[Feature]: Beauty Score

[sepandhaghighi]

Describe the feature you want to add

Add beauty score to Samila.

Describe your proposed solution

def beauty_score(x_vals, y_vals, bins=100):
    if len(x_vals) == 0 or len(y_vals) == 0:
        return 0.0
    
    # Basic sanity checks
    if np.any(np.isnan(x_vals)) or np.any(np.isnan(y_vals)):
        return 0.0
    if np.any(np.isinf(x_vals)) or np.any(np.isinf(y_vals)):
        return 0.0

    # Check spread (avoid too flat)
    std_x = np.std(x_vals)
    std_y = np.std(y_vals)
    if std_x < 1e-3 or std_y < 1e-3:
        return 0.0

    # Check diversity (avoid identical points)
    unique_ratio = len(set(np.round(x_vals, 4))) / len(x_vals)
    if unique_ratio < 0.05:
        return 0.0

    # Check entropy of x and y (avoid regular grids)
    hx, _ = np.histogram(x_vals, bins=bins, density=True)
    hy, _ = np.histogram(y_vals, bins=bins, density=True)
    ent_x = entropy(hx + 1e-9)
    ent_y = entropy(hy + 1e-9)

    # Normalize entropy to 0–1 (approximate)
    max_entropy = np.log(bins)
    ent_x /= max_entropy
    ent_y /= max_entropy

    # Combine all
    score = (
        0.2 * (std_x + std_y) +    # encourage spread
        0.3 * unique_ratio +       # encourage diversity
        0.5 * (ent_x + ent_y) / 2  # encourage organic layout
    )

    return min(max(score, 0.0), 1.0)

Describe alternatives you've considered, if relevant

No response

Additional context

No response