Question

如何在Python的PCA中创建相关矩阵？下面，我通过pca.components_创建了特征向量载荷的DataFrame，但是我不知道如何创建实际的相关矩阵（即这些载荷与主分量之间的相关性）。有什么线索吗？

此外，我已经意识到许多这些特征向量加载在Python中都是负数。我正在尝试复制在Stata中进行的一项研究，据推测，当Stata相关性为正时，Python加载为负（请参阅我尝试在Python中复制的相关矩阵图）。这只是我已经注意到的-这是怎么回事？

Stata-Created Correlation Matrix

谢谢。

import pandas as pd
import numpy as np
import datetime as dt
import matplotlib.pyplot as plt
from dateutil.relativedelta import relativedelta
import blpinterface.blp_interface as blp
from scipy.stats import zscore
from sklearn.decomposition import PCA

#Set dates for analysis
startDate = "20000101"

#Construct tickers for analysis
tickers = ["USGG2YR Index", "USGG5YR Index", "USGG10YR Index", "USGG30YR Index", "USGGT10Y Index", ".30YREAL Index",
       "USGGBE10 Index", "USGGBE30 Index", ".RATEVOL1 Index", ".RATEVOL2 Index", "SPX Index", "S5INDU Index", "S5CONS Index", "VIX Index",
       ".DMFX Index", ".EMFX Index", "CL1 Comdty", "HG1 Comdty", "XAU Curncy"]

#Begin dataframe construction
mgr = blp.BLPInterface()

df = mgr.historicalRequest(tickers, "PX_LAST", startDate, "20160317")
df = df.dropna()
df = df.apply(zscore)

#Conduct PCA analysis
pca=PCA(n_components=3)
pca.fit(df) #Estimates the eigenvectors of the dataframe with 18x variables for data dating back to 2000
print(pd.DataFrame(pca.components_, columns=tickersclean, index=["PC1", "PC2", "PC3"]).transpose()) #Eigenvectors with loadings, sorted from highest explained variance to lowest
print(pca.explained_variance_) #Eigenvalues (sum of squares of the distance between the projected data points and the origin along the eigenvector)
print(pca.explained_variance_ratio_) #Explained variance ratio (i.e. how much of the change in the variables in the time series is explained by change in the respective principal component); eigenvalue/(n variables)

#Project data onto the above loadings for each row in the time series
outputpca = pd.DataFrame(pca.transform(df), columns=['PCA%i' % i for i in range(3)], index=df.index)
outputpca.columns = ["PC1", "PC2", "PC3"]
print(outputpca) #Principal component time series, projecting the data onto the above loadings; this is the sum product of the data and the eigenvector loadings for all three PCs for each row
outputpca.plot(title="Principal Components")
plt.show()

Answer 1

您可以使用numpy模块中存在的相关性。示例：

cor_mat1 = np.corrcoef(X_std.T)
eig_vals, eig_vecs = np.linalg.eig(cor_mat1)
print('Eigenvectors \n%s' %eig_vecs)
print('\nEigenvalues \n%s' %eig_vals)

此link提出了在PCA中使用相关矩阵的应用程序。

您如何在Python的PCA中创建相关矩阵？

1 个答案: