在matplotlib热图中增加点的重要性

Question

关于matplotlib热图，我有两个问题。

1）是否可以在matplotlib热图上增加X和Y点的重要性？

2）是否可以通过白色绘制没有数据的坐标？

我的Python地图生成文件如下：

import sys
import os
import numpy as np
import pandas as pd
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from scipy import stats


csv_filename = 'heatmap_data.csv'

df = pd.read_csv(csv_filename)
red_df = df[df['type']=='red']
blue_df = df[df['type']=='blue']

def compute_KDE_from_pos(x_pos,y_pos):

    xmin = x_pos.min()
    xmax = x_pos.max()
    ymin = y_pos.min()
    ymax = y_pos.max()

    X, Y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
    positions = np.vstack([X.ravel(), Y.ravel()])
    values = np.vstack([x_pos, y_pos])
    kernel = stats.gaussian_kde(values)
    Z = np.reshape(kernel(positions).T, X.shape)

    return Z

Z_red = compute_KDE_from_pos(red_df.x_pos,red_df.y_pos)
Z_blue = compute_KDE_from_pos(blue_df.x_pos,blue_df.y_pos)
Z_diff = Z_blue-Z_red

fig, ax = plt.subplots()
ax.imshow(np.rot90(Z_diff), cmap='RdBu',
           extent=[0, 100, 0, 100])
ax.plot(red_df.x_pos, red_df.y_pos, 'r.', markersize=2)
ax.plot(blue_df.x_pos, blue_df.y_pos, 'b.', markersize=2)
ax.set_xlim([0, 100])
ax.set_ylim([100, 0])
ax.axis('equal')

plt.savefig("heatmap.png")

热图数据文件（heatmap_data.csv）：

x_pos,y_pos,type,importance
74,64,blue,0.011517617893368
68,64,blue,0.0041303878348102
32,64,red,0.049788810065569
8,64,red,0.12877712212094
88,64,red,0.0050599724578342
84,64,blue,0.00052412736663743
80,64,blue,0.020183850819375
78,64,blue,0.01297132988303
72,64,red,0.080092605800612
64,64,red,0.074683215098353
62,64,blue,0.011168199648943
58,64,red,0.030129086612831
56,64,red,0.085501996502871
54,64,red,0.042576289129223
50,64,red,0.0025580057348979
48,64,red,0.055198200767828
44,64,red,0.049788810065569
38,64,blue,0.0055840998244716
34,64,red,0.092714517439217
30,64,blue,0.025593241521634
28,64,red,0.07107695463018
26,64,red,0.0099452357934559
22,64,blue,0.043624543862498
20,64,blue,0.031002632223893
18,64,red,0.038795319538838
16,64,blue,0.023790111287548
12,64,blue,0.030827923101681
94,64,red,0.044728837607734
90,64,red,0.042750998251436
82,64,blue,0.066890527783408
76,64,blue,0.015123878361541
70,64,blue,0.045427674096584
66,64,blue,0.018206011463076
60,64,red,0.060607591470087
46,64,red,0.01227249339418
14,64,red,0.0048852633356217
92,64,red,0.041122577139562
52,64,blue,0.007387230058558
36,64,blue,0.025418532399422
4,64,red,0.02326598392091
86,64,blue,0.021812271931249
42,64,red,0.0034315513459603
40,64,blue,0.0037809695903852
24,64,blue,0.092134351060618
50,24,blue,0.034552853680104
92,24,red,0.021462853686824
86,24,red,0.039319446905475
82,24,red,0.0088409420482194
74,24,red,0.0088409420482194
66,24,red,0.015878753862352
64,24,blue,0.023790111287548
60,24,red,0.017332465852014
56,24,red,0.049089973576719
54,24,red,0.10661543194527
52,24,red,0.03140808948028
48,24,red,0.051067812933018
46,24,red,0.0081421055593695
44,24,red,0.097425071652626
42,24,blue,0.043624543862498
40,24,red,0.080092605800612
36,24,blue,0.034434183569854
10,24,red,0.044728837607734
34,24,red,0.03553847731509
84,24,red,0.019659723452738
80,24,red,0.010644072282306
58,24,red,0.040423740650712
32,24,blue,0.00017470912221247
30,24,red,0.046357258719608
8,24,red,0.019659723452738
90,24,red,0.021462853686824
70,24,red,0.026697535266871
62,24,blue,0.050662355676631
38,24,blue,0.021812271931249
68,24,blue,0.01640288122899
14,68,red,0.01570404474014
18,68,red,0.058629752113788
20,68,red,0.055023491645615
38,68,red,0.082070445156911
10,68,red,0.033735347081004
24,68,blue,0.0023272576007238
28,68,red,0.044379419363309
36,68,red,0.023091274798698
50,68,red,0.018960886963888
52,68,red,0.057001331001914
56,68,blue,0.0039556787125977
68,68,blue,0.052465485910717
72,68,blue,0.016577590351202
74,68,red,0.062061303459748
76,68,blue,0.038215153160239
78,68,red,0.044379419363309
80,68,red,0.010469363160093
82,68,red,0.010294654037881
84,68,red,0.033560637958791
86,68,red,0.0086662329260069
90,68,blue,0.00017470912221247
66,68,red,0.055198200767828
70,68,blue,0.00034941824442495
8,68,red,0.0034315513459603
12,68,blue,0.0091903602926443
16,68,blue,0.018380720585289
62,68,red,0.035363768192878
26,68,blue,0.039843574272113
32,68,blue,0.021812271931249
34,68,blue,0.010993490526731
40,68,red,0.021288144564612
44,68,blue,0.0055840998244716
46,68,blue,0.010993490526731
48,68,blue,0.0091903602926443
22,68,blue,0.048859225442545
30,68,blue,0.012796620760817
58,68,red,0.0050599724578342
88,68,blue,0.0055840998244716
84,68,red,0.028151247256532
22,68,red,0.14087490639291
90,68,red,0.015878753862352
70,68,red,0.040773158895137
68,68,red,0.0050599724578342
66,68,red,0.030129086612831
64,68,red,0.037166898426964
62,68,red,0.0086662329260069
58,68,red,0.039144737783263
54,68,blue,0.0055840998244716
52,68,red,0.030129086612831
50,68,red,0.077940057322101
48,68,blue,0.012796620760817
44,68,red,0.030129086612831
40,68,red,0.066016982172346
38,68,red,0.06421385193826
34,68,red,0.037341607549176
32,68,red,0.0050599724578342
28,68,red,0.01227249339418
24,68,blue,0.025593241521634
20,68,red,0.049614100943356
18,68,blue,0.013146039005242
14,68,red,0.01570404474014
76,68,red,0.022741856554273
74,68,red,0.056826621879702
72,68,red,0.037166898426964
26,68,blue,0.0075619391807704
94,68,red,0.042925707373648
82,68,red,0.024544986788359
56,68,blue,0.021812271931249
46,68,blue,0.014599750994903
42,68,blue,0.010993490526731
8,68,red,0.096495487029602
80,68,red,0.0032568422237478
30,68,blue,0.021812271931249
16,68,blue,0.029024792867594
10,68,blue,0.0019778393562988
86,68,blue,0.007387230058558
78,68,blue,0.038040444038026
12,68,blue,0.027221662633508
4,68,red,0.02326598392091
80,64,red,0.10335858972152
14,64,red,0.026522826144658
12,64,blue,0.00034941824442495
32,64,blue,0.01297132988303
34,64,red,0.049788810065569
38,64,red,0.028325956378745
44,64,blue,0.0021525484785113
46,64,red,0.0032568422237478
50,64,blue,0.040192992516538
54,64,red,0.0086662329260069
56,64,red,0.010294654037881
58,64,red,0.01227249339418
60,64,red,0.040947868017349
68,64,red,0.013726205383841
70,64,blue,0.011168199648943
74,64,red,0.0048852633356217
78,64,blue,0.057874876612976
82,64,red,0.020938726320187
84,64,red,0.1803690624206
86,64,red,0.049788810065569
88,64,blue,0.0055840998244716
10,64,red,0.0050599724578342
16,64,red,0.060258173225662
18,64,blue,0.014774460117116
26,64,blue,0.036412022926152
30,64,blue,0.041646704506199
36,64,red,0.037341607549176
40,64,blue,0.012796620760817
52,64,blue,0.020009141697163
64,64,blue,0.032631053335767
66,64,red,0.055198200767828
72,64,red,0.012097784271967
76,64,blue,0.041821413628412
20,64,blue,0.038215153160239
22,64,red,0.017332465852014
24,64,blue,0.079512439422013
42,64,red,0.0068631026919206
62,64,blue,0.025593241521634
92,64,red,0.012447202516392
66,32,red,0.089282966093256
50,32,red,0.068400278785031
44,32,red,0.05124252205523
84,32,red,0.026697535266871
82,32,red,0.05537290989004
72,32,red,0.051766649421867
64,32,red,0.0014537119896614
62,32,red,0.03897002866105
60,32,blue,0.007387230058558
48,32,red,0.051417231177442
46,32,red,0.033560637958791
40,32,blue,0.00034941824442495
38,32,blue,0.0021525484785113
36,32,red,0.03553847731509
32,32,blue,0.0039556787125977
30,32,red,0.026697535266871
28,32,blue,0.007387230058558
22,32,red,0.030303795735043
94,32,red,0.042925707373648
76,32,red,0.037516316671389
74,32,red,0.010644072282306
68,32,red,0.0050599724578342
58,32,red,0.0032568422237478
56,32,red,0.046007840475183
52,32,blue,0.021986981053461
34,32,blue,0.01640288122899
24,32,red,0.026697535266871
20,32,red,0.0016284211118739
12,32,red,0.0034315513459603
8,32,red,0.033910056203216
80,32,red,0.010644072282306
54,32,blue,0.021986981053461
42,32,blue,0.023615402165335
18,32,blue,0.0055840998244716
16,32,red,0.0052346815800466
4,32,red,0.017856593218651
10,32,red,0.0034315513459603
46,24,red,0.056477203635277
48,24,red,0.054848782523403
50,24,red,0.12720474002103
54,24,red,0.013551496261629
26,24,red,0.012447202516392
32,24,red,0.042750998251436
36,24,red,0.06421385193826
38,24,blue,0.032631053335767
40,24,red,0.024719695910572
52,24,red,0.14610958797296
56,24,blue,0.00087354561106237
60,24,red,0.01570404474014
64,24,blue,0.027221662633508
74,24,red,0.007037811814133
78,24,red,0.0052346815800466
16,24,red,0.016053462984565
44,24,blue,0.013146039005242
58,24,blue,0.068693658017495
62,24,blue,0.03623731380394
22,24,red,0.0052346815800466
28,24,red,0.010644072282306
30,24,red,0.017681884096439
42,24,red,0.0048852633356217
70,28,red,0.042750998251436
16,28,red,0.014250332750479
20,28,red,0.05537290989004
22,28,red,0.0034315513459603
34,28,red,0.040947868017349
40,28,red,0.073054793986479
42,28,blue,0.0095397785370693
50,28,red,0.026928283401045
56,28,red,0.018960886963888
58,28,red,0.085501996502871
60,28,red,0.0032568422237478
62,28,blue,0.030827923101681
64,28,red,0.0032568422237478
76,28,red,0.040947868017349
14,28,red,0.012447202516392
46,28,red,0.012097784271967
48,28,blue,0.057874876612976
52,28,red,0.0191355960861
54,28,blue,0.031002632223893
98,28,red,0.02326598392091
8,28,red,0.014250332750479
18,28,red,0.007037811814133
28,28,red,0.015878753862352
30,28,red,0.0068631026919206
32,28,blue,0.014599750994903
38,28,blue,0.023615402165335
82,28,red,0.012447202516392
90,28,red,0.019659723452738
36,28,blue,0.027221662633508
44,28,blue,0.054268616144804
68,28,blue,0.01640288122899
78,28,red,0.019659723452738
26,44,red,0.033735347081004
6,44,red,0.012447202516392
16,44,red,0.033735347081004
20,44,blue,0.0037809695903852
34,44,red,0.042750998251436
36,44,red,0.040773158895137
44,44,red,0.010469363160093
48,44,red,0.0032568422237478
50,44,blue,0.086899669480571
54,44,blue,0.032631053335767
58,44,red,0.060607591470087
66,44,red,0.014075623628266
68,44,blue,0.0091903602926443
76,44,red,0.058804461236
80,44,red,0.024894405032784
86,44,red,0.051766649421867
92,44,red,0.042925707373648
18,44,blue,0.010993490526731
40,44,blue,0.00017470912221247
42,44,red,0.083873575390997
74,44,blue,0.0057588089466841
88,44,red,0.030303795735043
24,44,blue,0.012796620760817
30,44,blue,0.023615402165335
60,44,red,0.015878753862352
78,44,blue,0.007387230058558
46,44,blue,0.0037809695903852
52,44,blue,0.012796620760817
56,44,blue,0.029024792867594
64,44,red,0.0052346815800466
12,60,red,0.024894405032784
14,60,blue,0.0019778393562988
16,60,red,0.019485014330525
20,60,red,0.0068631026919206
22,60,red,0.026522826144658
26,60,blue,0.020009141697163
34,60,red,0.0050599724578342
36,60,red,0.053569779655954
40,60,red,0.048160388953695
44,60,blue,0.010993490526731
50,60,blue,0.0077366483029829
58,60,red,0.067820112406432
62,60,red,0.028500665500957
64,60,red,0.051766649421867
68,60,red,0.01227249339418
76,60,red,0.0084915238037944
78,60,blue,0.010993490526731
86,60,red,0.037341607549176
84,60,red,0.010469363160093
10,60,red,0.016053462984565
24,60,blue,0.020009141697163
28,60,blue,0.0039556787125977
48,60,blue,0.0055840998244716
66,60,blue,0.00017470912221247
70,60,red,0.01227249339418
90,60,red,0.0016284211118739
30,60,blue,0.020009141697163
74,60,blue,0.0021525484785113
72,60,blue,0.025418532399422
88,52,red,0.033910056203216
86,52,red,0.026697535266871
84,52,red,0.039144737783263
82,52,red,0.019485014330525
80,52,blue,0.0091903602926443
76,52,red,0.0068631026919206
68,52,red,0.042750998251436
66,52,red,0.033735347081004
64,52,red,0.042750998251436
62,52,red,0.037341607549176
56,52,red,0.015878753862352
54,52,blue,0.025418532399422
48,52,red,0.0032568422237478
46,52,red,0.051591940299655
40,52,red,0.0032568422237478
38,52,red,0.047985679831482
34,52,red,0.017681884096439
32,52,red,0.03897002866105
22,52,blue,0.007387230058558
16,52,blue,0.0055840998244716
78,52,red,0.0086662329260069
60,52,red,0.01227249339418
52,52,red,0.033735347081004
44,52,blue,0.007387230058558
42,52,blue,0.023615402165335
36,52,red,0.01227249339418
24,52,blue,0.020009141697163
18,52,blue,0.018206011463076
8,52,red,0.039319446905475
6,52,red,0.019659723452738
74,52,blue,0.018206011463076
72,52,red,0.0014537119896614
70,52,red,0.0050599724578342
50,52,blue,0.059678006847063
12,52,red,0.010469363160093
58,52,red,0.017681884096439
26,52,blue,0.007387230058558
50,28,red,0.0029634629912845
92,28,red,0.02326598392091
78,28,red,0.0088409420482194
76,28,red,0.030303795735043
70,28,red,0.023091274798698
66,28,red,0.030129086612831
58,28,red,0.040598449772924
56,28,red,0.03140808948028
54,28,blue,0.029199501989807
52,28,red,0.07450850597614
44,28,blue,0.04920864368697
42,28,blue,0.0057588089466841
40,28,red,0.026522826144658
38,28,blue,0.03280576245798
34,28,red,0.040947868017349
22,28,red,0.0088409420482194
86,28,red,0.012447202516392
72,28,blue,0.0019778393562988
64,28,blue,0.018380720585289
48,28,blue,0.02396482040976
46,28,blue,0.047230804330671
30,28,blue,0.007387230058558
18,28,red,0.0034315513459603
6,28,red,0.017856593218651
90,28,red,0.039319446905475
62,28,red,0.013900914506054
26,28,red,0.0016284211118739
74,28,red,0.012447202516392
12,28,red,0.0088409420482194
20,48,red,0.017681884096439
18,48,red,0.01227249339418
26,48,blue,0.0091903602926443
36,48,red,0.031932216846917
38,48,red,0.049788810065569
44,48,red,0.089282966093256
46,48,blue,0.0021525484785113
48,48,blue,0.0021525484785113
50,48,red,0.036642771060327
52,48,red,0.037341607549176
56,48,red,0.062236012581961
74,48,red,0.0068631026919206
82,48,red,0.017507174974226
84,48,blue,0.0055840998244716
8,48,red,0.044728837607734
12,48,red,0.024894405032784
14,48,red,0.053395070533741
22,48,red,0.024719695910572
24,48,red,0.024719695910572
28,48,blue,0.021812271931249
34,48,red,0.014075623628266
70,48,red,0.0068631026919206
76,48,blue,0.012796620760817
78,48,red,0.01227249339418
58,48,blue,0.00034941824442495
64,48,red,0.01227249339418
66,48,blue,0.0055840998244716
72,48,blue,0.007387230058558
86,48,red,0.0052346815800466
32,48,blue,0.023615402165335
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26,56,red,0.10876798042378
88,56,red,0.03210692596913
84,56,blue,0.00017470912221247
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80,56,blue,0.0037809695903852
76,56,red,0.057001331001914
70,56,red,0.019485014330525
64,56,red,0.01227249339418
50,56,red,0.049439391821144
38,56,blue,0.0091903602926443
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20,56,red,0.030129086612831
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14,56,red,0.037341607549176
12,56,red,0.033910056203216
10,56,red,0.046357258719608
58,56,blue,0.00017470912221247
52,56,blue,0.007387230058558
48,56,blue,0.012796620760817
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图的限制为X（0 .. 100）和Y（0 .. 100）。

现在它生成了这个热图，但是从逻辑上讲是错误的。 heatmap example

热图应显示冰球场的正负部分。每个数据都是在特定坐标下的发射率。

结果应类似于以下示例。红点应该是红色，强调点的重要性，蓝点应该是蓝色，强调点的重要性（在CSV文件中）。没有数据的点应该是透明的（白色）。 example of result heatmap

Answer 1

在您要说明的问题中：

  

没有数据的点应该是透明的（白色）

在您附加的示例热图中的白色区域中可能包含点：实际上，对于两个点分布（红色和蓝色），它们具有相同的确切概率。他们。在示例热图所用的颜色图中，白色表示以下事实：两个Gaussian KDE之差非常接近于零。研究KDE是什么以及它代表什么很重要：它只是一种估计随机变量的概率密度函数的方法，仅此而已。 无论如何，请尝试将cmap='RdBu'替换为cmap='bwr'，并将Z_diff = Z_blue-Z_red替换为Z_diff = -Z_blue+Z_red，看看是否喜欢该结果。 Here是我所得到的。

就考虑到每一点的“重要性”而言，我认为该问题的一部分没有明确定义。在用于ML或统计数据的整洁数据集中，理想情况下，每一行应对应一个且只有一个观测值。如果列importance对应于具有一对坐标的点的相对出现频率，则建议计算该点的绝对频率，并将数据集中的每个点重复其绝对频率。这样，您的数据集将变得整洁干净。

尽管即使不知道所收集观测值的总数N，也可以根据相对频率估算绝对频率，但是如果您知道该数字N，则您自己做起来会容易得多。

>

编辑：

我重新阅读了您对importance的评论。您想根据“重要性”列中包含的值更改每个点的标记大小，对吗？

此代码可以做到。我将importance中的值乘以200，因为结果的比例合理，但是您可以根据需要更改它。这是代码的输出：

还：整个代码中根本没有使用os，sys，matplotlib（不仅是pyplot）。不要导入它们。除此之外，我刚刚将.plot的调用从Axes对象更改为.scatter，并将列red_df.importance传递给属性s=，该属性定义了对象的大小。给定点的标记。

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy import stats

csv_filename = 'heatmap_data.csv'

df = pd.read_csv(csv_filename)
red_df = df[df['type']=='red']
blue_df = df[df['type']=='blue']

def compute_KDE_from_pos(x_pos,y_pos):

    xmin = x_pos.min()
    xmax = x_pos.max()
    ymin = y_pos.min()
    ymax = y_pos.max()

    X, Y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
    positions = np.vstack([X.ravel(), Y.ravel()])
    values = np.vstack([x_pos, y_pos])
    kernel = stats.gaussian_kde(values)
    Z = np.reshape(kernel(positions).T, X.shape)

    return Z

Z_red = compute_KDE_from_pos(red_df.x_pos,red_df.y_pos)
Z_blue = compute_KDE_from_pos(blue_df.x_pos,blue_df.y_pos)
Z_diff = -Z_blue+Z_red

fig, ax = plt.subplots()
ax.imshow(np.rot90(Z_diff), cmap='bwr',
           extent=[0, 100, 0, 100])

ax.scatter(red_df.x_pos, red_df.y_pos, c='r', s=red_df.importance.values*200)
ax.scatter(blue_df.x_pos, blue_df.y_pos, c='b', s=blue_df.importance.values*200)
ax.set_xlim([0, 100])
ax.set_ylim([100, 0])
ax.axis('equal')

plt.show()