Overview
PolynomialFeatures generates a new feature matrix consisting of all polynomial combinations of features with degree less than or equal to the specified degree.
Constructor
new PolynomialFeatures(options?: PolynomialFeaturesOptions)
The degree of the polynomial features. Must be a non-negative integer.
If true, include a bias column (all ones) as the first feature.
If true, only interaction features are produced (no features raised to a power). For example, with features [a, b] and degree 2, only a*b is included, not a^2 or b^2.
Properties
Number of features seen during fit.
Total number of polynomial features in the output.
Exponent matrix. Each row represents one output feature, with values indicating the power of each input feature.
Methods
fit
Compute the polynomial feature combinations.
Training data matrix where each row is a sample and each column is a feature.
this - The fitted transformer instance.
transform(X: Matrix): Matrix
Data matrix to transform.
Matrix - Transformed data with polynomial features.
fitTransform(X: Matrix): Matrix
fit(X).transform(X).
Training data matrix to fit and transform.
Matrix - Transformed data.
Example
import { PolynomialFeatures } from 'bun-scikit';
// Original features: [a, b]
const X = [
[2, 3],
[3, 4],
[4, 5]
];
// Generate degree 2 polynomial features
const poly = new PolynomialFeatures({ degree: 2 });
const XPoly = poly.fitTransform(X);
console.log('Output features:', poly.nOutputFeatures_);
// Output: Output features: 6
// [1, a, b, a^2, a*b, b^2]
console.log('Powers:', poly.powers_);
// Output: Powers:
// [[0, 0], // bias: a^0 * b^0 = 1
// [1, 0], // a^1 * b^0 = a
// [0, 1], // a^0 * b^1 = b
// [2, 0], // a^2 * b^0 = a^2
// [1, 1], // a^1 * b^1 = a*b
// [0, 2]] // a^0 * b^2 = b^2
console.log('Transformed:', XPoly);
// Output for [2, 3]:
// [1, 2, 3, 4, 6, 9]
// 1, a=2, b=3, a^2=4, a*b=6, b^2=9
Example: Interaction-Only Features
import { PolynomialFeatures } from 'bun-scikit';
const X = [[2, 3, 4]];
// Only interaction terms (no powers)
const poly = new PolynomialFeatures({
degree: 2,
interactionOnly: true,
includeBias: false
});
const XPoly = poly.fitTransform(X);
console.log('Powers:', poly.powers_);
// Output: Powers:
// [[1, 0, 0], // a
// [0, 1, 0], // b
// [0, 0, 1], // c
// [1, 1, 0], // a*b
// [1, 0, 1], // a*c
// [0, 1, 1]] // b*c
// Note: a^2, b^2, c^2 are excluded
console.log('Transformed:', XPoly);
// Output: [2, 3, 4, 6, 8, 12]
// a=2, b=3, c=4, a*b=6, a*c=8, b*c=12
Example: Polynomial Regression
import { PolynomialFeatures, LinearRegression } from 'bun-scikit';
// Non-linear relationship: y = x^2
const X = [[1], [2], [3], [4], [5]];
const y = [1, 4, 9, 16, 25];
// Transform to polynomial features
const poly = new PolynomialFeatures({ degree: 2 });
const XPoly = poly.fitTransform(X);
console.log('Polynomial features:', XPoly);
// [[1, 1, 1], // [1, x, x^2] for x=1
// [1, 2, 4], // [1, x, x^2] for x=2
// [1, 3, 9], // [1, x, x^2] for x=3
// [1, 4, 16], // [1, x, x^2] for x=4
// [1, 5, 25]] // [1, x, x^2] for x=5
// Fit linear model on polynomial features
const model = new LinearRegression();
model.fit(XPoly, y);
// Predict
const XTest = [[6]];
const XTestPoly = poly.transform(XTest);
const prediction = model.predict(XTestPoly);
console.log('Prediction for x=6:', prediction);
// Output: Prediction for x=6: [36] (close to 6^2 = 36)
Example: Higher Degree
import { PolynomialFeatures } from 'bun-scikit';
const X = [[2, 3]];
// Degree 3 polynomial
const poly = new PolynomialFeatures({ degree: 3, includeBias: false });
const XPoly = poly.fitTransform(X);
console.log('Output features:', poly.nOutputFeatures_);
// Output: Output features: 9
// [a, b, a^2, a*b, b^2, a^3, a^2*b, a*b^2, b^3]
console.log('Powers:', poly.powers_);
// Shows all combinations up to degree 3
Notes
- Useful for polynomial regression and feature engineering
- The number of output features grows quickly with degree and input features
- For n input features and degree d, the number of output features is C(n+d, d)
- Setting
interactionOnly=true reduces the number of features
- The transformer must be fitted before calling
transform()
- Input data must be finite (no NaN or Infinity values)