基于连续优化的线性降维模型最佳子集解路径
Best Subset Solution Path for Linear Dimension Reduction Models using Continuous Optimization
AI总结：
本文针对高维数据中主成分分析和偏最小二乘的变量选择与可解释性问题，提出将最佳子集解路径方法与连续优化算法相结合，并通过模拟和两个真实数据集验证了方法的有效性。
摘要：
在监督学习和无监督学习中，最佳变量的选择是一个具有挑战性的问题，尤其是在变量数量通常远大于观测数量的高维情境下。本文聚焦于两种多元统计方法：主成分分析（principal components analysis）和偏最小二乘（partial least squares）。这两种方法都是流行的线性降维方法，在基因组学、生物学、环境科学和工程等多个领域有着广泛的应用。特别地，这些方法构建主成分，即由所有原始变量组合而成的新变量。主成分的一个主要缺点是当变量数量很大时难以解释它们。为了从最相关的变量中定义主成分，我们提出将最佳子集解路径（best subset solution path）方法引入主成分分析和偏最小二乘框架中。我们通过利用一种用于最佳子集解路径的连续优化算法，提供了一种新的替代方案。实证研究表明，我们的方法在提供最佳子集解路径方面具有有效性。通过分析两个真实数据集，进一步展示了我们算法的应用。第一个数据集使用主成分分析进行分析，而第二个数据集的分析基于偏最小二乘框架。
英文摘要：
The selection of best variables is a challenging problem in supervised and unsupervised learning, especially in high dimensional contexts where the number of variables is usually much larger than the number of observations. In this paper, we focus on two multivariate statistical methods: principal components analysis and partial least squares. Both approaches are popular linear dimension-reduction methods with numerous applications in several fields including in genomics, biology, environmental science, and engineering. In particular, these approaches build principal components, new variables that are combinations of all the original variables. A main drawback of principal components is the difficulty to interpret them when the number of variables is large. To define principal components from the most relevant variables, we propose to cast the best subset solution path method into principal component analysis and partial least square frameworks. We offer a new alternative by exploiting a continuous optimization algorithm for best subset solution path. Empirical studies show the efficacy of our approach for providing the best subset solution path. The usage of our algorithm is further exposed through the analysis of two real datasets. The first dataset is analyzed using the principle component analysis while the analysis of the second dataset is based on partial least square framework.
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