Dimensionality Reduction

Introduction

Dimensionality reduction techniques transform high-dimensional data into lower dimensions while preserving important structure.

PCA

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

iris = load_iris()
X = iris.data

pca = PCA(n_components=2)
X_pca = pca.fit_transform(X)

print(f"Explained variance ratio: {pca.explained_variance_ratio_}")
print(f"Total variance explained: {sum(pca.explained_variance_ratio_):.3f}")
print(f"Components shape: {pca.components_.shape}")

Incremental PCA

from sklearn.decomposition import IncrementalPCA

ipca = IncrementalPCA(n_components=2, batch_size=100)
X_pca = ipca.fit_transform(X_large)

t-SNE

from sklearn.manifold import TSNE
from sklearn.datasets import make_digits

digits = make_digits(n_samples=1000, random_state=42)

tsne = TSNE(n_components=2, perplexity=30, random_state=42)
X_tsne = tsne.fit_transform(digits.data)

UMAP

import umap

reducer = umap.UMAP(n_components=2, random_state=42)
X_umap = reducer.fit_transform(X_high_dim)

# For large datasets
reducer = umap.UMAP(n_neighbors=15, min_dist=0.1, n_components=3)
X_3d = reducer.fit_transform(X_large)

Practice Problems

1. Reduce dimensions with PCA
2. Visualize digits with t-SNE
3. Compare PCA vs UMAP
4. Determine optimal number of components
5. Use inverse_transform to reconstruct