How to apply euclidean distance function to a groupby object in pandas dataframe?

Question

I have a set of objects and their positions over time. I would like to get the average distance between objects for each time point. An example dataframe is as follows:

Answer 1

building this up from the first principles:

For each point at index n, it is necessary to compute the distance with all the points with index > n.

if the distance between two points is given by formula:

np.sqrt((x0 - x1)**2 + (y0 - y1)**2)

then for an array of points in a dataframe, we can get all the distances & then calculate its mean:

distances = []
for i in range(len(df)-1):
    distances += np.sqrt( (df.x[i+1:] - df.x[i])**2 + (df.y[i+1:] - df.y[i])**2 ).tolist()

np.mean(distances)

expressing the same logic using pd.concat & a couple of helper functions

def diff_sq(x, i):
    return (x.iloc[i+1:] - x.iloc[i])**2

def dist_df(x, y, i):
    d_sq = diff_sq(x, i) + diff_sq(y, i)
    return np.sqrt(d_sq)

def avg_dist(df):
    return pd.concat([dist_df(df.x, df.y, i) for i in range(len(df)-1)]).mean()

then it is possible to use the avg_dist function with groupby

df.groupby('time').apply(avg_dist)
# outputs:
time
0     1.550094
1    10.049876
2    53.037722
dtype: float64