pca_scale_effect.png

def fig_pca_scale_effect() -> None:
    """Show the effect of scaling on PCA (Scale Dependency)."""
    df = load_cohort().merge(load_labs(), on="patient_id", how="left").dropna(subset=["alter", "kreatinin_mg_dl"])
    X_raw = df[["alter", "kreatinin_mg_dl"]].values

    # Left: Without scaling
    pca_raw = PCA(n_components=2, random_state=SEED)
    X_raw_2d = pca_raw.fit_transform(X_raw)

    # Right: With scaling
    scaler = StandardScaler()
    X_scaled = scaler.fit_transform(X_raw)
    pca_scaled = PCA(n_components=2, random_state=SEED)
    X_scaled_2d = pca_scaled.fit_transform(X_scaled)

    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4.5))

    # Without scaling scatter
    sc1 = ax1.scatter(X_raw_2d[:, 0], X_raw_2d[:, 1], c=X_raw[:, 1], cmap="coolwarm", alpha=0.7)
    ax1.set_xlabel("PC 1 (Dominiert vom Alter)")
    ax1.set_ylabel("PC 2")
    ax1.set_title("Ohne Standardisierung\n(Alter dominiert wegen großer Varianz)")
    fig.colorbar(sc1, ax=ax1, label="Kreatinin (mg/dl)")
    ax1.grid(True, linestyle=":", alpha=0.6)

    # With scaling scatter
    sc2 = ax2.scatter(X_scaled_2d[:, 0], X_scaled_2d[:, 1], c=X_raw[:, 1], cmap="coolwarm", alpha=0.7)
    ax2.set_xlabel("PC 1")
    ax2.set_ylabel("PC 2")
    ax2.set_title("Mit Standardisierung (StandardScaler)\n(Beide Merkmale tragen gleichwertig bei)")
    fig.colorbar(sc2, ax=ax2, label="Kreatinin (mg/dl)")
    ax2.grid(True, linestyle=":", alpha=0.6)

    plt.tight_layout()
    save(fig, ASSETS / "pca_scale_effect.png")