# What can we learn from PCA on non linear data?

Suppose we have dataset with 10 features which are not linear:

import numpy as np
from sklearn.decomposition import PCA
import matplotlib
import matplotlib.pyplot as plt

v1 = np.random.rand(100)

print (type(v1))

v2 = 2**v1
v3 = 3**v1 + np.matmul(v1, v1)
v4 = 4**v1 + np.matmul(v2, v3)
v5 = 5**v1 + np.matmul(v1, v3)
v6 = 6**v1 + np.matmul(v1, v4)
v7 = 7**v1 + np.matmul(v2, v2)
v8 = 8**v1 + np.matmul(v4, v5)
v9 = 9**v1
v10 = 10**v1

v = [v1,v2, v3, v4,v5, v6,v7, v8, v9,v10]

pca = PCA()
pca.fit(v)
pca.explained_variance_ratio_

PC_values = np.arange(pca.n_components_) + 1
plt.plot(PC_values, pca.explained_variance_ratio_, 'ro-', linewidth=2)
plt.title('Scree Plot')
plt.xlabel('Principal Component')
plt.ylabel('Proportion of Variance Explained')
plt.show() • I know that PCA used to find linear correlation. But what can we learn from that example ?
• Can we use the PCA results and use only the first component of the PCA to train-predict our model ?
• Does the result show here are valid (correct for further processing) ? 