A radial dendrogram renders hierarchical clustering in a circular layout where the root node sits at the center and branches extend outward, with leaf nodes arranged around the circumference. This layout is a space-efficient alternative to linear dendrograms for large hierarchies, making it well-suited for datasets with hundreds of leaves. Branch lengths are proportional to distance or dissimilarity, preserving the quantitative interpretation of cluster merges.
""" anyplot.ai
dendrogram-radial: Radial Dendrogram
Library: bokeh 3.9.0 | Python 3.13.13
Quality: 84/100 | Created: 2026-05-14
"""
import math
import os
import sys
import time
from pathlib import Path
# Prevent the local bokeh.py from shadowing the installed bokeh package
sys.path = [p for p in sys.path if os.path.abspath(p) != os.path.dirname(os.path.abspath(__file__))]
import numpy as np
from bokeh.io import output_file, save
from bokeh.models import ColumnDataSource, LabelSet, Legend, LegendItem
from bokeh.plotting import figure
from scipy.cluster.hierarchy import leaves_list, linkage
from selenium import webdriver
from selenium.webdriver.chrome.options import Options
# Theme tokens
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
IMPRINT = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD"]
# Data — gene expression clustering scenario (40 genes, 4 clusters)
np.random.seed(42)
n_genes = 40
n_clusters = 4
cluster_size = n_genes // n_clusters
gene_names = [f"Gene-{i:02d}" for i in range(n_genes)]
cluster_centers = np.array(
[
[2.0, 0.5, -1.0, -0.5, 1.5, -0.8],
[-1.5, 2.0, 0.8, -1.2, 0.3, 1.5],
[0.5, -1.5, 2.0, 1.0, -1.0, 0.5],
[-0.8, 0.5, -1.5, 2.0, -0.5, -1.2],
]
)
expression_data = np.vstack(
[cluster_centers[c] + np.random.normal(0, 0.3, (cluster_size, 6)) for c in range(n_clusters)]
)
true_clusters = np.repeat(np.arange(n_clusters), cluster_size)
Z = linkage(expression_data, method="ward")
ordered_leaves = leaves_list(Z)
# Build radial dendrogram geometry
n_leaves = n_genes
angles = {i: 2 * math.pi * i / n_leaves for i in range(n_leaves)}
leaf_angles = {ordered_leaves[i]: angles[i] for i in range(n_leaves)}
# node_radius: leaves at 1.0, internal nodes scaled inversely by merge distance
max_dist = Z[-1, 2]
node_radius = dict.fromkeys(range(n_leaves), 1.0)
internal_id = n_leaves
for row in Z:
node_radius[internal_id] = 1.0 - row[2] / max_dist
internal_id += 1
# Angle for each internal node: mean of child angles
node_angle = {i: leaf_angles[i] for i in range(n_leaves)}
internal_id = n_leaves
for row in Z:
left, right = int(row[0]), int(row[1])
node_angle[internal_id] = (node_angle[left] + node_angle[right]) / 2
internal_id += 1
def polar_to_xy(r, theta):
return r * math.cos(theta), r * math.sin(theta)
def get_leaf_cluster(node_id):
if node_id < n_leaves:
return int(true_clusters[node_id])
stack = [node_id]
cluster_set = set()
while stack:
nid = stack.pop()
if nid < n_leaves:
cluster_set.add(int(true_clusters[nid]))
else:
row = Z[nid - n_leaves]
stack.extend([int(row[0]), int(row[1])])
return cluster_set.pop() if len(cluster_set) == 1 else -1
# Build branch segments
seg_xs, seg_ys, seg_colors = [], [], []
internal_id = n_leaves
for row in Z:
left, right = int(row[0]), int(row[1])
parent_id = internal_id
r_parent = node_radius[parent_id]
a_parent = node_angle[parent_id]
a_left = node_angle[left]
a_right = node_angle[right]
cl = get_leaf_cluster(left)
cr = get_leaf_cluster(right)
cp = get_leaf_cluster(parent_id)
color_left = IMPRINT[cl] if cl >= 0 else INK_SOFT
color_right = IMPRINT[cr] if cr >= 0 else INK_SOFT
color_arc = IMPRINT[cp] if cp >= 0 else INK_SOFT
px_l, py_l = polar_to_xy(r_parent, a_left)
cx_l, cy_l = polar_to_xy(node_radius[left], a_left)
seg_xs.append([px_l, cx_l])
seg_ys.append([py_l, cy_l])
seg_colors.append(color_left)
px_r, py_r = polar_to_xy(r_parent, a_right)
cx_r, cy_r = polar_to_xy(node_radius[right], a_right)
seg_xs.append([px_r, cx_r])
seg_ys.append([py_r, cy_r])
seg_colors.append(color_right)
n_arc = max(3, int(abs(a_right - a_left) / (2 * math.pi) * 60))
arc_angles = np.linspace(a_left, a_right, n_arc)
seg_xs.append([r_parent * math.cos(a) for a in arc_angles])
seg_ys.append([r_parent * math.sin(a) for a in arc_angles])
seg_colors.append(color_arc)
internal_id += 1
# Leaf label positions
label_r = 1.08
label_xs, label_ys, label_texts = [], [], []
for i, leaf_idx in enumerate(ordered_leaves):
a = angles[i]
lx, ly = polar_to_xy(label_r, a)
label_xs.append(lx)
label_ys.append(ly)
label_texts.append(gene_names[leaf_idx])
# Cluster color dots at leaf tips
dot_xs, dot_ys, dot_colors = [], [], []
for i, leaf_idx in enumerate(ordered_leaves):
a = angles[i]
dx, dy = polar_to_xy(1.03, a)
dot_xs.append(dx)
dot_ys.append(dy)
dot_colors.append(IMPRINT[int(true_clusters[leaf_idx])])
# Plot
W, H = 2700, 2700
p = figure(
width=W,
height=H,
title="dendrogram-radial · bokeh · anyplot.ai",
x_range=(-1.35, 1.35),
y_range=(-1.35, 1.35),
toolbar_location=None,
match_aspect=True,
)
p.background_fill_color = PAGE_BG
p.border_fill_color = PAGE_BG
p.outline_line_color = None
p.xgrid.grid_line_color = None
p.ygrid.grid_line_color = None
p.xaxis.visible = False
p.yaxis.visible = False
for xs, ys, color in zip(seg_xs, seg_ys, seg_colors, strict=False):
p.line(xs, ys, line_color=color, line_width=2.5, line_alpha=0.85)
p.scatter(x=dot_xs, y=dot_ys, size=10, color=dot_colors, line_color=None, alpha=0.9)
label_source = ColumnDataSource({"x": label_xs, "y": label_ys, "text": label_texts})
labels_set = LabelSet(
x="x",
y="y",
text="text",
text_font_size="11pt",
text_color=INK_SOFT,
text_align="center",
text_baseline="middle",
source=label_source,
)
p.add_layout(labels_set)
legend_items = []
for c_idx in range(n_clusters):
r = p.scatter([], [], size=18, color=IMPRINT[c_idx], line_color=None)
legend_items.append(LegendItem(label=f"Cluster {c_idx + 1}", renderers=[r]))
legend = Legend(
items=legend_items,
location="bottom_right",
background_fill_color=ELEVATED_BG,
border_line_color=INK_SOFT,
label_text_color=INK_SOFT,
label_text_font_size="14pt",
glyph_width=20,
glyph_height=20,
)
p.add_layout(legend)
p.title.text_font_size = "24pt"
p.title.text_color = INK
p.title.align = "center"
# Save
output_file(f"plot-{THEME}.html")
save(p)
opts = Options()
for arg in (
"--headless=new",
"--no-sandbox",
"--disable-dev-shm-usage",
"--disable-gpu",
f"--window-size={W},{H}",
"--hide-scrollbars",
):
opts.add_argument(arg)
driver = webdriver.Chrome(options=opts)
driver.set_window_size(W, H)
driver.get(f"file://{Path(f'plot-{THEME}.html').resolve()}")
time.sleep(3)
driver.save_screenshot(f"plot-{THEME}.png")
driver.quit()
Part of Radial Dendrogram on anyplot.ai.