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.

翻译：投影寻踪（PP）引导漫游通过优化一个称为PP指标的准则函数，以动画形式逐步揭示高维数据中感兴趣的投影。某些PP指标的优化可能具有挑战性，例如当它们是非光滑函数时，或当最优解具有较小的“斜视角”（仅能从极近距离检测到）时。本文定义了用于计算PP指标光滑性与斜视度特性的度量方法。这些度量被用于研究近期引入的基于种群的算法——水母搜索优化器（JSO）在优化PP指标方面的性能。JSO在检测目标模式（管道形状）方面的性能与PP中现有优化器进行了比较。此外，通过在不同数据维度（d = 4, 6, 8, 10, 12）和JSO超参数设置下，使用不同的PP指标（从而具有不同的光滑性与斜视度），评估了JSO在检测正弦波形方面的表现。我们通过实证观察到，较高的斜视度能提升PP指标优化的成功率，而光滑性则无显著影响。JSO算法已在R包`tourr`中实现，计算光滑性与斜视度度量的函数则实现在`ferrn`包中。