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Model Atlas · Dimensionality reduction

PCA

Rotates data into orthogonal directions that capture maximum variance.

core mathematical viewmaximize Var(Xw) subject to ||w||=1
Mental model

Understand it before memorizing it.

Find the directions through the data cloud that preserve the most variance.

Best fit

Where this model earns its place

Compression

Start with a simpler baseline then compare this model using the same evaluation split and operational constraints.

Visualization

Start with a simpler baseline then compare this model using the same evaluation split and operational constraints.

Noise reduction

Start with a simpler baseline then compare this model using the same evaluation split and operational constraints.

Strengths and limits

Trade-offs matter more than popularity.

Strengths

✓ Fast linear transform

✓ Uncorrelated components

✓ Useful diagnostic

Limitations

△ Linear only

△ Components can be hard to interpret

Evaluation

Metrics to watch

Explained varianceInterpret with the product objective and error cost.
Reconstruction errorInterpret with the product objective and error cost.
Production checklist

Before it reaches real users

  1. 01

    Fit only on training data

    Document the assumption and instrument the condition so regressions can be detected.

  2. 02

    Track variance retained

    Document the assumption and instrument the condition so regressions can be detected.

  3. 03

    Avoid leakage

    Document the assumption and instrument the condition so regressions can be detected.