Radial Single Linkage Light

import matplotlib.pyplot as plt
import numpy as np
from scipy.cluster.hierarchy import dendrogram, linkage, set_link_color_palette

np.random.seed(258)

n = 14
labels = [f'X{i}' for i in range(1, n+1)]
data = np.random.rand(n, 5) * 50
Z = linkage(data, method='single')

fig_temp, ax_temp = plt.subplots()
set_link_color_palette(['#F527B0', '#27D3F5', '#6CF527', '#F5B027', '#4927F5'])
dn = dendrogram(Z, labels=labels, no_plot=False, color_threshold=0.5*max(Z[:,2]),
                above_threshold_color='#9ca3af', ax=ax_temp)
plt.close(fig_temp)

icoord = np.array(dn['icoord'])
dcoord = np.array(dn['dcoord'])
colors = dn['color_list']

x_min, x_max = icoord.min(), icoord.max()
y_max = dcoord.max()

def to_polar(x, y):
    theta = (x - x_min) / (x_max - x_min) * 2 * np.pi * 0.9 + np.pi * 0.05
    r = y / y_max * 0.5 + 0.45
    return theta, r

fig, ax = plt.subplots(figsize=(10, 10), subplot_kw={'projection': 'polar'}, facecolor='#ffffff')
ax.set_facecolor('#ffffff')

# Radial grid lines
for angle in np.linspace(0, 2*np.pi, 13)[:-1]:
    ax.plot([angle, angle], [0.4, 0.98], color='#e5e7eb', linewidth=0.8, alpha=0.6)

for ic, dc, color in zip(icoord, dcoord, colors):
    thetas, rs = [], []
    for x, y in zip(ic, dc):
        t, r = to_polar(x, y)
        thetas.append(t)
        rs.append(r)
    
    ax.plot([thetas[0], thetas[1]], [rs[0], rs[1]], color=color, linewidth=2.5, alpha=0.9)
    ax.plot([thetas[2], thetas[3]], [rs[2], rs[3]], color=color, linewidth=2.5, alpha=0.9)
    if thetas[1] != thetas[2]:
        arc_thetas = np.linspace(min(thetas[1], thetas[2]), max(thetas[1], thetas[2]), 40)
        ax.plot(arc_thetas, [rs[1]]*len(arc_thetas), color=color, linewidth=2.5, alpha=0.9)

leaf_positions = np.linspace(x_min, x_max, n)
for i, (pos, label) in enumerate(zip(leaf_positions, dn['ivl'])):
    theta, _ = to_polar(pos, 0)
    rotation = np.degrees(theta) - 90 if np.pi/2 < theta < 3*np.pi/2 else np.degrees(theta) + 90
    ha = 'right' if np.pi/2 < theta < 3*np.pi/2 else 'left'
    ax.text(theta, 0.32, label, ha=ha, va='center', fontsize=9, color='#F527B0',
            rotation=rotation, rotation_mode='anchor', fontweight='bold')
    
    color = ['#F527B0', '#27D3F5', '#6CF527', '#F5B027', '#4927F5'][i % 5]
    ax.scatter(theta, 0.45, c=color, s=55, zorder=5, edgecolor='#ffffff', linewidth=1)

ax.set_ylim(0, 1.02)
ax.set_yticklabels([])
ax.set_xticklabels([])
ax.spines['polar'].set_visible(False)
ax.grid(False)

ax.set_title('Single Linkage - Radial View', fontsize=14, color='#1f2937', fontweight='bold', y=1.08)

plt.tight_layout()
plt.show()