← AI Terminology
PCA - Principal Component Analysis
PCA is a linear dimensionality-reduction method that finds orthogonal directions (principal components) of maximum variance and projects data onto a smaller subspace.
It is foundational for visualisation, compression, and noise reduction.
It is foundational for visualisation, compression, and noise reduction.
Why It Matters in AI
High-dimensional data is hard to see and often redundant. PCA remains the first linear tool for compression and exploratory analysis, and a conceptual base for modern representation learning discussions.
Key Points
| Aspect | Description |
|---|---|
| Use | Visualise, denoise, preprocess for classical ML |
| Math | Eigenvectors of covariance (or SVD of data) |
| Limit | Linear only; misses nonlinear manifolds |
| Tools | sklearn PCA, numpy SVD |
| Related | t-SNE, UMAP, autoencoders |
| Practice | Standardise features before PCA |
Simple Analogy
Rotating a cloud of points to align with its longest axes, then keeping only the longest few as a compact summary sketch.
Common Usage Examples
PCA(n_components=50).fit_transform(X)- Explained variance ratio plots
- Compress features before clustering
- Compare to nonlinear UMAP for viz
Summary
In short: PCA linearly compresses data onto top-variance axes — the classic dimensionality-reduction baseline.