kernel_pca_denoising.py

# %%
from sklearn.datasets import fetch_openml

usps = fetch_openml(data_id=41082)

# %%
data = usps.data
target = usps.target

# %%
import numpy as np

img = np.reshape(data.iloc[0].to_numpy(), (16, 16))

# %%
import matplotlib.pyplot as plt

plt.imshow(img)

# %%
from sklearn.model_selection import train_test_split

data_rest, data_train, target_rest, target_train = train_test_split(
    data, target, stratify=target, random_state=42, test_size=100,
)
data_rest, data_test, target_rest, target_test = train_test_split(
    data_rest, target_rest, stratify=target_rest, random_state=42,
    test_size=100,
)
data_train, data_test = data_train.to_numpy(), data_test.to_numpy()

# %%
fig, axs = plt.subplots(nrows=10, ncols=10, figsize=(15, 15))
for img, ax in zip(data_test, axs.ravel()):
    ax.imshow(img.reshape((16, 16)), cmap="Greys")
    ax.axis("off")
_ = fig.suptitle("Uncorrupted test dataset")

# %%
rng = np.random.RandomState(0)
noise = rng.normal(scale=0.5, size=(data_train.shape))
data_test_corrupted = data_test + noise

# %%
fig, axs = plt.subplots(nrows=10, ncols=10, figsize=(15, 15))
for img, ax in zip(data_test_corrupted, axs.ravel()):
    ax.imshow(img.reshape((16, 16)), cmap="Greys")
    ax.axis("off")
_ = fig.suptitle(
    f"Corrupted test data: "
    f"MSE={np.mean((data_test - data_test_corrupted) ** 2):.2f}",
    size=26,
)

# %%
from sklearn.decomposition import KernelPCA

kpca = KernelPCA(
    n_components=80, kernel="rbf", gamma=0.5, fit_inverse_transform=True,
    alpha=10,
)

# %%
kpca.fit(data_train)

# %%
import pandas as pd

data_reconstruct = kpca.inverse_transform(kpca.transform(data_test))

# %%
fig, axs = plt.subplots(nrows=10, ncols=10, figsize=(15, 15))
for img, ax in zip(data_reconstruct, axs.ravel()):
    ax.imshow(img.reshape((16, 16)), cmap="Greys")
    ax.axis("off")
_ = fig.suptitle(
    f"Denoising using Kernel PCA with RBF kernel: "
    f"MSE={np.mean((data_test - data_reconstruct) ** 2):.2f}",
    size=26,
)

# %%
from sklearn.decomposition import PCA

pca = PCA(n_components=32)
pca.fit(data_train)
data_reconstruct =  pca.inverse_transform(pca.transform(data_test_corrupted))

# %%
fig, axs = plt.subplots(nrows=10, ncols=10, figsize=(15, 15))
for img, ax in zip(data_reconstruct, axs.ravel()):
    ax.imshow(img.reshape((16, 16)), cmap="Greys")
    ax.axis("off")
_ = fig.suptitle(
    f"Denosing using PCA: "
    f"MSE={np.mean((data_test - data_reconstruct) ** 2):.2f}",
    size=26
)