sklearn: how to get coefficients of polynomial features

Question

I know it is possible to obtain the polynomial features as numbers by using: polynomial_features.transform(X). According to the manual, for a degree of two the

Answer 1

By the way, there is more appropriate function now: PolynomialFeatures.get_feature_names.

from sklearn.preprocessing import PolynomialFeatures
import pandas as pd
import numpy as np

data = pd.DataFrame.from_dict({
    'x': np.random.randint(low=1, high=10, size=5),
    'y': np.random.randint(low=-1, high=1, size=5),
})

p = PolynomialFeatures(degree=2).fit(data)
print p.get_feature_names(data.columns)

This will output as follows:

['1', 'x', 'y', 'x^2', 'x y', 'y^2']

N.B. For some reason you gotta fit your PolynomialFeatures object before you will be able to use get_feature_names().

If you are Pandas-lover (as I am), you can easily form DataFrame with all new features like this:

features = DataFrame(p.transform(data), columns=p.get_feature_names(data.columns))
print features

Result will look like this:

     1    x    y   x^2  x y  y^2
0  1.0  8.0 -1.0  64.0 -8.0  1.0
1  1.0  9.0 -1.0  81.0 -9.0  1.0
2  1.0  1.0  0.0  1.0   0.0  0.0
3  1.0  6.0  0.0  36.0  0.0  0.0
4  1.0  5.0 -1.0  25.0 -5.0  1.0

Answer 2

import numpy as np
from sklearn.preprocessing import PolynomialFeatures

X = np.array([2,3])

poly = PolynomialFeatures(3)
Y = poly.fit_transform(X)
print Y
# prints [[ 1  2  3  4  6  9  8 12 18 27]]
print poly.powers_

This code will print:

[[0 0]
 [1 0]
 [0 1]
 [2 0]
 [1 1]
 [0 2]
 [3 0]
 [2 1]
 [1 2]
 [0 3]]

So if the i'th cell is (x,y), that means that Y[i]=(a**x)*(b**y). For instance, in the code example [2 1] equals to (2**2)*(3**1)=12.

Answer 3

For a dataframe like this

import pandas as pd
import numpy as np
from sklearn.preprocessing import PolynomialFeatures

data = pd.DataFrame({
    'x': np.random.randint(low=1, high=10, size=5),
    'y': np.random.randint(low=-1, high=1, size=5)})

Here's how I did it,

PolyFeats = PolynomialFeatures(degree=2)
dfPoly = pd.DataFrame(
    data=PolyFeats.fit_transform(data), 
    columns=PolyFeats.get_feature_names(data.columns))

to get an output like this,

In [50]: dfPoly
Out[50]: 
     1    x    y   x^2  x y  y^2
0  1.0  5.0  0.0  25.0  0.0  0.0
1  1.0  6.0 -1.0  36.0 -6.0  1.0
2  1.0  1.0 -1.0   1.0 -1.0  1.0
3  1.0  5.0 -1.0  25.0 -5.0  1.0
4  1.0  6.0  0.0  36.0  0.0  0.0