Dimensionality Reduction Cheat Sheet
Techniques for reducing feature space while preserving structure, covering PCA, t-SNE, and UMAP with scikit-learn implementation examples.
2 PagesIntermediateMar 12, 2026
Principal Component Analysis
Linearly project data onto directions of maximum variance.
python
from sklearn.decomposition import PCAfrom sklearn.preprocessing import StandardScalerimport numpy as np# Always scale before PCA -- it's sensitive to feature variancescaler = StandardScaler()X_scaled = scaler.fit_transform(X)pca = PCA(n_components=0.95) # keep enough components for 95% varianceX_reduced = pca.fit_transform(X_scaled)print(f"Components kept: {pca.n_components_}")print(f"Explained variance ratio: {pca.explained_variance_ratio_}")print(f"Cumulative variance: {np.cumsum(pca.explained_variance_ratio_)}")
t-SNE & UMAP for Visualization
Non-linear projection into 2D for plotting.
python
from sklearn.manifold import TSNEimport umapimport matplotlib.pyplot as plt# t-SNE: good for visualizing clusters in 2D/3D, not for feature engineeringtsne = TSNE(n_components=2, perplexity=30, random_state=42)X_tsne = tsne.fit_transform(X_scaled)# UMAP: faster than t-SNE, better preserves global structurereducer = umap.UMAP(n_components=2, n_neighbors=15, min_dist=0.1, random_state=42)X_umap = reducer.fit_transform(X_scaled)plt.scatter(X_umap[:, 0], X_umap[:, 1], c=y, cmap="tab10", s=5)
Dimensionality Reduction Techniques
Common methods and what they're good for.
- PCA- linear technique projecting data onto orthogonal axes of maximum variance
- Explained variance ratio- fraction of total variance captured by each principal component
- t-SNE- non-linear technique optimized for visualizing local cluster structure in 2D/3D
- UMAP- non-linear technique, faster than t-SNE, better preserves both local and global structure
- LDA (Linear Discriminant Analysis)- supervised reduction maximizing class separability
- Autoencoders- neural networks that learn a compressed latent representation via reconstruction
- Feature selection vs extraction- selection keeps a subset of original features, extraction creates new combined features
When to Reach for Each Method
Practical guidance for choosing a technique.
- Speed up training / reduce noise- PCA is fast, linear, and reversible-ish via inverse_transform
- Visualize high-dimensional clusters- t-SNE or UMAP for a 2D/3D scatter plot
- Preserve class separability for a classifier- LDA when labels are available
- Non-linear structure with reconstruction needed- autoencoders for complex, learnable compression
- High curse-of-dimensionality risk- reduce dimensions before distance-based methods like KNN or clustering
Pro Tip
Never use t-SNE or UMAP output as input features for a downstream supervised model, and don't interpret distances between distant clusters in a t-SNE plot as meaningful — both techniques are designed for visualization and preserve local neighborhood structure, not global distances.
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