Classical Machine Learning
Centre the comparisons
BOTIE
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Use a copy of the example to try your own data. Keep the problem's assumptions in mind, and predict the effect of a change before checking the output. You can also add another branch to compare two ways of doing the calculation.
Context for this challenge
Calculate the original matrix's row means and subtract each mean from its corresponding row.
We want principal components in a feature space described through kernel comparisons. Even without writing out those feature vectors, their centre still matters. Let's remove the corresponding row and column means from the comparison table before extracting directions.
Inspect the component calculation
Subtract each row's reference(
Rows: Kernel matrix
Row reference values: Mean within each row(
Rows of measurements: Kernel matrix
)
)Examples and results
- Kernel matrix
1 2 2 4 - Required result
-0.5 0.5 -1 1
Try a fresh construction
This clears this draft, including its undo history. Earlier successful attempts stay recorded. Build again without opening hints to record an independent attempt.
Stuck? Inspect a worked construction
The tools below form one possible solution. You can assemble it, follow its signals, and undo that change to return to your own construction.
Assumptions and test precision
This is a small construction problem. The lesson explains the assumptions and the parts of the full method that this example leaves out. Numerical tests allow a difference of 0.001. Lists and structures must also have the right shape.
Your last tested pieces can start the full construction. An existing draft there keeps its own pieces.
Three mutually orthogonal feature vectors
This check uses the pieces from “Centre both sides of the comparison matrix”.
BOTIE
- Kernel matrix
1 0 0 0 1 0 0 0 1
Use a number, text, or an array matching the requested result. For a matrix, put each row in brackets. Saving your prediction runs your current construction on these inputs and checks the earlier examples too.
Build a construction in the workspace above first. This case will test those pieces.
Which row and column checks would expose a missing overall-mean restoration, and what PCA work remains after this construction?
Kernel operations can reproduce feature-space centring, but centring and extracting directions remain separate steps.
This is a small construction problem. The lesson explains the assumptions and the parts of the full method that this example leaves out.
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