Sum of distances from a point to all other points

Question

I have two lists

available_points = [[2,3], [4,5], [1,2], [6,8], [5,9], [51,35]]

and

solution = [[3,5], [2,1]]

I'm trying to pop a point in available_points and append it to solution for which the sum of euclidean distances from that point, to all points in the solution is the greatest.

So, I would get this

solution = [[3,5], [2,1], [51,35]]

---

I was able to select the initial 2 furthest points like this, but not sure how to proceed.

import numpy as np
from scipy.spatial.distance import pdist, squareform

available_points = np.array([[2,3], [4,5], [1,2], [6,8], [5,9], [51,35]])

D = squareform(pdist(available_points)
I_row, I_col = np.unravel_index(np.argmax(D), D.shape)
solution = available_points[[I_row, I_col]]

which gives me

solution = array([[1, 2], [51, 35]])

Answer 1

You can use cdist -

In [1]: from scipy.spatial.distance import cdist

In [2]: max_pt=available_points[cdist(available_points, solution).sum(1).argmax()]

In [3]: np.vstack((solution, max_pt))
Out[3]: 
array([[ 3,  5],
       [ 2,  1],
       [51, 35]])

Answer 2

I figured it out with using cdist

from scipy.spatial.distance import cdist

d = cdist(solution, available_points)

distances = []

for q in range(len(available_points)):
    y = d[:,q]
    distances.append(sum(y))

# Largest Distance
max_point = available_points[distances.index(max(distances))]

# Update datasets
solution = np.append(solution, [max_point], axis=0)
universe = np.delete(available_points, max_index, 0)

Answer 3

You can use the max function to find the maximum in a 'available_points' list & then append the maximum of 'available_points' list to 'solution' list ! I am also attached the screenshot of the output !

available_points = [[2,3], [4,5], [1,2], [6,8], [5,9], [51,35]];
solution = [[3,5], [2,1]]
solution.append(max(available_points));
print(solution);

Answer 4

Since you tag numpy

import numpy as np 

solution=np.array(solution)
available_points=np.array(available_points)
l=[]
for x in solution:
    l.append(np.linalg.norm(available_points-x, keepdims=True,axis=1))


np.append(solution,[available_points[np.argmax(np.array(l).sum(0))]],axis=0)
Out[237]: 
array([[ 3,  5],
       [ 2,  1],
       [51, 35]])