Principal component analysis (PCA) is the most widely used dimensionality reduction technique in the biological sciences, and is commonly employed to create 2D visualizations of geometric morphometric data. However, interesting biological information may be lost or misrepresented in these plots due to PCA’s inability to summarize nonlinear dependencies between variables. Nonlinear alternative methods exist, but their effectiveness has never been tested on morphometric data. Here, the performance of PCA on the task of visualizing morphometric variation is compared to four nonlinear techniques: Sammon Mapping, Isomap, Locally Linear Embedding, and Laplacian Eigenmaps. The performance of methods is assessed on the basis of global and local preservation of pairwise distances for a variety of simulated and empirical datasets. The relative performance of PCA varies in function of the distribution of variation, complexity, and size of datasets. Overall, nonlinear methods show superior preservation of small differences between morphologies compared to PCA.

中文翻译：

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可视化形态数据的降维技术：将主成分分析与非线性方法进行比较

主成分分析（PCA）是生物科学中使用最广泛的降维技术，通常用于创建几何形态计量数据的2D可视化。但是，由于PCA无法总结变量之间的非线性相关性，在这些图中有趣的生物学信息可能会丢失或显示不正确。存在非线性替代方法，但是从未在形态计量学数据上测试其有效性。在这里，将PCA在形态学变化可视化任务上的性能与四种非线性技术进行比较：Sammon映射，Isomap，局部线性嵌入和Laplacian特征图。在针对各种模拟和经验数据集的成对距离的全局和局部保留的基础上，评估方法的性能。PCA的相对性能随数据集的变化分布，复杂性和大小而变化。总体而言，与PCA相比，非线性方法显示出优异的形态间微小差异保留。