Practice Questions — Dimensionality Reduction - PCA and t-SNE

from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import load_wine
import numpy as np

wine = load_wine()
X_scaled = StandardScaler().fit_transform(wine.data)

pca = PCA()
pca.fit(X_scaled)

cum_var = pca.explained_variance_ratio_.cumsum()
n_90 = np.argmax(cum_var >= 0.90) + 1
print(f"Components for 90% variance: {n_90}")
print(f"Original features: {wine.data.shape[1]}")
print(f"Variance at {n_90} components: {cum_var[n_90-1]:.4f}")

import numpy as np
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import load_wine

wine = load_wine()
X = StandardScaler().fit_transform(wine.data)

for n in [1, 3, 5, 10, 13]:
    pca = PCA(n_components=n)
    X_pca = pca.fit_transform(X)
    X_recon = pca.inverse_transform(X_pca)
    mse = np.mean((X - X_recon)**2)
    var = pca.explained_variance_ratio_.sum()
    print(f"n={n:2d}: variance={var:.4f}, reconstruction_error={mse:.4f}")

from sklearn.decomposition import PCA
from sklearn.neighbors import KNeighborsClassifier
from sklearn.datasets import load_digits
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler

digits = load_digits()
X, y = digits.data, digits.target
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

scaler = StandardScaler()
X_train_sc = scaler.fit_transform(X_train)
X_test_sc = scaler.transform(X_test)

# Without PCA
knn = KNeighborsClassifier(n_neighbors=5)
knn.fit(X_train_sc, y_train)
acc_full = knn.score(X_test_sc, y_test)

# With PCA
pca = PCA(n_components=30)
X_train_pca = pca.fit_transform(X_train_sc)
X_test_pca = pca.transform(X_test_sc)
knn_pca = KNeighborsClassifier(n_neighbors=5)
knn_pca.fit(X_train_pca, y_train)
acc_pca = knn_pca.score(X_test_pca, y_test)

print(f"Full features (64): accuracy = {acc_full:.4f}")
print(f"PCA (30 components): accuracy = {acc_pca:.4f}")
print(f"Variance retained: {pca.explained_variance_ratio_.sum():.4f}")

from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import load_iris
import numpy as np

iris = load_iris()
X_scaled = StandardScaler().fit_transform(iris.data)

pca = PCA(n_components=2)
pca.fit(X_scaled)

print("PC1 loadings:")
for name, loading in zip(iris.feature_names, pca.components_[0]):
    print(f"  {name}: {loading:.4f}")

most_important = iris.feature_names[np.argmax(np.abs(pca.components_[0]))]
print(f"\nMost important feature for PC1: {most_important}")

import numpy as np
from sklearn.decomposition import PCA
from sklearn.manifold import TSNE
from sklearn.datasets import load_digits
from sklearn.preprocessing import StandardScaler

def class_var_ratio(X_2d, y):
    overall_mean = X_2d.mean(axis=0)
    between = 0
    within = 0
    for label in np.unique(y):
        points = X_2d[y == label]
        class_mean = points.mean(axis=0)
        between += len(points) * np.sum((class_mean - overall_mean)**2)
        within += np.sum((points - class_mean)**2)
    return between / within

digits = load_digits()
X_scaled = StandardScaler().fit_transform(digits.data)
y = digits.target

X_pca = PCA(n_components=2).fit_transform(X_scaled)
X_tsne = TSNE(n_components=2, perplexity=30, random_state=42).fit_transform(X_scaled)

print(f"PCA variance ratio: {class_var_ratio(X_pca, y):.4f}")
print(f"t-SNE variance ratio: {class_var_ratio(X_tsne, y):.4f}")
print("Higher ratio = better class separation")