Does PCA implementation in sklearn have an intercept?

Question

I'm using the PCA implementation from sklearn and wanted to export the loadings from the fitted model so I could transform anywhere else without using python.

However, I came up with an issue when I tried to validate that the dot product of the dataset with the loadings didn't give the same result as the transform function. Here's an example:

df = pd.DataFrame({'col1': [5,3,1,1,2,2,3,3,3],
                   'col2': [5,3,1,2,2,3,4,5,5],
                   'col3': [3,3,1,1,1,1,1,1,1]})

I import PCA from sklearn and fit the model with one component

from sklearn.decomposition import PCA
model = PCA(n_components=1)
model.fit(df)

With the fitted model, I transform the 3 columns dataset into one column

print(model.transform(df))
array([[ 3.13985669],
       [ 0.4068059 ],
       [-2.81207381],
       [-2.0684094 ],
       [-1.44554842],
       [-0.701884  ],
       [ 0.6646414 ],
       [ 1.40830581],
       [ 1.40830581]])

According to the sklearn docs I can access de loading in the components_ attribute. When I transform the dataset using the loadings I get a different output.

print(df.dot(model.components_.T).values)
array([[7.56137036],
       [4.82831957],
       [1.60943986],
       [2.35310427],
       [2.97596525],
       [3.71962967],
       [5.08615507],
       [5.82981948],
       [5.82981948]])

However, the difference between bot output seems to be constant

print(model.transform(df) - df.dot(model.components_.T).values)
[[-4.42151367]
 [-4.42151367]
 [-4.42151367]
 [-4.42151367]
 [-4.42151367]
 [-4.42151367]
 [-4.42151367]
 [-4.42151367]
 [-4.42151367]]

I was taught that PCA doesn't have intercept, but does this mean that the PCA implementation in sklearn includes the intercept? If so, is there a way to access this intercept without calling the difference between the transform funcion and the dot product of the data with the loadings?

Note: I know data normalization solves the problem of the intercept but I can't use it in this situation.

Does PCA implementation in sklearn have an intercept?

0 Answers