31 — Generative & Prob.

PCA & Eigenvectors#

Dimensionality✓ Mathematical
◆ The PatternFinding the directions of maximum variance for dimensionality reduction

PCA finds the axes along which data varies the most. These are the eigenvectors of the covariance matrix.

C = (1/n)·XᵀX     Cv = λv
C = covariance matrix  |  v = eigenvector  |  λ = eigenvalue (variance explained)
// 2D data with principal components — adjust correlation
Correlation0.70
PC1 explains—
PC2 explains—
Pattern bridge: Finding the axis of maximum variance is the geometric core of variance itself. In markets, ADX extracts the principal direction of trend from noisy price data.
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