Dimensionality reduction is an important technique in surrogate modeling and machine learning. In this article, we propose a supervised dimensionality reduction method, “least squares regression principal component analysis” (LSR-PCA), applicable to both classification and regression problems. To show the efficacy of this method, we present different examples in visualization, classification, and regression problems, comparing it with several state-of-the-art dimensionality reduction methods. Finally, we present a kernel version of LSR-PCA for problems where the inputs are correlated nonlinearly. The examples demonstrate that LSR-PCA can be a competitive dimensionality reduction method.

中文翻译：

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最小二乘回归主成分分析：一种有监督的降维方法

降维是代理建模和机器学习中的一项重要技术。在本文中，我们提出了一种有监督的降维方法，“最小二乘回归主成分分析”（LSR-PCA），适用于分类和回归问题。为了展示这种方法的有效性，我们展示了可视化、分类和回归问题中的不同示例，并将其与几种最先进的降维方法进行了比较。最后，我们针对输入非线性相关的问题提出了 LSR-PCA 的内核版本。这些例子表明 LSR-PCA 可以是一种有竞争力的降维方法。