silhouette_k.png

def fig_silhouette_k(X: np.ndarray) -> None:
    """Bar chart of silhouette scores for k = 2..8, plus inertia on twin axis."""
    k_values = list(range(2, 9))
    silhouettes, inertias = [], []

    for k in k_values:
        km = KMeans(n_clusters=k, random_state=SEED, n_init=10)
        labels = km.fit_predict(X)
        silhouettes.append(silhouette_score(X, labels))
        inertias.append(km.inertia_)

    fig, ax1 = plt.subplots(figsize=(7, 4))

    bars = ax1.bar(k_values, silhouettes, color=PRIMARY, alpha=0.85, width=0.6,
                   label="Silhouettenkoeffizient")
    # Highlight the best k
    best_idx = int(np.argmax(silhouettes))
    bars[best_idx].set_color(EVENT)
    ax1.set_xlabel("Anzahl Cluster k")
    ax1.set_ylabel("Silhouettenkoeffizient", color=PRIMARY)
    ax1.tick_params(axis="y", labelcolor=PRIMARY)
    ax1.set_ylim(0, max(silhouettes) * 1.25)
    ax1.set_xticks(k_values)

    ax2 = ax1.twinx()
    ax2.plot(k_values, inertias, color=SECONDARY, marker="o", lw=1.5,
             linestyle="--", label="Inertia (Elbow)")
    ax2.set_ylabel("Inertia", color=SECONDARY)
    ax2.tick_params(axis="y", labelcolor=SECONDARY)
    ax2.grid(False)

    ax1.set_title("Silhouettenkoeffizient und Inertia je k\n"
                  "(roter Balken = bestes k nach Silhouette)")
    # Combined legend
    lines1, labels1 = ax1.get_legend_handles_labels()
    lines2, labels2 = ax2.get_legend_handles_labels()
    ax1.legend(lines1 + lines2, labels1 + labels2, loc="upper right")

    save(fig, ASSETS / "silhouette_k.png")