翻译成英文，不要在线翻译。急需！主成分分析和因子分析比较摘 要 ： 主成分分析和因子分析都是从变量的方差—协方差结构入手，在尽可能多地保留原始信息的基础上，用少数新变量来解释原始变量的多元统计分析方法。本文就主成分分析和因子分析的异同进行比较。关键词 ： 主成分分析；因子分析；比较主成分分析和因子分析是多元统计方法中关系密切的两种方法,它们能解决经济、教育、科技、社会等领域中的问题。但是在进行综合分析时，常出现主成分分析与因子分析这两种方法运用混淆的错误。本文就主成分分析和因子分析的异同进行比较。一、 主成分分析 主成分分析又称主分量分析或主轴分析，由皮尔逊首先引入，后来被霍特林发展了。它是一种通过降维技术把多个变量 化为少数几个主成分的统计分析方法。这些主成分能够反映原 始变量的绝大部分信息，它们通常表示为原始变量的某种线性 组合并要求它们之间互不相关。主成分分析的一般目的是：1. 变量的降维；2.主成分的解释。主成分分析的应用主要有以下几种：(1)指标分类(变量分类)；(2)样品分类；(3)样品排 序或系统评估；(4)主成分回归；(5)主成分检验法。二、因子分析因子分析可看作是对主成分分析的推广和发展。它是研究相关阵或协方差阵的内部依赖关系，它将具有错综复杂关系的 变量综合为数量较少的几个因子，以再现原始变量与因子之间的相互关系，同时根据不同因子还可以对变量进行分类。因子分析的目的是，用几个不可观测的隐变量来解释原始变量间的协方差关系。三、两者的不同点两者的不同点：(1)主成分分析不能作为一个模型来描述，它只是通常的变量变换，而因子分析需要构造因子模型；(2)主成分分析中主成分的个数和变量个数相同，它是将一组具有相关关系的变量变换为一组互不相关的变量，而因子分析的目的是要尽可能少的公因子，以便构造一个结构简单的因子模型；(3)主成分分析是将主成分表示为原始变量的线性组合，而因子分析是将原始变量表示为公因子和特殊因子的线性组合，用假设的公因子来“解释”相关阵的内部依赖关系。四、两者的相同点时两者的相同点：(1)思想一致：都是降维的思想；(2)应用范围一致：都要求变量之间具有不完全的相关性；(3)数据处理过程一致：数据的无量纲化，求相关系数矩阵的特征值和特征向量，通过累计贡献率确定主成分个数、因子个数；(4)合成方法一致：都没有考虑原始变量之间的关系，直接用线性关系处理变量与主成分和因子之间的关系。

Principal component analysis and factor analysis of variance from the variables - start with the covariance structure, in as much as possible to retain the original information, based on variables with a small number of new variables to explain the original method of multivariate statistical analysis. In this paper, principal component analysis and factor analysis to compare the similarities and differences. Key words: principal component analysis; factor analysis; comparison Principal component analysis and factor analysis multivariate statistical methods is closely related to the two methods, they can solve the economic, educational, scientific, technological, and social issues in the field. Conducting comprehensive analysis, however, often the principal component analysis and factor analysis methods to use to confuse the two errors. In this paper, principal component analysis and factor analysis to compare the similarities and differences. First, principal component analysis Principal component analysis, also known as principal component analysis or principal axis analysis, first introduced by Pearson, and later developed by Hotelling. It is a dimensionality reduction technology through a number of variables into a few principal components method of statistical analysis. Principal component of these variables to reflect the vast majority of original information, they are usually stated as the original variables and demands a certain linear combination between them neatly. Principal component analysis of the general purpose is: 1. Dimensionality reduction of variables; 2. The interpretation of principal components. Application of principal component analysis are mainly the following: (1) indicators (classification variables); (2) sample classification; (3) sample order or system assessment; (4) principal component regression; (5) the principal component test . Second, factor analysis Factor analysis can be considered as a principal component analysis of the promotion and development. It is relevant to the study or covariance matrix of the internal dependencies, it will have integrated the complex relationship between the variables for the small number of several factors, in order to reproduce the original variables and the relationship between factors at the same time can also be based on different factors classification of variables. The purpose of factor analysis is that with a few non-observation of latent variables to explain the original variables the relationship between the covariance. Third, the differences between the two Two different points: (1) principal component analysis can not be used as a model to describe, it is just the normal transform variables, and factor analysis of the needs of structure-factor model; (2) principal component analysis of the number of principal components and variable number of the same, it is the relationship between a group of variables is transformed into a set of unrelated variables, and factor analysis is to common factor as small as possible in order to construct a simple factor model; (3) principal component principal component analysis is expressed as a linear combination of original variables, and factor analysis of the original variables are expressed as a common factor and a linear combination of special factors, the assumption that the common factor used to "explain" the relevant array of internal dependencies. Fourth, the same two points The same two points: (1) thinking: the idea of dimensionality reduction are; (2) application of the same: between demand variables associated incomplete; (3) data processing line: data of the non-dimensional and the correlation coefficient matrix for eigenvalues and eigenvectors, through a total contribution rate to determine the number of principal components, factor number; (4) synthesis of the same: do not consider the relationship between the original variables, the direct use of linear relations with the principal component variables and the relationship between factors.