[python] 基于matplotlib实现树形图的绘制

树形图Tree diagram (代码下载)

本文旨在描述如何使用Python实现基本的树形图。要实现这样的树形图,首先需要有一个数值矩阵。每一行代表一个实体(这里是一辆汽车)。每列都是描述汽车的变量。目标是将实体聚类以了解谁与谁有共同点。python下通过scipy中hierarchy.linkage进行聚类,hierarchy.dendrogram画树形图。参考文档:https://python-graph-gallery.com/dendrogram/
该章节主要内容有:

  1. 数据处理 data processing
  2. 基础树形图 basic dendrogram
  3. 自定义树形图 customised dendrogram
  4. 彩色树形图标签 color dendrogram labels

1. 数据处理 data processing

画树形图,往往第一列是数据实体名字,即物体种类。其他列分别为物体变量。

# 导入库
import pandas as pd
from matplotlib import pyplot as plt
from scipy.cluster import hierarchy
import numpy as np

# Import the mtcars dataset from the web + keep only numeric variables
url = 'https://python-graph-gallery.com/wp-content/uploads/mtcars.csv'
df = pd.read_csv(url)
df
model mpg cyl disp hp drat wt qsec vs am gear carb
0 Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
1 Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
2 Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
3 Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
4 Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2
5 Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1
6 Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4
7 Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
8 Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2
9 Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4
10 Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 0 4 4
11 Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3
12 Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 0 3 3
13 Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 0 3 3
14 Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4
15 Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 0 3 4
16 Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4
17 Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1
18 Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
19 Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
20 Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1
21 Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 0 3 2
22 AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 0 3 2
23 Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4
24 Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2
25 Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1
26 Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2
27 Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2
28 Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4
29 Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6
30 Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 1 5 8
31 Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2
# 通常获得数据表格需要将车名设置行标题,这里model代表车的类型
df = df.set_index('model')
df
mpg cyl disp hp drat wt qsec vs am gear carb
model
Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2
Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1
Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4
Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2
Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4
Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 0 4 4
Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3
Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 0 3 3
Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 0 3 3
Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4
Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 0 3 4
Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4
Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1
Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1
Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 0 3 2
AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 0 3 2
Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4
Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2
Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1
Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2
Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2
Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4
Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6
Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 1 5 8
Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2
# 同时需要删除行标索引的标题名
del df.index.name
df
mpg cyl disp hp drat wt qsec vs am gear carb
Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2
Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1
Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4
Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2
Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4
Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 0 4 4
Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3
Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 0 3 3
Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 0 3 3
Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4
Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 0 3 4
Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4
Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1
Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1
Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 0 3 2
AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 0 3 2
Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4
Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2
Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1
Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2
Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2
Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4
Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6
Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 1 5 8
Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2

2. 基础树形图 basic dendrogram

# 执行分层聚类
Z = hierarchy.linkage(df, 'ward')
# 函数原型如下:
# scipy.cluster.hierarchy.linkage(y, method='single', metric='euclidean', optimal_ordering=False)
# y输入矩阵,method聚类方法,metric距离计算方法。通常ward比较靠谱
# optimal_ordering重新排序链接矩阵,以使连续叶之间的距离最小,这样树形结构更为直观,但是计算速度变慢。
# 参数选择见:https://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.linkage.html
# Make the dendrogram
plt.title('Hierarchical Clustering Dendrogram')
plt.xlabel('sample index')
plt.ylabel('distance (Ward)')
# 画聚类图,常用参数labels设定横坐标下标,leaf_rotation标题旋转
# 详细使用见:https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.cluster.hierarchy.dendrogram.html
hierarchy.dendrogram(Z, labels=df.index, leaf_rotation=90);

[python] 基于matplotlib实现树形图的绘制_第1张图片

3. 自定义树形图 customised dendrogram

  • 叶标签 leaf label
  • 聚类簇数 number of clusters
  • 颜色 color
  • 截减 truncate
  • 方向 orientation
# 叶标签 leaf label
# Calculate the distance between each sample
Z = hierarchy.linkage(df, 'ward')
 
# Plot with Custom leaves
# 常用参数labels设定横坐标下标,leaf_rotation标题旋转,leaf_font_size设置字号
hierarchy.dendrogram(Z, leaf_rotation=90, leaf_font_size=8, labels=df.index);

[python] 基于matplotlib实现树形图的绘制_第2张图片

# 聚类簇数 number of clusters
# Calculate the distance between each sample
Z = hierarchy.linkage(df, 'ward')
 
# Control number of clusters in the plot + add horizontal line.
# color_threshold设定颜色阈值,小于olor_threshold根据簇节点为一簇
hierarchy.dendrogram(Z, color_threshold=240)
# 画水平线,y纵坐标,c颜色,lw线条粗细,linestyle线形
plt.axhline(y=240, c='grey', lw=1, linestyle='dashed');

[python] 基于matplotlib实现树形图的绘制_第3张图片

# 颜色 color
# Calculate the distance between each sample
Z = hierarchy.linkage(df, 'ward')

# Set the colour of the cluster here: 设置聚类颜色
hierarchy.set_link_color_palette(['#b30000','#996600', '#b30086'])
 
# Make the dendrogram and give the colour above threshold
# above_threshold_color设置color_threshold上方链接的颜色
hierarchy.dendrogram(Z, color_threshold=240, above_threshold_color='grey')
 
# Add horizontal line.
plt.axhline(y=240, c='grey', lw=1, linestyle='dashed');

[python] 基于matplotlib实现树形图的绘制_第4张图片

# 截减 truncate
# 原始观察矩阵很大时,树形图很难读取。截断用于压缩树形图。有几种模式:
# 1 None 不执行截断
# 2 lastp lastp设置叶子节点数,最底层节点数
# 3 level 根据level设置图中层最大数
# Calculate the distance between each sample
Z = hierarchy.linkage(df, 'ward')
  
# method 1: lastp
# you will have 4 leaf at the bottom of the plot  
hierarchy.dendrogram(Z, truncate_mode = 'lastp', p=4);

[python] 基于matplotlib实现树形图的绘制_第5张图片

# method 2: level
# No more than ``p`` levels of the dendrogram tree are displayed.
hierarchy.dendrogram(Z, truncate_mode = 'level', p=2);

[python] 基于matplotlib实现树形图的绘制_第6张图片

# 方向 orientation

# Calculate the distance between each sample
Z = hierarchy.linkage(df, 'ward')
 
# Orientation of the dendrogram
# 设置层次树的朝向,orientation可选"top", "left", "bottom", "right",默认top
hierarchy.dendrogram(Z, orientation="right", labels=df.index);

[python] 基于matplotlib实现树形图的绘制_第7张图片

# Orientation of the dendrogram
hierarchy.dendrogram(Z, orientation="bottom", labels=df.index);

[python] 基于matplotlib实现树形图的绘制_第8张图片

4. 彩色树形图标签 color dendrogram labels

# Calculate the distance between each sample
Z = hierarchy.linkage(df, 'ward')

# Make the dendro
# 画树状图
hierarchy.dendrogram(Z, labels=df.index, leaf_rotation=0, orientation="left", color_threshold=240, above_threshold_color='grey')

# Create a color palette with 3 color for the 3 cyl possibilities
# 设置渐变颜色,共三种颜色
my_palette = plt.cm.get_cmap("Accent", 3)

# transforme the 'cyl' column in a categorical variable. It will allow to put one color on each level.
# 根据cyl设置颜色参数,对参数进行分类
df['cyl']=pd.Categorical(df['cyl'])
# 获得每种汽车cyl对应的颜色
my_color=df['cyl'].cat.codes

# Apply the right color to each label
ax = plt.gca()
# 获得y轴坐标标签
xlbls = ax.get_ymajorticklabels()
num=-1
for lbl in xlbls:
    num+=1
    val=my_color[num]
    # 设置颜色
    lbl.set_color(my_palette(val))

[python] 基于matplotlib实现树形图的绘制_第9张图片

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