Impara Visualizing Explained Variance and Component Loadings

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After fitting PCA, it's important to understand how much information (variance) each principal component captures. The explained variance ratio tells you this. You can also inspect the component loadings to see how original features contribute to each principal component.


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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()

The bar plot shows the proportion of variance explained by each principal component. The heatmap displays the loadings, which indicate how much each original feature contributes to each principal component. Large absolute values mean a feature is important for that component.

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