PCA

# Import packages
import pandas as pd 
import numpy as np
import matplotlib.pyplot as plt
from sklearn.decomposition import PCA
# n_components == min(n_samples, n_features)
from sklearn.preprocessing import StandardScaler
%matplotlib inline

# Import data and standardize it
url = "https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data"
df = pd.read_csv(url, names=['sepal length','sepal width','petal length','petal width','target'])

from sklearn.preprocessing import StandardScaler
features = ['sepal length', 'sepal width', 'petal length', 'petal width']
x = df.loc[:, features].values
y = df.loc[:,['target']].values
#x = StandardScaler().fit_transform(x)

# Standardize data by subtracting mean
mean_vec = np.mean(x, axis=0)
mean_vec.shape
x.shape
x1 = x - mean_vec
pd.DataFrame(data = x1, columns = features).head()

# Determine covariance matrix
A = np.cov(x.T)
A.shape
print(A)

# Find eigenvalues and eigenvectors
e, v = np.linalg.eig(A)
print(e)

# Shows variance of eigenvalues
variance = (e)/e.sum()
print(variance)

# Sort eigenvalues and eigenvectors
idx = np.argsort(e)[::-1]
e = e[idx]
e = np.real_if_close(e)
v = v[:, idx]
print(e)
print(v)