from sklearn.datasets import make_swiss_roll
from sklearn.metrics import mean_squared_error
from sklearn.decomposition import KernelPCA

X_swiss, t = make_swiss_roll(n_samples=1500, noise=0.3, random_state=2)

kPCA_dict = {
    "linear": KernelPCA(n_components=2, kernel='linear', fit_inverse_transform=True),
    "sigmoid": KernelPCA(n_components=2, kernel='sigmoid', gamma=1e-3, coef0=1, fit_inverse_transform=True)
}

X_pca_swiss = {}
X_preimage = {}

for kernel_type in kPCA_dict.keys():
    X_pca_swiss[kernel_type] = kPCA_dict[kernel_type].fit_transform(X_swiss)
    X_preimage[kernel_type] = kPCA_dict[kernel_type].inverse_transform(X_pca_swiss[kernel_type])
    mse = mean_squared_error(X_swiss, X_preimage[kernel_type])
    print('{} kernel -> MSE: {}'.format(kernel_type, mse))