Find the index of the min value in a pdist condensed distance matrix

Question

I have used scipy.spatial.distance.pdist(X) to calculate the euclidian distance metric between each pair of elements of the below list X:

X = [[0, 3, 4, 2], [23, 5, 32, 1], [3, 4, 2, 1], [33, 54, 5, 12]]

This returns a condensed distance matrix:

array([ 36.30426972,   3.87298335,  61.57109712,  36.06937759,
        57.88782255,  59.41380311])

For each element X, I need to find the index of the closest other element.

Converting the condensed distance matrix to square form help visualize the results, but I can't figure out how to programmatically identify the index of the closest element X for each element in X.

array([[  0.        ,  36.30426972,   3.87298335,  61.57109712],
       [ 36.30426972,   0.        ,  36.06937759,  57.88782255],
       [  3.87298335,  36.06937759,   0.        ,  59.41380311],
       [ 61.57109712,  57.88782255,  59.41380311,   0.        ]])

I believe argmin() is the function to use, but I'm lost from here. Thanks for any help in advance.

Answer 1

We'll operate on the square form of the results. First, to exclude "New York is closest to New York" answers,

numpy.fill_diagonal(distances, numpy.inf)

Then, it's a simple argmin along an axis:

closest_points = distances.argmin(axis=0)