@ai-on-browser/data-analysis-models
Version:
Data analysis model package without any dependencies
290 lines (273 loc) • 6.6 kB
JavaScript
import Matrix from '../util/matrix.js'
const normal_random = function (m = 0, s = 1) {
const std = Math.sqrt(s)
const x = Math.random()
const y = Math.random()
const X = Math.sqrt(-2 * Math.log(x)) * Math.cos(2 * Math.PI * y)
const Y = Math.sqrt(-2 * Math.log(x)) * Math.sin(2 * Math.PI * y)
return [X * std + m, Y * std + m]
}
/**
* Stochastic Neighbor Embedding
*/
export class SNE {
// https://qiita.com/g-k/items/120f1cf85ff2ceae4aba
/**
* @param {Array<Array<number>>} datas Training data
* @param {number} [rd] Reduced dimension
* @param {number} [perplexity] Perplexity
*/
constructor(datas, rd = 1, perplexity = 30) {
this._x = datas
this._epoch = 0
this._rd = rd
this._learning_rate = 0.1
this._perplexity = perplexity
this._y = []
for (let i = 0; i < datas.length; i++) {
this._y[i] = []
for (let k = 0; k < rd; k++) {
this._y[i][k] = normal_random(0, 1.0e-4)[0]
}
}
}
_pj_i(x) {
const n = x.length
const pj_i = []
const norms = []
let maxnorm = 1.0
for (let i = 0; i < n; i++) {
norms[i] = []
norms[i][i] = 0
for (let j = 0; j < i; j++) {
norms[i][j] = norms[j][i] = x[i].reduce((a, v, k) => a + (v - x[j][k]) ** 2, 0)
if (norms[i][j] > maxnorm) {
maxnorm = norms[i][j]
}
}
}
for (let i = 0; i < n; i++) {
let sigma = maxnorm
let lowsigma = 0,
highsigma = null
const tol = 1.0e-8
let pi = Array(n).fill(0)
while (1) {
let s = 0
const sgm = 2 * sigma ** 2
pi[i] = 0
for (let j = 0; j < n; j++) {
if (i === j) continue
s += pi[j] = Math.exp(-norms[i][j] / sgm)
}
let entropy = 0
for (let j = 0; j < n; j++) {
pi[j] /= s
if (pi[j] > tol) {
entropy -= pi[j] * Math.log2(pi[j])
}
}
if (!isFinite(sigma)) {
break
}
const perp = 2 ** entropy
if (Math.abs(perp - this._perplexity) < tol) {
break
} else if (perp < this._perplexity) {
lowsigma = sigma
sigma = highsigma === null ? sigma * 2 : (sigma + highsigma) / 2
} else {
highsigma = sigma
sigma = (sigma + lowsigma) / 2
}
}
pj_i.push(pi)
}
return pj_i
}
/**
* Fit model and returns reduced values.
* @returns {Array<Array<number>>} Predicted values
*/
fit() {
const x = this._x
const y = this._y
const n = x.length
const pj_i = this._pj_i(x)
const q = []
for (let i = 0; i < n; i++) {
let s = 0
q[i] = Array(n).fill(0)
for (let j = 0; j < n; j++) {
if (i === j) continue
const v = Math.exp(-y[i].reduce((a, v, k) => a + (v - y[j][k]) ** 2, 0))
q[i][j] = v
s += v
}
if (s > 0) {
q[i] = q[i].map(r => r / s)
}
}
const d = this._rd
const dy = []
for (let i = 0; i < n; i++) {
dy[i] = Array(d).fill(0)
for (let j = 0; j < n; j++) {
if (j === i) continue
const c = pj_i[i][j] - q[i][j] + pj_i[j][i] - q[j][i]
for (let k = 0; k < d; k++) {
dy[i][k] += c * (y[i][k] - y[j][k])
}
}
}
for (let i = 0; i < n; i++) {
for (let k = 0; k < d; k++) {
y[i][k] -= dy[i][k] * 2 * this._learning_rate
}
}
this._epoch += 1
return new Matrix(n, d, this._y).toArray()
}
/**
* Returns reduced values.
* @returns {Array<Array<number>>} Predicted values
*/
predict() {
return Matrix.fromArray(this._y).toArray()
}
}
/**
* T-distributed Stochastic Neighbor Embedding
*/
export class tSNE {
// https://www.slideshare.net/TakayukiYagi1/tsne
// https://blog.albert2005.co.jp/2015/12/02/tsne/
// https://lvdmaaten.github.io/publications/papers/JMLR_2008.pdf
/**
* @param {Array<Array<number>>} datas Training data
* @param {number} [rd] Reduced dimension
* @param {number} [perplexity] Perplexity
*/
constructor(datas, rd = 1, perplexity = 30) {
this._x = datas
this._epoch = 0
this._rd = rd
this._learning_rate = 200
this._perplexity = perplexity
this._y = []
for (let i = 0; i < datas.length; i++) {
this._y[i] = []
for (let k = 0; k < rd; k++) {
this._y[i][k] = normal_random(0, 1.0e-4)[0]
}
}
}
_pj_i(x) {
const n = x.length
const pj_i = []
const norms = []
let maxnorm = 1.0
for (let i = 0; i < n; i++) {
norms[i] = []
norms[i][i] = 0
for (let j = 0; j < i; j++) {
norms[i][j] = norms[j][i] = x[i].reduce((a, v, k) => a + (v - x[j][k]) ** 2, 0)
if (norms[i][j] > maxnorm) {
maxnorm = norms[i][j]
}
}
}
for (let i = 0; i < n; i++) {
let sigma = maxnorm
let lowsigma = 0,
highsigma = null
const tol = 1.0e-8
let pi = Array(n).fill(0)
while (1) {
let s = 0
const sgm = 2 * sigma ** 2
pi[i] = 0
for (let j = 0; j < n; j++) {
if (i === j) continue
s += pi[j] = Math.exp(-norms[i][j] / sgm)
}
let entropy = 0
for (let j = 0; j < n; j++) {
pi[j] /= s
if (pi[j] > tol) {
entropy -= pi[j] * Math.log2(pi[j])
}
}
if (!isFinite(sigma)) {
break
}
const perp = 2 ** entropy
if (Math.abs(perp - this._perplexity) < tol) {
break
} else if (perp < this._perplexity) {
lowsigma = sigma
sigma = highsigma === null ? sigma * 2 : (sigma + highsigma) / 2
} else {
highsigma = sigma
sigma = (sigma + lowsigma) / 2
}
}
pj_i.push(pi)
}
return pj_i
}
/**
* Fit model and returns reduced values.
* @returns {Array<Array<number>>} Predicted values
*/
fit() {
const x = this._x
const y = this._y
const n = x.length
const pj_i = this._pj_i(x)
const p = []
for (let i = 0; i < n; i++) {
p[i] = []
for (let j = 0; j <= i; j++) {
p[i][j] = p[j][i] = (pj_i[i][j] + pj_i[j][i]) / (2 * n)
}
}
const qtmp = []
let qden = 0
for (let i = 0; i < n; i++) {
qtmp[i] = []
for (let j = 0; j <= i; j++) {
const v = 1 / (1 + y[i].reduce((a, v, k) => a + (v - y[j][k]) ** 2, 0))
qtmp[i][j] = qtmp[j][i] = v
if (i !== j) qden += v * 2
}
}
const q = qtmp.map(r => r.map(v => v / qden))
const d = this._rd
const dy = []
for (let i = 0; i < n; i++) {
dy[i] = Array(d).fill(0)
for (let j = 0; j < n; j++) {
if (j === i) continue
const c = (p[i][j] - q[i][j]) * qtmp[i][j]
for (let k = 0; k < d; k++) {
dy[i][k] += c * (y[i][k] - y[j][k])
}
}
}
for (let i = 0; i < n; i++) {
for (let k = 0; k < d; k++) {
y[i][k] -= dy[i][k] * 4 * this._learning_rate
}
}
this._epoch += 1
return new Matrix(n, d, this._y).toArray()
}
/**
* Returns reduced values.
* @returns {Array<Array<number>>} Predicted values
*/
predict() {
return Matrix.fromArray(this._y).toArray()
}
}