@ai-on-browser/data-analysis-models
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Data analysis model package without any dependencies
239 lines (219 loc) • 5.49 kB
JavaScript
import Matrix from '../util/matrix.js'
/**
* Linear discriminant analysis
*/
export class LinearDiscriminant {
// http://alice.info.kogakuin.ac.jp/public_data/2013/J110033b.pdf
constructor() {
this._x = null
this._y = null
this._w = null
this._w0 = null
}
_s(x) {
x.map(v => 1 / (1 + Math.exp(-v)))
}
/**
* Initialize this model.
* @param {Array<Array<number>>} train_x Training data
* @param {Array<1 | -1>} train_y Target values
*/
init(train_x, train_y) {
this._x = train_x
this._y = train_y
}
/**
* Fit model parameters.
*/
fit() {
const x = Matrix.fromArray(this._x)
const x0 = Matrix.fromArray(this._x.filter((_, i) => this._y[i] === 1))
const x1 = Matrix.fromArray(this._x.filter((_, i) => this._y[i] === -1))
const m0 = x0.mean(0)
const m1 = x1.mean(0)
const s = x.cov()
const sinv = s.inv()
this._w = Matrix.sub(m0, m1).dot(sinv).t
this._w0 =
-m0.dot(sinv).dot(m0.t).toScaler() / 2 + m1.dot(sinv).dot(m1.t).toScaler() / 2 + Math.log(x0.rows / x1.rows)
}
/**
* Returns predicted datas.
* @param {Array<Array<number>>} data Sample data
* @returns {(1 | -1)[]} Predicted values
*/
predict(data) {
const x = Matrix.fromArray(data)
const r = x.dot(this._w)
r.add(this._w0)
this._s(r)
r.sub(0.5)
return r.value.map(v => (v <= 0 ? -1 : 1))
}
}
/**
* Fishers linear discriminant analysis
*/
export class FishersLinearDiscriminant {
constructor() {
this._x = null
this._y = null
this._w = null
this._m = null
}
/**
* Initialize this model.
* @param {Array<Array<number>>} train_x Training data
* @param {Array<1 | -1>} train_y Target values
*/
init(train_x, train_y) {
this._x = train_x
this._y = train_y
}
/**
* Fit model parameters.
*/
fit() {
const x0 = Matrix.fromArray(this._x.filter((_, i) => this._y[i] === 1))
const x1 = Matrix.fromArray(this._x.filter((_, i) => this._y[i] === -1))
const m0 = x0.mean(0)
const m1 = x1.mean(0)
x0.sub(m0)
x1.sub(m1)
const Sw = x0.tDot(x0)
Sw.add(x1.tDot(x1))
this._w = Matrix.sub(m0, m1).dot(Sw.inv()).t
this._m = Matrix.fromArray(this._x).mean(0)
}
/**
* Returns predicted datas.
* @param {Array<Array<number>>} data Sample data
* @returns {(1 | -1)[]} Predicted values
*/
predict(data) {
const x = Matrix.fromArray(data)
x.sub(this._m)
return x.dot(this._w).value.map(v => (v <= 0 ? -1 : 1))
}
}
/**
* Multiclass linear discriminant analysis
*/
export class MulticlassLinearDiscriminant {
// http://www.personal.psu.edu/jol2/course/stat597e/notes2/mda.pdf
// https://en.wikipedia.org/wiki/Linear_discriminant_analysis#Multiclass_LDA
/**
* Fit model.
* @param {Array<Array<number>>} x Training data
* @param {*[]} y Target values
*/
fit(x, y) {
const d = x[0].length
this._c = [...new Set(y)]
this._a = []
this._m = []
this._s = Matrix.zeros(d, d)
for (let i = 0; i < this._c.length; i++) {
let xi = x.filter((_, k) => y[k] === this._c[i])
this._a[i] = xi.length / x.length
xi = Matrix.fromArray(xi)
this._m[i] = xi.mean(0)
xi.sub(this._m[i])
this._s.add(xi.tDot(xi))
}
this._s.div(x.length)
this._sinv = this._s.inv()
}
/**
* Returns predicted categories.
* @param {Array<Array<number>>} data Sample data
* @returns {*[]} Predicted values
*/
predict(data) {
const x = Matrix.fromArray(data)
const p = new Matrix(x.rows, this._c.length)
for (let i = 0; i < this._c.length; i++) {
const xi = Matrix.sub(x, this._m[i])
const v = xi.dot(this._sinv)
v.mult(xi)
const s = v.sum(1)
s.map(v => Math.exp(-v / 2) * this._a[i])
p.set(0, i, s)
}
return p.argmax(1).value.map(v => this._c[v])
}
}
/**
* Linear discriminant analysis
*/
export class LinearDiscriminantAnalysis {
// https://axa.biopapyrus.jp/machine-learning/preprocessing/lda.html
/**
* @param {number | null} [rd] Reduced dimension
*/
constructor(rd = null) {
this._rd = rd ?? 0
}
/**
* Returns reduced values.
* @param {Array<Array<number>>} x Training data
* @param {number[]} t Target values
* @returns {Array<Array<number>>} Predicted values
*/
predict(x, t) {
x = Matrix.fromArray(x)
const d = x.cols
const n = x.rows
const c = {}
let cn = 0
for (let i = 0; i < n; i++) {
if (c[t[i]] === undefined) c[t[i]] = cn++
t[i] = c[t[i]]
}
const mean = x.mean(0).value
const cmean = []
for (let i = 0; i < cn; cmean[i++] = Array(d).fill(0));
const cnum = Array(cn).fill(0)
for (let k = 0; k < n; k++) {
cnum[t[k]]++
for (let j = 0; j < d; j++) {
cmean[t[k]][j] += x.at(k, j)
}
}
for (let i = 0; i < cn; i++) {
for (let j = 0; j < d; j++) {
cmean[i][j] /= cnum[i]
}
}
let w = []
for (let i = 0; i < d; w[i++] = []);
for (let i = 0; i < d; i++) {
for (let j = 0; j <= i; j++) {
let v = 0
for (let k = 0; k < n; k++) {
v += (x.at(k, i) - cmean[t[k]][i]) * (x.at(k, j) - cmean[t[k]][j])
}
w[i][j] = w[j][i] = v / n
}
}
w = new Matrix(d, d, w)
let b = []
for (let i = 0; i < d; b[i++] = []);
for (let i = 0; i < d; i++) {
for (let j = 0; j <= i; j++) {
let v = 0
for (let k = 0; k < cn; k++) {
v += (cmean[k][i] - mean[i]) * (cmean[k][j] - mean[j]) * cnum[k]
}
b[i][j] = b[j][i] = v / n
}
}
b = new Matrix(d, d, b)
const cov = w.solve(b)
const ev = cov.eigenVectors()
if (this._rd > 0 && this._rd < ev.cols) {
ev.resize(ev.rows, this._rd)
}
return x.dot(ev).toArray()
}
}