Inspired by this felicitous, highly concentrated and rather exhaustive review of a rapidly growing field, many larger research areas that warrant further investigation come to mind. In this comment, three areas are selected: fully satisfactory PCA on tori and polyspheres, harnessing linearity through Lie algebras underlying homogeneous spaces such as those for directional data, and statistical analysis based on critical points (e.g. mode and antimodes) of Fréchet \(L^p\)-functions.

中文翻译：

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评论：定向统计的最新进展

受到对迅速发展的领域的这一有趣，高度集中且详尽无遗的评论的启发，许多需要进一步研究的更大的研究领域浮现在脑海。在此评论中，选择了三个区域：对圆托和多球面的完全令人满意的PCA；通过均匀空间下的李代数（如方向数据）利用线性，以及基于Fréchet \（L的临界点（例如众数和反众数）的统计分析）^ p \） -功能。