A rotation matrix
Penguin learning project
The project uses 342 complete Palmer penguin records: 240 training-pool and 102 held-out rows. The selected training rows determine feature scaling and model parameters. Source CSV
This project trains weights with softmax, unlike the homepage lab, which uses nearest species averages. Same penguin measurements; different classification methods. Predictions can differ.
Vectors and matrices · Combine numbers using vector and matrix operations.
Project vectors have two features; the training matrix has n rows and two columns. Mathematical tools may operate on these values when their assumptions apply.
Consider this concept alongside the project; its source assumptions may differ. These observations do not prove a theorem.
Input: 12 × 2; Held-out evaluation: 102 · #58 · 40.6 mm, 193 mm. Known answer: Adélie; Prediction: Adélie · [≈0.7383, ≈0.2444, ≈0.01737].
Used in these source sections: 3.1 A rule based on distance
SO(d) contains d-by-d real orthogonal matrices with determinant 1. Such matrices are rotations.
The source uses a rotation associated with a direction vector.
Source formula example
illustration · This is one two-dimensional rotation; the source chooses a rotation for its stated direction.
Symbols
- A rotation associated with the vector wⱼ.
- The real orthogonal d-by-d matrices of determinant 1.
Source formula example
This source example uses its own inputs and assumptions. Editing it does not change the project.
Edit a value or the code, then run the example. This is a finite demonstration, not a proof of the paper’s theorem.
This example’s data flow
Code changed. Reset to restore this example’s data flow.
Initial values in code
R=[ [0, -1], [1, 0], ]x=[1, 0]
Calculated here
Result expression: {
R,
x,
rotated: R.map((row) => row.reduce((s, v, i) => s + v * x[i], 0)),
determinant: 1,
}
Returns
R- array (2 items): [array (2 items): [0, -1], array (2 items): [1, 0]]
x- array (2 items): [1, 0]
rotated- array (2 items): [0, 1]
determinant- 1
Read numbers from input and return the result. JavaScript basics.
Result
Technical statement
The numerical values are invented unless a source value is specified. This is one two-dimensional rotation; the source chooses a rotation for its stated direction.
Source: Inline notation