Data Scientist Breaks Down PCA in 5 Steps, From Standardization to Projection
mdancho84 · x · 2026-10-10
Data scientist Matt Dancho published a step-by-step thread on Principal Component Analysis (PCA), calling it the gold standard of dimensionality reduction while acknowledging it confuses beginners.
- What PCA is: a statistical technique for dimensionality reduction, useful for large multi-variable datasets, simplifying complexity while retaining variability.
- Five steps: ① Standardization ② Covariance matrix computation ③ Eigenvalue/eigenvector calculation ④ Choosing principal components ⑤ Transforming the data.
- Covariance matrix: captures how features vary individually and together; each element is the covariance between two features.
- Eigenvectors & eigenvalues: eigenvectors are the directions of maximum variance (the principal components); eigenvalues quantify the variance each component carries.
- Choosing components: eigenvectors are sorted by eigenvalues; the number kept is usually based on cumulative explained variance ratio.
- Transformation: projecting original data onto principal components yields uncorrelated variables where the first few retain most of the original variability.
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