Dimensionality Reduction

Dimensionality Reduction Techniques

Dimensionality reduction simplifies high-dimensional data while preserving structure.

PCA

PCA (Principal Component Analysis) finds orthogonal directions of maximum variance. PCA(n_components=k) selects k components.

explained_variance_ratio_ shows variance captured. transform(X) projects data. inverse_transform recovers approximate original.

t-SNE

t-SNE provides non-linear dimensionality reduction for visualization. Perplexity controls balance between local and global structure.

tsne = TSNE(n_components=2). perplexity=30. Results are stochastic; set random_state.

UMAP

UMAP is faster than t-SNE and preserves global structure better. UMAP(n_components=2).

Key Takeaways

1. PCA is linear and interpretable
2. t-SNE is for visualization, not downstream tasks
3. UMAP balances local and global structure