CODEWITHSUNDEEP
pythonnumpy
peter.petrov
peter.petrov

Reputation: 39477

Pairs of distances squared - numpy - python

I am reading a text (see K-nearest neighors example)

which gives this line of code

   dist_sq = np.sum((X[:,np.newaxis,:] - X[np.newaxis,:,:]) ** 2, axis=-1)

Here X is a numpy 10x2 array which represents 10 points in the 2D plane.
It was initialized like this:

X = np.random.rand(10, 2)

OK... The text claims this line computes the pairs of squared distances between the points.
I have no idea why this works and if it works. I tried understanding it but I just can't. I personally try to avoid such cryptic code. This is just not human IMHO. The text explains this code in some details but it seems I don't get that explanation either.

Also, axis=-1 adds up to the confusion.

Could someone decrypt this line of code?

Also, what is the point of saying e.g. X[:,np.newaxis,:], X[np.newaxis,:,:]?

Isn't X[:,np.newaxis], X[np.newaxis,:] enough? Isn't it doing the same?!

Also, from combinatorics, the squared distances count should be 10*9/2 or 10*10/2 (if we include equal points which have distance 0), but this dist_sq is a 10x10x2 array. So this also adds up to the confusion?! Why 200 elements?!

Upvotes: 1

Views: 239

Answers (1)

BarzanHayati
BarzanHayati

Reputation: 961

You could analysis different parts of your code simply.

Check X shape: X.shape=(10, 2) .What does X[np.newaxis,:,:] do in this command? It adds new dimension as first dimension of X and convert to (1, 10, 2) dimension numpy array. Similarly X[:,np.newaxis,:] creats (10, 1, 2) numpy array.

(X[:,np.newaxis,:] - X[np.newaxis,:,:]) ** 2 has (10, 10, 2) dimension.

How about: dist_sq = np.sum((X[:,np.newaxis,:] - X[np.newaxis,:,:]) ** 2, axis=-1). It calculates euclidean distance between each pair of points in X

for example:

Y =
array([[0.79410882, 0.38156374],
           [0.93574123, 0.6510161 ]])

Results of (Y[:,np.newaxis,:] - Y[np.newaxis,:,:]) ** 2 has (2, 2, 2) dimension and np.sum do summation on specific dimension: which one : axis=-1.

dist_sq = np.sum((Y[:,np.newaxis,:] - Y[np.newaxis,:,:]) ** 2, axis=-1)

dist_sq=
array([[0.        , 0.09266431],
       [0.09266431, 0.        ]])

For example :

(0.79410882-0.93574123)**2 + (0.38156374-0.6510161)**2  = 0.09266431387197768

So final solution is a square matrix that is symmetrical.

Upvotes: 2

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