摘要
主成分分析是一种常用的简化数据集的技术,也是一种应用广泛的多元统计分析方法。在各高校开设的多门课程中,主成分分析的理论都是重点内容。但在教学过程中,我们发现其理论与实际应用间还有很多值得理解、挖掘和实践验证的地方。本文针对主成分分析过程进行回顾,并主要探讨其几个应用情况,即基于主成分分析的数据降维、基于主成分分析的综合评价、基于主成分分析的关键特征确定、基于主成分分析的样本聚类等几个方面。我们详细梳理并部分推导和补充每个应用的理论过程,整理各种应用在一些文献里的使用场景,给出我们对各个应用的R语言实践代码和相应分析等。这些应用的理论过程和R语言实践,有助于对主成分分析进行深刻理解和融会贯通,为主成分分析的学习和使用提供重要的参考。
Principal component analysis is a commonly used technology to simplify data sets, it is also one kind of widely used methods of multivariate statistical analysis. In many courses offered by colleges, the theory of principal component analysis is a key content. But in the teaching process, we find that there are a lot of things which are worth understanding, exploring and verifying by practice be-tween the theory and the practical applications. This paper reviews the process of principal com-ponent analysis, and mainly discusses about its several applications, namely the data dimension reduction based on principal component analysis, comprehensive evaluation based on principal component analysis, determination of the key features based on principal component analysis, samples clustering based on principal component analysis. We detailedly reorganize, partially derivate and complete the theoretical process of each application, organize some usage scenario of applications in literature, give codes of R language practice and the corresponding analysis for each application. The theoretical process and R language practice of these applications are helpful for some researchers to further understand and master the principal component analysis, and also provide important reference for the initial learner to learn and use it.
出处
《数据挖掘》
2021年第4期203-216,共14页
Hans Journal of Data Mining
