BIZNIQUE / LINEAR ALGEBRA / 23
Create new features through linear combinations
Create new features through linear combinations
Rotate, combine or project existing features while keeping the map explicit.
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THE IDEA
Read the example.
Read the example.
Each new feature is a weighted combination of the original coordinates. An invertible square transformation changes representation without losing information; a lower-rank transformation can remove directions.
z = Ax
Use it well
Use it well
A linear transform cannot create information that was absent from its inputs. Its value depends on how the chosen model uses the new representation.
TRY IT YOURSELF
A quick check.
A quick check.
If z₁ = x₁ + x₂ and z₂ = x₁ − x₂, can x be recovered?
Check your reasoning
Check your reasoning
Yes: x₁ = (z₁ + z₂)/2 and x₂ = (z₁ − z₂)/2.
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