Evaluating the squared term of a gaussian kernel for having a covariance matrix for multi-dimensional inputs

Asked Dec 18 '17 at 21:34

Active Dec 18 '17 at 22:34

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I have two 2-dimensional numpy arrays of shape say m x d, and n x d. What is the optimized(i.e. without for loops) or the numpy way of creating the squared term of a Gaussian kernel for ultimately having a covariance matrix of size m x n.

I have already checked numpy's outer function, but it didn't serve my purpose.

This is what an equivalent code with for looks like

difference_squared = np.zeros((x.shape[0], x_.shape[0]))
for row_iterator in range(difference_squared.shape[0]):
    for column_iterator in range(difference_squared.shape[1]):
        difference_squared[row_iterator, column_iterator] = np.sum(np.power(x[row_iterator]-x_[column_iterator], 2))

edited Dec 18 '17 at 22:34

asked Dec 18 '17 at 21:34

Sanjay

Show us your loopy try? – Divakar Dec 18 '17 at 22:13
@Divakar, I have added my equivalent code snippet for computing the squared term of the Gaussian kernel in the question itself now. Take a look. – Sanjay Dec 18 '17 at 22:36
1

Use [SciPy cdist](https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.distance.cdist.html) : `cdist(x,x_, 'sqeuclidean')`. – Divakar Dec 18 '17 at 22:39
Thank you @Divakar, that worked. – Sanjay Dec 19 '17 at 16:15

Evaluating the squared term of a gaussian kernel for having a covariance matrix for multi-dimensional inputs

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