← All workshopsRead Principal Component Analysis

Data Preparation

Describe the cloud along its main direction

BOTIE

Find the length of [1, 1] from its squared entries and divide the direction by that length.
Ready to test
0 passed · 0 failed · 1 not run

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Examples, experiments and workspace controls
Live values

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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.

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Context for this challenge

Find the length of [1, 1] from its squared entries and divide the direction by that length.

We have a cloud of measurements, but much of its variation follows one direction. Can we describe a point by its position along that direction? The direction is supplied here so we can concentrate on what projecting onto it means. The points are already centred.

Inspect the component calculation
Divide(
  Amount: Chosen principal direction
  Divisor: Square root(
    Squared value: Add a list(
      Numbers: Square(
        Value or list: Chosen principal direction
      )
    )
  )
)
Examples and results
Chosen principal direction
  1. 01
  2. 11
Required result
  1. 00.7071
  2. 10.7071
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

The principal direction is supplied. This challenge constructs projection and normalisation; finding that direction from a general dataset requires the decomposition explained in the lesson. 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.

A longer direction arrow along one axis

This check uses the pieces from “Read a centred point along one direction”.

BOTIE

The supplied direction is vertical but is not a unit vector. Predict the centred point's signed coordinate along that direction after normalising it.
Centred point
  1. 04
  2. 1-2
Chosen principal direction
  1. 00
  2. 13

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.

Why does normalising the direction matter even though it leaves the line unchanged, and which PCA step was supplied rather than learned?

Keep centring, finding a direction and projecting onto it distinct when building a dimensionality-reduction method.

The principal direction is supplied. This challenge constructs projection and normalisation; finding that direction from a general dataset requires the decomposition explained in the lesson.

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