使用 sklearn 的因子载荷 [英] Factor Loadings using sklearn

问题描述

我想要python中各个变量和主成分之间的相关性.我在 sklearn 中使用 PCA.我不明白分解数据后如何实现加载矩阵?我的代码在这里.

I want the correlations between individual variables and principal components in python. I am using PCA in sklearn. I don't understand how can I achieve the loading matrix after I have decomposed my data? My code is here.

iris = load_iris()
data, y = iris.data, iris.target
pca = PCA(n_components=2)
transformed_data = pca.fit(data).transform(data)
eigenValues = pca.explained_variance_ratio_

http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html 没有提到如何实现这一点.

http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html doesn't mention how this can be achieved.

推荐答案

我认为 @RickardSjogren 是在描述特征向量，而 @BigPanda 是在给出载荷.有一个很大的区别:Loadings vs eigenvectors在 PCA 中:何时使用一种或另一种?.

I think that @RickardSjogren is describing the eigenvectors, while @BigPanda is giving the loadings. There's a big difference: Loadings vs eigenvectors in PCA: when to use one or another?.

我创建了这个PCA类加载方法.

I created this PCA class with a loadings method.

加载，由 pca.components_ * np.sqrt(pca.explained_variance_) 给出，更类似于多元线性回归中的系数.我在这里不使用 .T 因为在上面链接的 PCA 类中，组件已经转置了.numpy.linalg.svd 产生 u, s, and vt，其中 vt 是 Hermetian 转置，所以你首先需要回到 v 和 vt.T.

Loadings, as given by pca.components_ * np.sqrt(pca.explained_variance_), are more analogous to coefficients in a multiple linear regression. I don't use .T here because in the PCA class linked above, the components are already transposed. numpy.linalg.svd produces u, s, and vt, where vt is the Hermetian transpose, so you first need to back into v with vt.T.

还有一个重要的细节:sklearn.PCA 中组件和加载的符号(正/负)可能与 R 等软件包不同.更多相关信息:

There is also one other important detail: the signs (positive/negative) on the components and loadings in sklearn.PCA may differ from packages such as R. More on that here:

在 sklearn.decomposition.PCA 中，为什么 components_ 是负的?.

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