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Add GPLVM
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‎README.md

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@@ -31,7 +31,7 @@ Javascript AI package and online demo.
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| regression | Least squares, Ridge, Lasso, Elastic net, RLS, Bayesian linear, Poisson, Least absolute deviations, Least trimmed squares, Least median squares, Lp norm linear, Segmented, LOWESS, spline, Gaussian process, Principal components, Partial least squares, Projection pursuit, Quantile regression, k nearest neighbor, IDW, Nadaraya Watson, Priestley Chao, Gasser Muller, RBF Network, RVM, Decision tree, Random forest, GBDT, XGBoost, SVR, MLP, GMR, Isotonic, Ramer Douglas Peucker |
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| interpolation | Nearest neighbor, IDW, Linear, Brahmagupta, Logarithmic, Cosine, (Inverse) Smoothstep, Cubic, (Centripetal) Catmull-Rom, Hermit, Polynomial, Lagrange, Trigonometric, Spline, RBF Network, Akima |
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| anomaly detection | Percentile, MAD, Tukey's fences, Grubbs's test, Thompson test, Tietjen Moore test, Generalized ESD, Hotelling, MT, MCD, k nearest neighbor, LOF, PCA, OCSVM, KDE, GMM, Isolation forest, Autoencoder, GAN |
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| dimensionality reduction | Random projection, (Dual/Kernel) PCA, Incremental PCA, Probabilistic PCA, LSA, MDS, Linear discriminant analysis, NCA, ICA, Principal curve, Sammon, FastMap, Sliced inverse regression, LLE, Laplacian eigenmaps, Isomap, SNE, t-SNE, SOM, GTM, NMF, Autoencoder, VAE |
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| dimensionality reduction | Random projection, (Dual/Kernel) PCA, Incremental PCA, Probabilistic PCA, GPLVM, LSA, MDS, Linear discriminant analysis, NCA, ICA, Principal curve, Sammon, FastMap, Sliced inverse regression, LLE, Laplacian eigenmaps, Isomap, SNE, t-SNE, SOM, GTM, NMF, Autoencoder, VAE |
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| feature selection | Mutual information, Ridge, Lasso, Elastic net, Decision tree, NCA |
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| transformation | Box-Cox, Yeo-Johnson |
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| density estimation | Histogram, Average shifted histogram, Polynomial histogram, Maximum likelihood, Kernel density estimation, k nearest neighbor, GMM, HMM |

‎js/model_selector.js

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@@ -249,6 +249,7 @@ const AIMethods = [
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{ value: 'pca', title: 'PCA' },
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{ value: 'incremental_pca', title: 'Incremental PCA' },
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{ value: 'probabilistic_pca', title: 'Probabilistic PCA' },
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{ value: 'gplvm', title: 'GPLVM' },
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{ value: 'lsa', title: 'LSA' },
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{ value: 'mds', title: 'MDS' },
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{ value: 'lda', title: 'Linear Discriminant Analysis' },

‎js/view/gplvm.js

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import GPLVM from '../../lib/model/gplvm.js'
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var dispGPLVM = function (elm, platform) {
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let model = null
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const fitModel = () => {
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platform.fit((tx, ty, pred_cb) => {
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if (!model) {
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const dim = platform.dimension
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const alpha = +elm.select('[name=alpha]').property('value')
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const sigma = +elm.select('[name=sigma]').property('value')
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const ez = +elm.select('[name=ez]').property('value')
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const ea = +elm.select('[name=ea]').property('value')
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const ep = +elm.select('[name=ep]').property('value')
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model = new GPLVM(dim, alpha, ez, ea, ep, 'gaussian', [1.0, sigma])
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model.init(tx)
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}
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model.fit()
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console.log(model._kernel._b)
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const y = model.predict(tx)
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pred_cb(y)
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})
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}
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const kernelElm = elm.append('span')
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kernelElm
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.append('select')
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.attr('name', 'kernel')
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.selectAll('option')
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.data(['gaussian'])
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.enter()
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.append('option')
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.attr('value', d => d)
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.text(d => d)
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const gauss_sigma = kernelElm.append('span')
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gauss_sigma
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.append('span')
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.text(' sigma = ')
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.append('input')
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.attr('type', 'number')
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.attr('name', 'sigma')
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.attr('value', 1)
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.attr('min', 0)
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.attr('max', 10)
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.attr('step', 0.1)
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elm.append('span')
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.text(' alpha = ')
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.append('input')
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.attr('type', 'number')
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.attr('name', 'alpha')
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.attr('value', 0.05)
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.attr('min', 0)
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.attr('max', 10)
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.attr('step', 0.01)
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elm.append('span')
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.text(' ez = ')
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.append('input')
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.attr('type', 'number')
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.attr('name', 'ez')
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.attr('value', 0.01)
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.attr('min', 0)
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.attr('max', 10)
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.attr('step', 0.001)
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elm.append('span')
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.text(' ea = ')
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.append('input')
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.attr('type', 'number')
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.attr('name', 'ea')
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.attr('value', 0.00005)
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.attr('min', 0)
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.attr('max', 10)
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.attr('step', 0.001)
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elm.append('span')
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.text(' ep = ')
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.append('input')
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.attr('type', 'number')
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.attr('name', 'ep')
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.attr('value', 0.0002)
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.attr('min', 0)
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.attr('max', 10)
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.attr('step', 0.001)
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platform.setting.ml.controller
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.stepLoopButtons()
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.init(() => {
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model = null
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platform.init()
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})
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.step(fitModel)
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.epoch()
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}
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export default function (platform) {
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platform.setting.ml.usage = 'Click and add data point. Next, click "Fit" button.'
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dispGPLVM(platform.setting.ml.configElement, platform)
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}

‎lib/model/gplvm.js

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import { Matrix } from '../util/math.js'
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class GaussianKernel {
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constructor(a = 1.0, b = 1.0, e = 0.1) {
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this._a = a
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this._b = b
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this._e = e
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}
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_calc(x0, x1) {
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const s = x0.copySub(x1).reduce((acc, v) => acc + v * v, 0)
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return this._a * Math.exp(-s / (2 * this._b))
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}
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_grad(x0, x1, k) {
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const g = x0.copySub(x1)
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g.mult((-this._a * k) / this._b)
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return g
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}
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calc(x, y) {
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if (!y) {
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y = x
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}
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const n = x.rows
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const m = y.rows
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const K = new Matrix(n, m)
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for (let i = 0; i < n; i++) {
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const xi = x.row(i)
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for (let j = 0; j < m; j++) {
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const v = this._calc(xi, y.row(j))
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K.set(i, j, v)
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}
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}
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return K
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}
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grad(x, k) {
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const n = x.rows
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const d = new Matrix(n, n)
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for (let i = 0; i < n; i++) {
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const xi = x.row(i)
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for (let j = 0; j < n; j++) {
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const v = this._grad(xi, x.row(j), k.at(i, j))
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d.set(i, j, v.value)
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}
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}
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return d
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}
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update(x, k, G) {
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if (this._e === 0) {
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return
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}
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const n = x.rows
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const d = new Matrix(n, n)
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for (let i = 0; i < n; i++) {
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const xi = x.row(i)
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for (let j = 0; j < n; j++) {
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const di = xi.copySub(x.row(j))
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di.map(v => v ** 2)
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const s = -(this._a * di.sum()) / (2 * this._b ** 2)
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d.set(i, j, s * k.at(i, j))
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}
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}
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const dsig = G.copyMult(d.t).sum()
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this._b = Math.exp(Math.log(this._b) + this._e / n * dsig)
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if (this._b === 0) {
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this._b = 1.0e-8
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}
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}
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}
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/**
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* Gaussian Process Latent Variable Model
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*/
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export default class GPLVM {
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// https://qiita.com/student-i/items/328030426fa42b6010f9
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// https://cmbnur.com/?p=1621
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// https://ayatoashihara.github.io/my_blog/post/post9/
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/**
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* @param {number} rd
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* @param {number} alpha
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* @param {number} ez
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* @param {number} ea
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* @param {number} ep
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* @param {'gaussian'} [kernel='gaussian']
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* @param {*[]} [kernelArgs]
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*/
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constructor(rd, alpha, ez = 0.01, ea = 0.00005, ep = 0.002, kernel = 'gaussian', kernelArgs = []) {
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this._rd = rd
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this._alpha = alpha
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if (kernel === 'gaussian') {
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this._kernel = new GaussianKernel(...kernelArgs, ep)
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}
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this._ez = ez
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this._ea = ea
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}
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/**
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* Initialize model.
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* @param {Array<Array<number>>} x
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*/
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init(x) {
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this._x = Matrix.fromArray(x)
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this._z = Matrix.randn(x.length, this._rd, 0, 0.01)
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this._s = this._x.dot(this._x.t)
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}
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/**
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* Fit model.
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*/
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fit() {
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const n = this._x.rows
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const ker = this._kernel.calc(this._z)
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const K = ker.copyAdd(Matrix.eye(n, n, this._alpha))
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const Kinv = K.inv()
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const G = Kinv.dot(this._s).dot(Kinv)
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G.sub(Kinv.copyMult(this._x.cols))
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G.div(2)
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const dK = this._kernel.grad(this._z, K)
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const dz = new Matrix(n, this._rd)
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for (let i = 0; i < n; i++) {
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const dzi = Matrix.zeros(1, this._rd)
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for (let j = 0; j < n; j++) {
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const v = new Matrix(1, this._rd, dK.at(i, j))
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v.mult(G.at(i, j))
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dzi.add(v)
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}
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dz.set(i, 0, dzi)
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}
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dz.mult(this._ez / n)
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this._kernel.update(this._z, ker, G)
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this._z.add(dz)
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this._alpha = Math.exp(Math.log(this._alpha) + this._ea / n * G.trace() * this._alpha)
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}
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/**
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* Returns reduced datas.
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*/
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predict() {
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return this._z.toArray()
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}
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/**
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* Returns reconstruct datas.
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* @param {Array<Array<number>>} z
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*/
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reconstruct(z) {
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z = Matrix.fromArray(z)
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const n = this._z.rows
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const K = this._kernel.calc(this._z)
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const Ka = K.copyAdd(Matrix.eye(n, n, this._alpha))
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const ks = this._kernel.calc(z, this._z)
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return ks.dot(Ka.solve(this._x)).toArray()
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}
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}

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