Principal Component Analysis (PCA)
PCA rotates your data so the directions with the most spread become the first axes. Keep those, drop the flat ones, and you compress, denoise, and visualize — with the exact linear algebra (eigenvectors of the covariance, or SVD of the centered matrix) doing the finding.
01.The Problem: Too Many Numbers, and Most of Them Repeat Themselves
You embed 10,000 product photos with a vision model. Each photo is now a list of 1,536 numbers.
Two problems stare at you:
Problem 1: you cannot plot 1,536 axes. You want to look at your data — to spot clusters, duplicates, junk. Human eyes get two axes, maybe three.
Problem 2: most of those 1,536 numbers are redundant. Neighboring dimensions move together (highly correlated), so the real information may live in far fewer "effective" directions.
So the question becomes:
Can I throw away many of the numbers while throwing away barely any information?
The naive move — keep 2 random columns — is a disaster: you might drop the two columns that carry everything and keep two duplicates of the same thing.
What you actually want is to invent new axes: combinations of the old features that pack the most spread first. Then keeping the first few new axes loses very little.
That rotation is Principal Component Analysis — the classic, exact, all-linear-algebra way to shrink dimensions. It was published by Karl Pearson in 1901, and it still quietly preprocesses a huge share of the world's ML data.
PCA Pipeline: Center, Factorize, Truncate 🧭
PCA Pipeline: Center, Factorize, Truncate 🧭
PCA is exact linear algebra on the centered data matrix: singular vectors give orthogonal directions of maximal variance; truncation gives the best rank-k linear approximation.
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