ridge.js

import Matrix from '../util/matrix.js'

/**
 * Ridge regressioin
 */
export class Ridge {
	/**
	 * @param {number} [lambda] Regularization strength
	 */
	constructor(lambda = 0.1) {
		this._w = null
		this._lambda = lambda
	}

	/**
	 * Fit model.
	 *
	 * @param {Array<Array<number>>} x Training data
	 * @param {Array<Array<number>>} y Target values
	 */
	fit(x, y) {
		x = Matrix.fromArray(x)
		y = Matrix.fromArray(y)
		const xtx = x.tDot(x)
		for (let i = 0; i < xtx.rows; i++) {
			xtx.addAt(i, i, this._lambda)
		}

		this._w = xtx.solve(x.t).dot(y)
	}

	/**
	 * Returns predicted values.
	 *
	 * @param {Array<Array<number>>} x Sample data
	 * @returns {Array<Array<number>>} Predicted values
	 */
	predict(x) {
		x = Matrix.fromArray(x)
		return x.dot(this._w).toArray()
	}

	/**
	 * Returns importances of the features.
	 *
	 * @returns {number[]} Importances
	 */
	importance() {
		return this._w.value
	}
}

/**
 * Multiclass ridge regressioin
 */
export class MulticlassRidge {
	/**
	 * @param {number} [lambda] Regularization strength
	 */
	constructor(lambda = 0.1) {
		this._w = null
		this._lambda = lambda
		this._classes = []
	}

	/**
	 * Category list
	 *
	 * @type {*[]}
	 */
	get categories() {
		return this._classes
	}

	/**
	 * Fit model.
	 *
	 * @param {Array<Array<number>>} x Training data
	 * @param {*[]} y Target values
	 */
	fit(x, y) {
		x = Matrix.fromArray(x)
		this._classes = [...new Set(y)]
		const p = new Matrix(y.length, this._classes.length, -1)
		for (let i = 0; i < y.length; i++) {
			p.set(i, this._classes.indexOf(y[i]), 1)
		}
		const xtx = x.tDot(x)
		for (let i = 0; i < xtx.rows; i++) {
			xtx.addAt(i, i, this._lambda)
		}

		this._w = xtx.solve(x.t).dot(p)
	}

	/**
	 * Returns predicted values.
	 *
	 * @param {Array<Array<number>>} x Sample data
	 * @returns {*[]} Predicted values
	 */
	predict(x) {
		x = Matrix.fromArray(x)
		return x
			.dot(this._w)
			.argmax(1)
			.value.map(i => this._classes[i])
	}

	/**
	 * Returns importances of the features.
	 *
	 * @returns {number[]} Importances
	 */
	importance() {
		return this._w.toArray()
	}
}

/**
 * Kernel ridge regression
 */
export class KernelRidge {
	/**
	 * @param {number} [lambda] Regularization strength
	 * @param {'gaussian' | { name: 'gaussian', s?: number } | function (number[], number[]): number} [kernel] Kernel name
	 */
	constructor(lambda = 0.1, kernel = 'gaussian') {
		this._w = null
		this._x = null
		this._lambda = lambda
		this._kernel = null
		if (typeof kernel === 'function') {
			this._kernel = (a, b) => kernel(a.value, b.value)
		} else {
			if (typeof kernel === 'string') {
				kernel = { name: kernel }
			}
			const s = kernel.s ?? 1.0
			this._kernel = (x, y, sigma = s) => {
				const s = Matrix.sub(x, y).reduce((acc, v) => acc + v * v, 0)
				return Math.exp(-s / sigma ** 2)
			}
		}
	}

	/**
	 * Fit model.
	 *
	 * @param {Array<Array<number>>} x Training data
	 * @param {Array<Array<number>>} y Target values
	 */
	fit(x, y) {
		x = Matrix.fromArray(x)
		y = Matrix.fromArray(y)
		const K = new Matrix(x.rows, x.rows)
		this._x = []
		for (let i = 0; i < x.rows; i++) {
			this._x.push(x.row(i))
			K.set(i, i, this._kernel(this._x[i], this._x[i]) + this._lambda)
			for (let j = 0; j < i; j++) {
				const v = this._kernel(this._x[i], this._x[j])
				K.set(i, j, v)
				K.set(j, i, v)
			}
		}
		this._w = K.solve(y)
	}

	/**
	 * Returns predicted values.
	 *
	 * @param {Array<Array<number>>} x Sample data
	 * @returns {Array<Array<number>>} Predicted values
	 */
	predict(x) {
		x = Matrix.fromArray(x)
		const K = new Matrix(x.rows, this._x.length)
		for (let i = 0; i < x.rows; i++) {
			const xi = x.row(i)
			for (let j = 0; j < this._x.length; j++) {
				const v = this._kernel(xi, this._x[j])
				K.set(i, j, v)
			}
		}
		return K.dot(this._w).toArray()
	}

	/**
	 * Returns importances of the features.
	 *
	 * @returns {number[]} Importances
	 */
	importance() {
		return this._w.value
	}
}