Having come upon the wonderful little module of matplotlib-venn I've used it for a bit, I'm wondering if there's a nicer way of doing things than what I have done so far. I know that you can use the following lines for a very simple Venn diagram:

union = set1.union(set2).union(set3)
indicators = ['%d%d%d' % (a in set1, a in set2, a in set3) for a in union]
subsets = Counter(indicators)

... but also want to have lists of entries in the various combinations of the three sets.

import numpy as np
from matplotlib_venn import venn3, venn3_circles
from matplotlib import pyplot as plt
import pandas as pd

# Read data
data = pd.read_excel(input_file, sheetname=sheet)

# Create three sets of the lists to be compared
set_1 = set(data[compare[0]].dropna())
set_2 = set(data[compare[1]].dropna())
set_3 = set(data[compare[2]].dropna())

# Create a third set with all elements of the two lists
union = set_1.union(set_2).union(set_3)

# Gather names of all elements and list them in groups
lists = [[], [], [], [], [], [], []]
for gene in union:
    if (gene in set_1) and (gene not in set_2) and (gene not in set_3):
    elif (gene in set_1) and (gene in set_2) and (gene not in set_3):
    elif (gene in set_1) and (gene not in set_2) and (gene in set_3):
    elif (gene in set_1) and (gene in set_2) and (gene in set_3):
    elif (gene not in set_1) and (gene in set_2) and (gene not in set_3):
    elif (gene not in set_1) and (gene in set_2) and (gene in set_3):
    elif (gene not in set_1) and (gene not in set_2) and (gene in set_3):

# Write gene lists to file
ew = pd.ExcelWriter('../Gene lists/Venn lists/' + compare[0] + ' & '
                    + compare[1] + ' & ' + compare[2] + ' gene lists.xlsx')

pd.DataFrame(lists[0], columns=[compare[0]]) \
    .to_excel(ew, sheet_name=compare[0], index=False)

pd.DataFrame(lists[1], columns=[compare[0] + ' & ' + compare[1]]) \
    .to_excel(ew, sheet_name=compare[0] + ' & ' + compare[1], index=False)

pd.DataFrame(lists[2], columns=[compare[0] + ' & ' + compare[2]]) \
    .to_excel(ew, sheet_name=compare[0] + ' & ' + compare[2], index=False)

pd.DataFrame(lists[3], columns=['All']) \
    .to_excel(ew, sheet_name='All', index=False)

pd.DataFrame(lists[4], columns=[compare[1]]) \
    .to_excel(ew, sheet_name=compare[1], index=False)

pd.DataFrame(lists[5], columns=[compare[1] + ' & ' + compare[2]]) \
    .to_excel(ew, sheet_name=compare[1] + ' & ' + compare[2], index=False)

pd.DataFrame(lists[6], columns=[compare[2]]) \
    .to_excel(ew, sheet_name=compare[2], index=False)


# Count the elements in each group
subsets = [len(lists[0]), len(lists[4]), len(lists[1]), len(lists[6]),
           len(lists[2]), len(lists[5]), len(lists[3])]

# Basic venn diagram
fig = plt.figure(1)
ax = fig.add_subplot(1, 1, 1)
v = venn3(subsets, (compare[0], compare[1], compare[2]), ax=ax)
c = venn3_circles(subsets)

# Annotation
ax.annotate('Total genes:\n' + str(len(union)),
            xy=v.get_label_by_id('111').get_position() - np.array([-0.5,
            xytext=(0,-70), ha='center', textcoords='offset points',
            bbox=dict(boxstyle='round,pad=0.5', fc='gray', alpha=0.3))

# Title
plt.title(compare[0] + ' & ' + compare[1] + ' & ' + compare[2] +
          ' gene expression overlap')


So, there's basically a lot of different cases, each handled manually, and I'm wondering if there's a more "automated" / less verbose / better way of doing this. For example, can I get out the entries from the three line code snippet in the beginning somehow?


2 Answers 2


Perhaps something like the following?

values_to_sets = {a : (a in set1, a in set2, a in set3) for a in union}
sets_to_values = {}
for a, s in values_to_sets.items():
    if s not in sets_to_values:
        sets_to_values[s] = []

This first identifies each item with a tuple indicating which sets that item belongs to. Then you flip the dictionary mapping, where each tuple maps to a list of items belonging to the combination of sets indicated in the tuple.

You could even expand this to an arbitrary number of sets:

sets = [set1, set2, set3, set4]
values_to_sets = {a : (a in s for s in sets) for a in union}
  • \$\begingroup\$ Thanks, that works great! Some questions, though - I don't understand the code fully... For each a in union, check if a exists in (set1,set2,set3) (i.e. only checking for values of a that exist in union) must be me misunderstanding the code, since the results are the same as for my other code. What am I missing? Also, the second part: (a,s) equals (keys,values) (from .items())? But looking at the code is looks to be the other way around... "For the tuple s (keys) append gene a that maps to s"? \$\endgroup\$
    – erikfas
    Dec 12, 2014 at 8:56
  • \$\begingroup\$ @ErikF. I'm not sure I understand your first question. Are you asking what the difference is between a in (set1, set2, set3) versus (a in set1, a in set2, a in set3)? The first will return a single boolean stating whether a is set1, set2, or set3, while the second will return a tuple of booleans indicating whether a is in set1, a is in set2, and a is in set3. a,s are the key,value pairs for values_to_sets, but we are using them in reverse roles for sets_to_values to organize the data by the tuples, not the objects. \$\endgroup\$ Dec 12, 2014 at 17:23
  • \$\begingroup\$ No; sorry for being unclear. I'm asking how for a in union somehow finds all of the genes, and not only those that exist in union (seeing as union is the union of the three sets of the three different cell types), which is what I read for a in union as. The second part you cleared up nicely though! \$\endgroup\$
    – erikfas
    Dec 15, 2014 at 13:51
  • \$\begingroup\$ I think you may be confusing union and intersect? Nothing is excluded in the union - if an element exists in a subset, it exists in the union. The intersection is comprised of only the elements that exist in ALL the subsets. So, in the case of for a in union(set1,set2,set3), a is guaranteed to exist in at least one set, whereas for for a in intersect(...), a is guaranteed to exist in all three. \$\endgroup\$ Dec 15, 2014 at 19:23
  • \$\begingroup\$ Oh, I see, then it all makes sense! Thanks again for the help! \$\endgroup\$
    – erikfas
    Dec 16, 2014 at 8:01

The wonderful code provided by Gordon (above) does wonders, but I just found out that it doesn't work when the lists compared contain cases where one of the lists have zero unique entries. In such cases, the code snippet

for a, s in values_to_sets.items():
    if s not in sets_to_values:
        sets_to_values[s] = []

Fails to list all the (1/0, 1/0, 1/0) tuples, since at least one of the tuples s does not exist in values_to_sets.items(). I'm not sure if there's a nice and general workaround for this, but I found that simply removing the last two lines of the above and substituting

sets_to_values = {}

... for ...

sets_to_values = {(1, 0, 0): [], (0, 1, 0): [], (1, 1, 0): [],
                  (0, 0, 1): [], (1, 0, 1): [], (0, 1, 1): [],
                  (1, 1, 1): []}

... does the trick. Just in case anybody happens to stumble upon this thread, the solution should now be more complete!


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