Correlation Analysis — Feature Relationships

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.datasets import load_breast_cancer

cancer = load_breast_cancer()
df = pd.DataFrame(cancer.data, columns=cancer.feature_names)
df["target"] = cancer.target

# Select first 10 features for clarity
features_10 = list(cancer.feature_names[:10]) + ["target"]
df_10 = df[features_10]

# PEARSON CORRELATION MATRIX
corr_matrix = df_10.corr(method="pearson")

fig, axes = plt.subplots(1, 2, figsize=(18, 7))

# Full heatmap
mask = np.triu(np.ones_like(corr_matrix, dtype=bool))  # upper triangle mask
sns.heatmap(
    corr_matrix, ax=axes[0], mask=mask,
    annot=True, fmt=".2f", cmap="RdYlGn", center=0,
    vmin=-1, vmax=1, linewidths=0.5,
    cbar_kws={"label": "Pearson Correlation"},
)
axes[0].set_title("Feature Correlation Matrix\n(lower triangle only)")

# Feature-target correlation bar chart
target_corr = corr_matrix["target"].drop("target").sort_values()
colors = ["tomato" if v < 0 else "steelblue" for v in target_corr]
target_corr.plot(kind="barh", ax=axes[1], color=colors)
axes[1].axvline(0, color="black", linewidth=0.8)
axes[1].set_title("Correlation with Target")
axes[1].set_xlabel("Pearson Correlation")

plt.tight_layout()
plt.savefig("correlations.png", dpi=100, bbox_inches="tight")
plt.show()

# IDENTIFY HIGHLY CORRELATED FEATURE PAIRS (potential redundancy)
print("Highly correlated feature pairs (|r| > 0.85):")
high_corr = []
for i in range(len(corr_matrix.columns)):
    for j in range(i+1, len(corr_matrix.columns)):
        r = corr_matrix.iloc[i, j]
        if abs(r) > 0.85 and corr_matrix.columns[i] != "target":
            high_corr.append((corr_matrix.columns[i], corr_matrix.columns[j], round(r, 3)))
            
for feat1, feat2, r in sorted(high_corr, key=lambda x: abs(x[2]), reverse=True):
    print(f"  {feat1:20s} <-> {feat2:20s}: r = {r:+.3f}")

# SPEARMAN CORRELATION -- handles non-linear monotonic relationships
spearman_corr = df_10.corr(method="spearman")
target_spearman = spearman_corr["target"].drop("target").sort_values()
print("\nTop 5 features by Spearman correlation with target:")
print(target_spearman.abs().sort_values(ascending=False).head(5).round(3))