Distance calculation between rows in Pandas Dataframe using a distance matrix

Question

I have the following Pandas DataFrame:

In [31]:
import pandas as pd
sample = pd.DataFrame({'Sym1': ['a','a','a','d'],'Sym2':['a','c','b','b'],'Sym3':['a','c','b','d'],'Sym4':['b','b','b','a']},index=['Item1','Item2','Item3','Item4'])
In [32]: print(sample)
Out [32]:
      Sym1 Sym2 Sym3 Sym4
Item1    a    a    a    b
Item2    a    c    c    b
Item3    a    b    b    b
Item4    d    b    d    a

and I want to find the elegant way to get the distance between each Item according to this distance matrix:

In [34]:
DistMatrix = pd.DataFrame({'a': [0,0,0.67,1.34],'b':[0,0,0,0.67],'c':[0.67,0,0,0],'d':[1.34,0.67,0,0]},index=['a','b','c','d'])
print(DistMatrix)
Out[34]:
      a     b     c     d
a  0.00  0.00  0.67  1.34
b  0.00  0.00  0.00  0.67
c  0.67  0.00  0.00  0.00
d  1.34  0.67  0.00  0.00 

For example comparing Item1 to Item2 would compare aaab -> accb -- using the distance matrix this would be 0+0.67+0.67+0=1.34

Ideal output:

       Item1   Item2  Item3  Item4
Item1      0    1.34     0    2.68
Item2     1.34    0      0    1.34
Item3      0      0      0    2.01
Item4     2.68  1.34   2.01    0

Answer 1

This is an old question, but there is a Scipy function that does this:

from scipy.spatial.distance import pdist, squareform

distances = pdist(sample.values, metric='euclidean')
dist_matrix = squareform(distances)

pdist operates on Numpy matrices, and DataFrame.values is the underlying Numpy NDarray representation of the data frame. The metric argument allows you to select one of several built-in distance metrics, or you can pass in any binary function to use a custom distance. It's very powerful and, in my experience, very fast. The result is a "flat" array that consists only of the upper triangle of the distance matrix (because it's symmetric), not including the diagonal (because it's always 0). squareform then translates this flattened form into a full matrix.

The docs have more info, including a mathematical rundown of the many built-in distance functions.