Function Lp norm
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.
Norms and distances · Measure size or difference in a specified space.
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: 1.2.2 Can the network express the answer? · 1.3 The questions ahead · 3.1 A rule based on distance · More source sections
An Lp norm measures a function using an integral of the absolute value raised to p. On a finite probability space, the integral is a weighted sum.
It measures the size of a function over its domain.
Source formula example
illustration · This finite weighted sum is an exact finite-space example; general Lp spaces use an integral and L∞ uses an essential supremum.
Symbols
- An exponent at least 1.
- Functions with finite p-integral, identified when equal almost everywhere.
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
values=[1, 3]probabilities=[0.5, 0.5]p=2
Calculated here
Result expression: {
values,
p,
norm: Math.sqrt(values.reduce((s, v, i) => s + probabilities[i] * v * v, 0)),
}
Returns
values- array (2 items): [1, 3]
p- 2
norm- ≈2.236
Read numbers from input and return the result. JavaScript basics.
Result
Technical statement
The numerical values in this example are invented. This finite weighted sum is an exact finite-space example; general Lp spaces use an integral and L∞ uses an essential supremum.
Source: Inline notation