Visualizing Explained Variance and Component Loadings

              
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import numpy as np
import pandas as pd
from sklearn.datasets import load_iris
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
import matplotlib.pyplot as plt
import seaborn as sns

# Load the Iris dataset
data = load_iris()
X = data.data
feature_names = data.feature_names

# Standardize features (important for PCA)
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)

# Apply PCA to reduce to 2 components
pca = PCA(n_components=2)
X_pca = pca.fit_transform(X_scaled)

# Plot explained variance ratio
plt.figure(figsize=(6,4))
plt.bar(range(1, len(pca.explained_variance_ratio_)+1), pca.explained_variance_ratio_, alpha=0.7)
plt.ylabel('Explained Variance Ratio')
plt.xlabel('Principal Component')
plt.title('Explained Variance by Principal Components')
plt.show()

# Display component loadings as a heatmap
loadings = pd.DataFrame(pca.components_.T, columns=['PC1', 'PC2'], index=feature_names)
plt.figure(figsize=(6,4))
sns.heatmap(loadings, annot=True, cmap='coolwarm')
plt.title('Principal Component Loadings')
plt.show()