I am building a polynomial regression without using Sklearn. I'm having trouble with Polynomial Expansion of features right now.
I have a dataframe with columns A and B. When I imported and ran PolynomialFeatures(degree of 2) from Sklearn, I found that it returns 6 different features.
I understand that 2 features became 6 features because it is (A + B + Constant)*(A + B + Constant)
which becomes A2 + 2AB + 2AC + 2BC + B2 + C2, 6 different features. I am trying to recapitulate this with Python and Numpy.
As there is constant c, I created a new column C to my dataframe. However, I am very stuck on how to proceed after this. I tried for loop for (number of features * degree #) times but got confused for the combination of features.
'''
def polynomial_expansion(features_df, order):
return expanded_df
'''
Can someone help me out? What would be Python/Numpy/Pandas method I can use for this situation? Thank you.
I created a simple example of what you need to do in order to create your polynomial features from scratch. The first part of the code creates the result from Scikit Learn:
from sklearn.preprocessing import PolynomialFeatures
import pandas as pd
import numpy as np
df = pd.DataFrame.from_dict({
'x': [2],
'y': [5],
'z': [6]})
p = PolynomialFeatures(degree=2).fit(df)
f = pd.DataFrame(p.transform(df), columns=p.get_feature_names(df.columns))
print('deg 2\n', f)
p = PolynomialFeatures(degree=3).fit(df)
f = pd.DataFrame(p.transform(df), columns=p.get_feature_names(df.columns))
print('deg 3\n', f)
The result looks like:
deg 2
1 x y z x^2 x y x z y^2 y z z^2
0 1.0 2.0 5.0 6.0 4.0 10.0 12.0 25.0 30.0 36.0
deg 3
1 x y z x^2 x y x z y^2 y z z^2 x^3 x^2 y x^2 z x y^2 x y z x z^2 y^3 y^2 z y z^2 z^3
0 1.0 2.0 5.0 6.0 4.0 10.0 12.0 25.0 30.0 36.0 8.0 20.0 24.0 50.0 60.0 72.0 125.0 150.0 180.0 216.0
Now to create a similar feature without Scikit Learn, we can write our code like this:
row = [2, 5, 6]
#deg = 1
result = [1]
result.extend(row)
#deg = 2
for i in range(len(row)):
for j in range(len(row)):
res=row[i]*row[j]
if res not in result:
result.append(res)
print("deg 2", result)
#deg = 3
for i in range(len(row)):
for j in range(len(row)):
for z in range(len(row)):
res=row[i]*row[j]*row[z]
if res not in result:
result.append(res)
print("deg 3", result)
The result looks like:
deg 2 [1, 2, 5, 6, 4, 10, 12, 25, 30, 36]
deg 3 [1, 2, 5, 6, 4, 10, 12, 25, 30, 36, 8, 20, 24, 50, 60, 72, 125, 150, 180, 216]
To get the same results recursively, you can use the following code:
row = [2, 5, 6]
def poly_feats(input_values, degree):
if degree==1:
if 1 not in input_values:
result = input_values.insert(0,1)
result=input_values
return result
elif degree > 1:
new_result=[]
result = poly_feats(input_values, degree-1)
new_result.extend(result)
for item in input_values:
for p_item in result:
res=item*p_item
if (res not in result) and (res not in new_result):
new_result.append(res)
return new_result
print('deg 2', poly_feats(row, 2))
print('deg 3', poly_feats(row, 3))
And the results will be:
deg 2 [1, 2, 5, 6, 4, 10, 12, 25, 30, 36]
deg 3 [1, 2, 5, 6, 4, 10, 12, 25, 30, 36, 8, 20, 24, 50, 60, 72, 125, 150, 180, 216]
Also, if you need to use Pandas data frame as an input to the function, you can use the following:
def get_poly_feats(df, degree):
result = {}
for index, row in df.iterrows():
result[index] = poly_feats(row.tolist(), degree)
return result