In many fields of science and engineering, we frequently encounter experiments or simulations datasets that describe the behavior of complex systems and uncovering human interpretable patterns between their inputs and outputs via exploratory data analysis is essential for building intuition and facilitating discovery. Often, we resort to 2D embeddings for examining these high-dimensional relationships (e.g. dimensionality reduction). However, most existing embedding methods treat the dimensions as coordinates for samples in a high-dimensional space, which fail to capture the potential functional relationships, and the few methods that do take function into consideration either only focus on linear patterns or produce non-linear embeddings that are hard to interpret. To address these challenges, we proposed function preserving projections (FPP), which construct 2D linear embeddings optimized to reveal interpretable yet potentially non-linear patterns between the domain and the ra...

中文翻译：

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通过功能保留预测发现高维科学数据中可解释的关系

在科学和工程学的许多领域，我们经常遇到描述复杂系统行为的实验或模拟数据集，并且通过探索性数据分析来揭示其输入和输出之间的人类可解释模式对于建立直觉和促进发现至关重要。通常，我们求助于2D嵌入来检查这些高维关系（例如，降维）。但是，大多数现有的嵌入方法都将维数作为高维空间中样本的坐标，无法捕获潜在的函数关系，并且很少考虑功能的方法要么只关注线性模式，要么产生非线性难以解释的嵌入。为了应对这些挑战，我们提出了功能保留预测（FPP），