[学习资料] 300论坛币请问主成分分析与topsis的异同 [推广有奖]

不同点：topsis，主要用于方案比较，包含正负效应；主成分主要用于抽取主要的因子，简化变量个数。
相同点：都是一种简化数据的方式。
附件有简要介绍其过程，供参考。

Principal component analysis (PCA) is a mathematical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. The number of principal components is less than or equal to the number of original variables. This transformation is defined in such a way that the first principal component has the largest possible variance (that is, accounts for as much of the variability in the data as possible), and each succeeding component in turn has the highest variance possible under the constraint that it be orthogonal to (i.e., uncorrelated with) the preceding components.

TOPSIS METHOD T echnique of O rder P reference by S imilarity to I deal S olution This method considers three types of attributes or criteria Qualitative benefit attributes/criteria Quantitative benefit attributes Cost attributes or criteria
TOPSIS METHOD In this method two artificial alternatives are hypothesized : Ideal alternative : the one which has the best level for all attributes considered. Negative ideal alternative : the one which has the worst attribute values. TOPSIS selects the alternative that is the closest to the ideal solution and farthest from negative ideal alternative.
Input to TOPSIS TOPSIS assumes that we have m alternatives (options) and n attributes/criteria and we have the score of each option with respect to each criterion. Let x ij score of option i with respect to criterion j We have a matrix X = (x ij ) m  n matrix. Let J be the set of benefit attributes or criteria (more is better) Let J ' be the set of negative attributes or criteria (less is better)

谢谢高手，我下载后先学习一下，不懂再请教！！

很感兴趣。先占个座

其实他们说的不对。说穿了，PCA实际是多个指标的线性组合，而topsis法是非线性组合。
共同点：都可以用于多指标的综合评价
此外，topsis主要用于样本数量比较少的场合，而PCA必须是大样本，国外通常要求，样本数量是指标个数的3~5倍以上，或者至少50个样本以上。

请问如果某个方案里，所有指标都是最小的，那算出来的结果不都是0吗？？？？？结果可以为0吗？

https://bbs.pinggu.org/thread-10814157-1-1.html