主成分分析和按变量进行聚类分析

shiyiming

请问主成分分析和按变量进行聚类分析，这两种分析之间的区别是什么？

shiyiming

Hey, it is not a fair question.  The principal component analysis and classification are quite different from each other, but you have to do your homework.  Basically, a principal component is a linear combination of several factors, and the impact is measured by the characteristic values associated with each combination; while the classification deals with one or several individual factors without considering the linear combinations.  I took multivariate analysis long time ago, this statement came from my memory, I am not 100 percent sure.

shiyiming

主成分分析:
对多个变量进行降纬,把几个变量线形组合为一个变量,同时使丧失的信息最少,
对于一些有多重共线性的模型很有帮助(把相关性很高的变量组合成一个变量,避免
多重共线性),

聚类:
聚类的思想是对集合进行划分(分类),划分的标准是类内差距小,类间差距大,一个类往往是几个指标共同定义的.
总之.你只要记住一点:
主成分用来降纬,聚类用来分类(cluster)(注意,不是classification,类在分前未知)

shiyiming

[quote="claudchen76":dd7f1]主成分分析:
对多个变量进行降纬,把几个变量线形组合为一个变量,同时使丧失的信息最少,
对于一些有多重共线性的模型很有帮助(把相关性很高的变量组合成一个变量,避免
多重共线性),

聚类:
聚类的思想是对集合进行划分(分类),划分的标准是类内差距小,类间差距大,一个类往往是几个指标共同定义的.
总之.你只要记住一点:
主成分用来降纬,聚类用来分类(cluster)(注意,不是classification,类在分前未知)[/quote:dd7f1]


主成分分析只是通常的变量变换，而且只是原变量的线形组合，分量的个数与变量的个数相同，一般降维的方法基本用因子分析，而不是主成分分析。

shiyiming

hey, r u one of our team? if yes, u should ask me in person, it is easier for me to explain to you in details.

any way, in summary

For factor based clustering
* Pros: free of multi collinearity
* Cons: hard to implement, because more variables in final model and hard to explain the factor meaning to business. Sometimes may come out meaningless results

For variable based clustering
*Pros: easy to understand and easy to implement
*Cons: may suffer from multi collinearity

Personally, I will not say factor based clustering is better or variable based clustering is better.  The quality of the analysis depends on a lot of factors. Among these factors, techniques comprise for only a very small part.

shiyiming

[quote="amiao":81e8d]主成分分析只是通常的变量变换，而且只是原变量的线形组合，分量的个数与变量的个数相同，一般降维的方法基本用因子分析，而不是主成分分析。[/quote:81e8d]
这种说法第一次听说，不过细想下，确实是这样的！不过进行因子分析之前还要检验是否符合进行因子分析的条件，不符合的话只有进行主成分分析了！