How to calculate pairwise Euclidean distance between a collection of vectors

Question

I have a pandas data frame like this. Where the index is pd.DatetimeIndex and the columns are timeseries.

	x_1	x_2	x_3
2020-08-17	133.23	2457.45	-4676
2020-08-18	-982	-6354.56	-245.657
2020-08-19	5678.642	245.2786	2461.785
2020-08-20	-2394	154.34	-735.653
2020-08-20	236	-8876	-698.245

I need to calculate the Euclidean distance of all the columns against each other. I.e., (x_1 - x_2), (x_1 - x_3), (x_2 - x_3), and return a square data frame like this: (Please realize that the values in this table are just an example and not the actual result of the Euclidean distance)

	x_1	x_2	x_3
x_1	0	123	456
x_2	123	0	789
x_3	456	789	0

I tried this resource but I could not figure out how to pass the columns of my df. If understand correctly the example passes the rows as the series to calculate the ED from.

Answer 1

An explicit way of achieving this would be:

from itertools import combinations

import numpy as np

dist_df = pd.DataFrame(index=df.columns, columns=df.columns)

for col_a, col_b in combinations(df.columns, 2):
    dist = np.linalg.norm(df[col_a] - df[col_b])
    dist_df.loc[col_a, col_b] = dist
    dist_df.loc[col_b, col_a] = dist

print(dist_df)

outputs

              x_1           x_2           x_3
x_1           NaN  12381.858429   6135.306973
x_2  12381.858429           NaN  12680.121047
x_3   6135.306973  12680.121047           NaN

If you want 0 instead of NaN use DataFrame.fillna:

dist_df.fillna(0, inplace=True)