from sklearn.decomposition import PCA
from sklearn.datasets import make_swiss_roll

# Create synthetic data
X, t = make_swiss_roll(n_samples=1000, noise=0.2, random_state=42)

# Instantiate a PCA object
pca = PCA(n_components=1)

# Fit the PCA object on the data
pca.fit(X)

# Transform the data
X_transformed = pca.transform(X)

print('Original data shape: ', X.shape)
print('Transformed data shape: ', X_transformed.shape)