Creating interaction terms quickly without SKLearn
I am using the following code to create interaction terms in my data:
def Interaction(x): for k in range(0,x.shape[1]-1): for j in range(k+1,x.shape[1]-1): new = x[:,k] * x[:,j] x = np.hstack((x,new[:,None])) return x My problem is that it is extremely slow compared to SKLearn’s PolynomialFeatures. How can I speed it up? I can’t use SKLearn because there are a few customizations that I would like to make. For example, I would like to make an interaction variable of X1 * X2 but also X1 * (1-X2), etc.
We should multiply each element of each row pairwise we can do it as np.einsum('ij,ik->ijk, x, x). This is 2 times redundand but still 2 times faster than PolynomialFeatures.
import numpy as np def interaction(x): """ >>> a = np.arange(9).reshape(3, 3) >>> b = np.arange(6).reshape(3, 2) >>> a array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> interaction(a) array([[ 0, 1, 2, 0, 0, 2], [ 3, 4, 5, 12, 15, 20], [ 6, 7, 8, 42, 48, 56]]) >>> b array([[0, 1], [2, 3], [4, 5]]) >>> interaction(b) array([[ 0, 1, 0], [ 2, 3, 6], [ 4, 5, 20]]) """ b = np.einsum('ij,ik->ijk', x, x) m, n = x.shape axis1, axis2 = np.triu_indices(n, 1) axis1 = np.tile(axis1, m) axis2 = np.tile(axis2, m) axis0 = np.arange(m).repeat(n * (n - 1) // 2) return np.c_[x, b[axis0, axis1, axis2].reshape(m, -1)] Performance comparision:
c = np.arange(30).reshape(6, 5) from sklearn.preprocessing import PolynomialFeatures poly = PolynomialFeatures(2, interaction_only=True) skl = poly.fit_transform print(np.allclose(interaction(c), skl(c)[:, 1:])) # True In [1]: %timeit interaction(c) 118 µs ± 172 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each) In [2]: %timeit skl(c) 243 µs ± 4.69 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each) 
