no significant impact on optimization performance.

JSO outperforms existing optimizers in detecting target patterns.

Abstract

The projection pursuit (PP) guided tour optimizes a criterion function, known as the PP index, to gradually reveal projections of interest from high-dimensional data through animation. Optimization of some PP indexes can be non-trivial, if they are non-smooth functions, or when the optimum has a small "squint angle", detectable only from close proximity. Here, measures for calculating the smoothness and squintability properties of the PP index are defined. These are used to investigate the performance of a recently introduced swarm-based algorithm, Jellyfish Search Optimizer (JSO), for optimizing PP indexes. The performance of JSO in detecting the target pattern (pipe shape) is compared with existing optimizers in PP. Additionally, JSO's performance on detecting the sine-wave shape is evaluated using different PP indexes (hence different smoothness and squintability) across various data dimensions (d = 4, 6, 8, 10, 12) and JSO hyper-parameters. We observe empirically that higher squintability improves the success rate of the PP index optimization, while smoothness has no significant effect. The JSO algorithm has been implemented in the R package, `tourr`, and functions to calculate smoothness and squintability measures are implemented in the `ferrn` package.