more pca

doc/src/DimRed/Programs/PCAsimple.py

@@ -2,28 +2,47 @@ import numpy as np
 import pandas as pd
 from IPython.display import display
 import matplotlib.pyplot as plt
-from sklearn.model_selection import  train_test_split 
-from sklearn.preprocessing import MinMaxScaler, StandardScaler
 
-
-n = 10000
+n = 1000
 mean = (-1, 2)
 cov = [[4, 2], [2, 2]]
-print(cov)
 X = np.random.multivariate_normal(mean, cov, n)
-print(np.cov(X.T))
 
 df = pd.DataFrame(X)
 # Pandas does the centering for us
 df = df -df.mean()
-correlation_matrix = df.cov()
-print(correlation_matrix)
+print("Centered covariance with Pandas")
+covarianceX = df.cov()
+
+print(covarianceX)
 
 # we center it ourselves
 X_centered = X - X.mean(axis=0)
+print("Centered covariance using numpy")
 print(np.cov(X_centered.T))
-#print("test that we get the same as Pandas")
-#print(X_centered-X_train_scaled)
+# extract the relevant columns from the centered design matrix
+x = X_centered[:,[0]]
+y = X_centered[:,[1]]
+Cov = np.zeros((2,2))
+cov_xy = np.sum(x.T@y)/(n-1.0)
+cov_xx = np.sum(x.T@x)/(n-1.0)
+cov_yy = np.sum(y.T@y)/(n-1.0)
+
+Cov[0,0]= cov_xx
+Cov[1,1]= cov_yy
+Cov[0,1]= cov_xy
+Cov[1,0]= Cov[0,1]
+print("Centered covariance using own code")
+print(Cov)
+
+plt.plot(x, y, 'x')
+plt.axis('equal')
+plt.show()
+
+
+
+
+"""
 #Now we do an SVD
 U, s, V = np.linalg.svd(X_centered)
 c1 = V.T[:, 0]
@@ -38,6 +57,6 @@ print("Check that we get the same")
 print(X2D-X2Dsl)
 
 print(pca.components_.T[:, 0])
-
+"""