Using Python for asymmetric calculation of jaccard distance

Question

I have some SAS coding that I am trying to convert to Python. I am having difficulties calculating the jaccard distance on asymmetric data – where the zeros should be ignored in the calculation. I do find some examples on jaccard but they do not calculate the asymmetric distance. Just checking to see if a library has this available before I try to reinvent the wheel. If someone could please steer me in the right direction, I would really appreciate it.

My test dataset contains 5 headers and 5 rows

H0  H1  H2  H3  H4

A  1  1  1  1  0

B  1  0  1  1  0

C  1  1  1  1  0

D  0  0  1  1  1

E  1  1  0  1  0

below is the expected result(distance) calculated by shorthand and also from using SAS:

. |  A   |    B   |    C   |   D   |   E

A |  0   |    0.25|    0   |   0.6 |   0.25

B |  0.25|    0   |    0.25|   0.5 |   0.5

C |  0   |    0.25|    0   |   0.6 |   0.25

D |  0.6 |    0.5 |    0.6 |   0   |   0.8

E |  0.25|    0.5 |    0.25|   0.8 |   0        

But, using jaccard in python, I get results like:

.  |A    |   B   |   C   |   D  |   E

A  |1.00 | 0.43  |  0.61 | 0.55 |   0.46

B  |0.43 | 1.00  |  0.52 | 0.56 |   0.49

C  |0.61 | 0.52  |  1.00 | 0.48 |   0.53

D  |0.55 | 0.56  |  0.48 | 1.00 |   0.49

E  |0.46 | 0.49  |  0.53 | 0.49 |   1.00

Below is the code I experimented on. I am new to Python so I might be making an obvious mistake. I have added the SAS code at the bottom in case someone would like it for reference:

Python Code:

np.random.seed(0)
df = pd.DataFrame(np.random.binomial(1, 0.5, size=(100, 5)), 
columns=list('ABCDE'))
print(df.head())

jac_sim = 1 - pairwise_distances(df.T, metric = "jaccard")
jac_sim = pd.DataFrame(jac_sim, index=df.columns, columns=df.columns)

import itertools
sim_df = pd.DataFrame(np.ones((5, 5)), index=df.columns, columns=df.columns)
for col_pair in itertools.combinations(df.columns, 2):
    sim_df.loc[col_pair] = sim_df.loc[tuple(reversed(col_pair))] = 
    jaccard_similarity_score(df[col_pair[0]], df[col_pair[1]])
print(sim_df)

SAS Code:

proc import datafile = '/home/xxx/xxx.csv'  
 out = work.Binary2 replace
 dbms = CSV;
 GUESSINGROWS=MAX;
run;
proc sort;
by VAR1;
run;
title ’Data Clustering of BN’;
proc distance data=Binary2 method=djaccard absent=0 out=distjacc;
var anominal (r0--r4);
id VAR1;
run;

Answer 1

I found some obvious mistakes. First thing is that you need to create matrix of size=(5,5):

import pandas as pd
import numpy as np
from sklearn.metrics import pairwise_distances, jaccard_similarity_score

np.random.seed(0)
df = pd.DataFrame(np.random.binomial(1, 0.5, size=(5, 5)).T, columns=list('ABCDE'))
print(df.T)

Second thing is that if you print just head, you do not see that matrix has more than 5 rows. With just 5 lines, these two:

print(df.T.head())

print(df.T)

print the same result:

   0  1  2  3  4
A  1  1  1  1  0
B  1  0  1  1  0
C  1  1  1  1  0
D  0  0  1  1  1
E  1  1  0  1  0

After the above change it is possible to use pairwise_distances:

jac_sim = pairwise_distances(df.T.astype(bool), metric = "jaccard")
jac_sim = pd.DataFrame(jac_sim, index=df.columns, columns=df.columns)
print(jac_sim)

in order to obtain the desired result:

      A     B     C    D     E
A  0.00  0.25  0.00  0.6  0.25
B  0.25  0.00  0.25  0.5  0.50
C  0.00  0.25  0.00  0.6  0.25
D  0.60  0.50  0.60  0.0  0.80
E  0.25  0.50  0.25  0.8  0.00

There is also .astype(bool) in the above code in order to prevent warning when running pairwise_distance.

It is necessary to be careful in applying transposes .T, as pairwise_distance seem to work rather with columns than with rows.

With function jaccard_similarity_score

import itertools
sim_df = pd.DataFrame(np.zeros((5, 5)), index=df.columns, columns=df.columns)
for col_pair in itertools.combinations(df.columns, 2):
    sim_df.loc[col_pair] = sim_df.loc[tuple(reversed(col_pair))] = \
        1 - jaccard_similarity_score(df[col_pair[0]], df[col_pair[1]], normalize = True)
print(sim_df)

I got a different matrix:

     A    B    C    D    E
A  0.0  0.2  0.0  0.6  0.2
B  0.2  0.0  0.2  0.4  0.4
C  0.0  0.2  0.0  0.6  0.2
D  0.6  0.4  0.6  0.0  0.8
E  0.2  0.4  0.2  0.8  0.0

Looking more closely jaccard_similarity_score:

print(df['A'])
print(df['B'])
jaccard_similarity_score(df['A'], df['B'], normalize = True)

reveals that zeros were not excluded the result:

0    1
1    1
2    1
3    1
4    0
Name: A, dtype: int32
0    1
1    0
2    1
3    1
4    0
Name: B, dtype: int32
Out[123]: 0.8

Because the result is 4 similar / 5 total = 0.8, not 3 similar nonzeros / 4 total nonzeros = 0.75.