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coll.js
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coll.js
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import Matrix from '../util/matrix.js'
/**
* Conscience on-line learning
*/
export default class COLL {
// A Conscience On-line Learning Approach for Kernel-Based Clustering
// https://03e7422d-a-62cb3a1a-s-sites.googlegroups.com/site/sunnycdwhl/2010_ICDM_Wang_COLL.pdf
/**
* @param {number} c Number of clusters
* @param {number} [eta] Initial learning rate
* @param {'gaussian' | 'polynomial' | { name: 'gaussian', s?: number } | { name: 'polynomial', d?: number } | function (number[], number[]): number} [kernel] Kernel name
*/
constructor(c, eta = 1, kernel = 'gaussian') {
this._c = c
this._eta = eta
if (typeof kernel === 'function') {
this._kernel = kernel
} else {
if (typeof kernel === 'string') {
kernel = { name: kernel }
}
switch (kernel.name) {
case 'gaussian':
this._s = kernel.s ?? 1
this._kernel = (a, b) =>
Math.exp(-(a.reduce((s, v, i) => s + (v - b[i]) ** 2, 0) ** 2) / this._s ** 2)
break
case 'polynomial':
this._d = kernel.d ?? 2
this._kernel = (a, b) => (1 + a.reduce((s, v, i) => s + v * b[i])) ** this._d
break
}
}
}
/**
* Initialize model.
*
* @param {Array<Array<number>>} datas Training data
*/
init(datas) {
this._datas = datas
const n = datas.length
this._k = []
this._nu = []
this._t = 0
this._nk = Array(this._c).fill(0)
for (let i = 0; i < n; i++) {
this._nu[i] = Math.floor(Math.random() * this._c)
this._nk[this._nu[i]]++
this._k[i] = []
this._k[i][i] = this._kernel(datas[i], datas[i])
for (let j = 0; j < i; j++) {
this._k[i][j] = this._k[j][i] = this._kernel(datas[i], datas[j])
}
}
this._f = this._nk.map(v => v / n)
const A = Matrix.zeros(this._c, n)
for (let i = 0; i < n; i++) {
A.set(this._nu[i], i, 1 / this._nk[this._nu[i]])
}
const K = Matrix.fromArray(this._k)
const AK = A.dot(K)
this._w = new Matrix(this._c, n + 1)
this._w.set(0, 0, AK)
for (let k = 0; k < this._c; k++) {
let v = 0
for (let i = 0; i < n; i++) {
v += AK.at(k, i) * A.at(k, i)
}
this._w.set(k, n, v)
}
}
/**
* Fit model once.
*
* @returns {number} Convergence criterion
*/
fit() {
const n = this._datas.length
const pi = Array.from({ length: this._c }, () => [])
const idx = Array.from({ length: n }, (_, i) => i)
for (let i = idx.length - 1; i > 0; i--) {
const r = Math.floor(Math.random() * (i + 1))
;[idx[i], idx[r]] = [idx[r], idx[i]]
}
this._t++
const eta = this._eta / this._t
for (let l = 0; l < n; l++) {
const i = idx[l]
let min_nu = -1
let min_v = Infinity
for (let k = 0; k < this._c; k++) {
const v = this._f[k] * (this._k[i][i] + this._w.at(k, n) - 2 * this._w.at(k, i))
if (v < min_v) {
min_v = v
min_nu = k
}
}
this._nu[i] = min_nu
pi[min_nu].push(i)
for (let j = 0; j < n; j++) {
this._w.set(min_nu, j, (1 - eta) * this._w.at(min_nu, j) + eta * this._k[i][j])
}
this._w.set(
min_nu,
n,
(1 - eta) ** 2 * this._w.at(min_nu, n) +
eta ** 2 * this._k[i][i] +
2 * (1 - eta) * eta * this._w.at(min_nu, i)
)
this._nk[min_nu] += 1
const sumn = this._nk.reduce((s, v) => s + v, 0)
this._f = this._nk.map(v => v / sumn)
}
if (eta === 1) {
return Infinity
}
let err = 0
for (let k = 0; k < this._c; k++) {
err += (1 - 1 / (1 - eta) ** pi[k].length) ** 2 * this._w.at(k, n)
for (let h = 0; h < pi[k].length; h++) {
for (let l = 0; l < pi[k].length; l++) {
err += (eta ** 2 * this._k[pi[k][h]][pi[k][l]]) / (1 - eta) ** (h + l)
}
}
const s = 2 * eta * (1 - 1 / (1 - eta) ** pi[k].length)
for (let l = 0; l < pi[k].length; l++) {
err += (s * this._w.at(k, pi[k][l])) / (1 - eta) ** l
}
}
return err
}
/**
* Returns predicted categories.
*
* @returns {number[]} Predicted values
*/
predict() {
return this._nu
}
}