Draw longest possible vertical line between two curves in seaborn

Question

I currently have a plot like this (consider that data is the dataframe I pasted at the very bottom):

import seaborn as sns

sns.relplot(
    data = data,
    x = "Threshold",
    y = "Value",
    kind = "line",
    hue="Metric"
).set(xlabel="Threshold")

Which produces:

Now, I want to know how can I annotate a line in this plot, such that it is located between the curves, at the x-Axis value where the distance between curves are maximized. I would also need to annotate text to show the distance value.

It should be something like this:

Here is the pandas dataframe:

Threshold,Metric,Value
0.0,Recall,1.0
0.010101010101010102,Recall,0.9802536231884058
0.020202020202020204,Recall,0.9706521739130435
0.030303030303030304,Recall,0.9621376811594203
0.04040404040404041,Recall,0.9541666666666667
0.05050505050505051,Recall,0.9456521739130435
0.06060606060606061,Recall,0.9322463768115942
0.07070707070707072,Recall,0.9173913043478261
0.08080808080808081,Recall,0.908695652173913
0.09090909090909091,Recall,0.8976449275362319
0.10101010101010102,Recall,0.8813405797101449
0.11111111111111112,Recall,0.8644927536231884
0.12121212121212122,Recall,0.8498188405797101
0.13131313131313133,Recall,0.8358695652173913
0.14141414141414144,Recall,0.818659420289855
0.15151515151515152,Recall,0.7967391304347826
0.16161616161616163,Recall,0.7748188405797102
0.17171717171717174,Recall,0.7521739130434782
0.18181818181818182,Recall,0.7269927536231884
0.19191919191919193,Recall,0.6952898550724638
0.20202020202020204,Recall,0.6704710144927536
0.21212121212121213,Recall,0.648731884057971
0.22222222222222224,Recall,0.6097826086956522
0.23232323232323235,Recall,0.5847826086956521
0.24242424242424243,Recall,0.5521739130434783
0.25252525252525254,Recall,0.5023550724637681
0.26262626262626265,Recall,0.4766304347826087
0.27272727272727276,Recall,0.42047101449275365
0.2828282828282829,Recall,0.3958333333333333
0.29292929292929293,Recall,0.3539855072463768
0.30303030303030304,Recall,0.3327898550724638
0.31313131313131315,Recall,0.3036231884057971
0.32323232323232326,Recall,0.2798913043478261
0.33333333333333337,Recall,0.2371376811594203
0.3434343434343435,Recall,0.22119565217391304
0.3535353535353536,Recall,0.17300724637681159
0.36363636363636365,Recall,0.15996376811594204
0.37373737373737376,Recall,0.13568840579710145
0.38383838383838387,Recall,0.11938405797101449
0.393939393939394,Recall,0.10652173913043478
0.4040404040404041,Recall,0.09891304347826087
0.4141414141414142,Recall,0.08894927536231884
0.42424242424242425,Recall,0.07681159420289856
0.43434343434343436,Recall,0.06557971014492754
0.4444444444444445,Recall,0.05253623188405797
0.4545454545454546,Recall,0.04655797101449275
0.4646464646464647,Recall,0.024456521739130436
0.4747474747474748,Recall,0.019384057971014494
0.48484848484848486,Recall,0.009782608695652175
0.494949494949495,Recall,0.0034420289855072463
0.5050505050505051,Recall,0.002173913043478261
0.5151515151515152,Recall,0.0016304347826086956
0.5252525252525253,Recall,0.0007246376811594203
0.5353535353535354,Recall,0.00018115942028985507
0.5454545454545455,Recall,0.0
0.5555555555555556,Recall,0.0
0.5656565656565657,Recall,0.0
0.5757575757575758,Recall,0.0
0.5858585858585859,Recall,0.0
0.595959595959596,Recall,0.0
0.6060606060606061,Recall,0.0
0.6161616161616162,Recall,0.0
0.6262626262626263,Recall,0.0
0.6363636363636365,Recall,0.0
0.6464646464646465,Recall,0.0
0.6565656565656566,Recall,0.0
0.6666666666666667,Recall,0.0
0.6767676767676768,Recall,0.0
0.686868686868687,Recall,0.0
0.696969696969697,Recall,0.0
0.7070707070707072,Recall,0.0
0.7171717171717172,Recall,0.0
0.7272727272727273,Recall,0.0
0.7373737373737375,Recall,0.0
0.7474747474747475,Recall,0.0
0.7575757575757577,Recall,0.0
0.7676767676767677,Recall,0.0
0.7777777777777778,Recall,0.0
0.787878787878788,Recall,0.0
0.797979797979798,Recall,0.0
0.8080808080808082,Recall,0.0
0.8181818181818182,Recall,0.0
0.8282828282828284,Recall,0.0
0.8383838383838385,Recall,0.0
0.8484848484848485,Recall,0.0
0.8585858585858587,Recall,0.0
0.8686868686868687,Recall,0.0
0.8787878787878789,Recall,0.0
0.888888888888889,Recall,0.0
0.8989898989898991,Recall,0.0
0.9090909090909092,Recall,0.0
0.9191919191919192,Recall,0.0
0.9292929292929294,Recall,0.0
0.9393939393939394,Recall,0.0
0.9494949494949496,Recall,0.0
0.9595959595959597,Recall,0.0
0.9696969696969697,Recall,0.0
0.9797979797979799,Recall,0.0
0.98989898989899,Recall,0.0
1.0,Recall,0.0
0.0,Fall-out,1.0
0.010101010101010102,Fall-out,0.6990465720990212
0.020202020202020204,Fall-out,0.58461408367334
0.030303030303030304,Fall-out,0.516647992727734
0.04040404040404041,Fall-out,0.4643680104855929
0.05050505050505051,Fall-out,0.4172674037587468
0.06060606060606061,Fall-out,0.3796376551170116
0.07070707070707072,Fall-out,0.3507811343889394
0.08080808080808081,Fall-out,0.33186055852694335
0.09090909090909091,Fall-out,0.3152231359533222
0.10101010101010102,Fall-out,0.29964272879098575
0.11111111111111112,Fall-out,0.2855844238208993
0.12121212121212122,Fall-out,0.27161068008371564
0.13131313131313133,Fall-out,0.25719298987379235
0.14141414141414144,Fall-out,0.24338836860241422
0.15151515151515152,Fall-out,0.2312538316808659
0.16161616161616163,Fall-out,0.22026087140350506
0.17171717171717174,Fall-out,0.2083377375642137
0.18181818181818182,Fall-out,0.19694311143056467
0.19191919191919193,Fall-out,0.18402638310466565
0.20202020202020204,Fall-out,0.17440754286197493
0.21212121212121213,Fall-out,0.16548633279073208
0.22222222222222224,Fall-out,0.15278100754709004
0.23232323232323235,Fall-out,0.14292962391391667
0.24242424242424243,Fall-out,0.1317252605542989
0.25252525252525254,Fall-out,0.11555292476164303
0.26262626262626265,Fall-out,0.10612434729298353
0.27272727272727276,Fall-out,0.08902183793839714
0.2828282828282829,Fall-out,0.08331395471745978
0.29292929292929293,Fall-out,0.07232099444009894
0.30303030303030304,Fall-out,0.06735302200706086
0.31313131313131315,Fall-out,0.061454876012092256
0.32323232323232326,Fall-out,0.05665602604485973
0.33333333333333337,Fall-out,0.048982094158932836
0.3434343434343435,Fall-out,0.045641925459273196
0.3535353535353536,Fall-out,0.03748176648415534
0.36363636363636365,Fall-out,0.0341415977844957
0.37373737373737376,Fall-out,0.029321607509037482
0.38383838383838387,Fall-out,0.026996173604211148
0.393939393939394,Fall-out,0.024353635075999407
0.4040404040404041,Fall-out,0.022514428260364035
0.4141414141414142,Fall-out,0.01940680295118703
0.42424242424242425,Fall-out,0.017165930279263473
0.43434343434343436,Fall-out,0.014459970826374648
0.4444444444444445,Fall-out,0.011035240893812233
0.4545454545454546,Fall-out,0.009386296852208105
0.4646464646464647,Fall-out,0.004756569350781135
0.4747474747474748,Fall-out,0.003868676405301989
0.48484848484848486,Fall-out,0.002135171130795087
0.494949494949495,Fall-out,0.0008033317125763693
0.5050505050505051,Fall-out,0.0004228061645138786
0.5151515151515152,Fall-out,0.00031710462338540896
0.5252525252525253,Fall-out,4.228061645138786e-05
0.5353535353535354,Fall-out,0.0
0.5454545454545455,Fall-out,0.0
0.5555555555555556,Fall-out,0.0
0.5656565656565657,Fall-out,0.0
0.5757575757575758,Fall-out,0.0
0.5858585858585859,Fall-out,0.0
0.595959595959596,Fall-out,0.0
0.6060606060606061,Fall-out,0.0
0.6161616161616162,Fall-out,0.0
0.6262626262626263,Fall-out,0.0
0.6363636363636365,Fall-out,0.0
0.6464646464646465,Fall-out,0.0
0.6565656565656566,Fall-out,0.0
0.6666666666666667,Fall-out,0.0
0.6767676767676768,Fall-out,0.0
0.686868686868687,Fall-out,0.0
0.696969696969697,Fall-out,0.0
0.7070707070707072,Fall-out,0.0
0.7171717171717172,Fall-out,0.0
0.7272727272727273,Fall-out,0.0
0.7373737373737375,Fall-out,0.0
0.7474747474747475,Fall-out,0.0
0.7575757575757577,Fall-out,0.0
0.7676767676767677,Fall-out,0.0
0.7777777777777778,Fall-out,0.0
0.787878787878788,Fall-out,0.0
0.797979797979798,Fall-out,0.0
0.8080808080808082,Fall-out,0.0
0.8181818181818182,Fall-out,0.0
0.8282828282828284,Fall-out,0.0
0.8383838383838385,Fall-out,0.0
0.8484848484848485,Fall-out,0.0
0.8585858585858587,Fall-out,0.0
0.8686868686868687,Fall-out,0.0
0.8787878787878789,Fall-out,0.0
0.888888888888889,Fall-out,0.0
0.8989898989898991,Fall-out,0.0
0.9090909090909092,Fall-out,0.0
0.9191919191919192,Fall-out,0.0
0.9292929292929294,Fall-out,0.0
0.9393939393939394,Fall-out,0.0
0.9494949494949496,Fall-out,0.0
0.9595959595959597,Fall-out,0.0
0.9696969696969697,Fall-out,0.0
0.9797979797979799,Fall-out,0.0
0.98989898989899,Fall-out,0.0
1.0,Fall-out,0.0

user_13138364 · Answer

Use pivot to transform the data from long to wide
Use idxmax to find the x (Threshold) of the max difference between y1 and y2 (Fall-out and Recall)
Use vlines to plot the vertical line at x from y1 to y2
Use annotate to plot the label at the midpoint of y1 and y2

g = sns.relplot(data=data, x='Threshold', y='Value', hue='Metric', kind='line')

# pivot to wide form
p = data.pivot(index='Threshold', columns='Metric', values='Value')

# find x, y1, and y2 corresponding to max difference
diff = p['Fall-out'].sub(p['Recall']).abs()
x = diff.idxmax()
y1, y2 = p.loc[x]

# plot line and label
ax = g.axes.flat[0]
ax.vlines(x, y1, y2, ls='--')
ax.annotate(f'Dist = {diff.loc[x]:.2f}', ha='left', va='center',
            xy=(x, 0.5*(y1+y2)), xycoords='data',
            xytext=(5, 0), textcoords='offset pixels')

user_13858953 · Answer

The easiest way which I can think of is to create two separate lists of all values where the metric is Recall and another with all values where metric is Fall-out. This can be easily done using pandas operations as follows (Assuming the dataframe has name df) -

import math
import matplotlib.pyplot as plt
ls_metric = df['Metric'].to_list()
ls_value = df['Value'].to_list()
ls_threshold = df['Threshold'].to_list()
ls_value_recall = []
ls_value_fallout = []
ls_threshold_recall = []
ls_threshold_fallout = []
for i, j, k in zip(ls_metric, ls_value, ls_threshold):
    if (i == 'Recall'):
        ls_value_recall.append(j)
        ls_threshold_recall.append(k)
    elif(i == 'Fall-out'):
        ls_value_fallout.append(j)
        ls_threshold_recall.append(k)
ls_dist = []
for i, j in zip(ls_value_recall, ls_value_fallout):
    ls_dist.append(math.abs(i-j))
max_diff = max(ls_dist)
location_of_max_diff = ls_dist.index(max_diff)
value_of_threshold_at_max_diff = ls_threshold_recall[location_of_max_diff]
value_of_recall_at_max_diff = ls_value_recall[location_of_max_diff]
value_of_fallout_at_max_diff = ls_value_fallout[location_of_max_diff]
x_values = [value_of_threshold_at_max_diff, value_of_threshold_at_max_diff]
y_values = [value_of_recall_at_max_diff, value_of_fallout_at_max_diff]
plt.plot(x_values, y_values)

Certain Assumptions - The Threshold Values are the same and same number of readings are present for both metrics which I think is true having had a brief glance at the data but if not I believe it's still pretty easy to modify the code

You can add this plot to your own figure for which the syntax is readily available, now as far as the label for the line is concerned one way to do this is use matplotlib.pyplot.text to add a textbox but with that you'll need to tweak with the location to get the desired location another way to do this would be to add it as a legend only

Draw longest possible vertical line between two curves in seaborn

2 Answers