Add Monothetic Clustering (#38)

Author: ishii-norimi

README.md

@@ -121,7 +121,7 @@ for (let i = 0; i < n; i++) {
 
 | task | model |
 | ---- | ----- |
-| clustering | k-means, k-means++, k-medois, k-medians, x-means, G-means, LBG, ISODATA, Soft k-means, Fuzzy c-means, Possibilistic c-means, Kernel k-means, Agglomerative (complete linkage, single linkage, group average, Ward's, centroid, weighted average, median), DIANA, Mean shift, DBSCAN, OPTICS, HDBSCAN, PAM, CLARA, CLARANS, BIRCH, CURE, ROCK, PLSA, Latent dirichlet allocation, GMM, VBGMM, Affinity propagation, Spectral clustering, Mountain, SOM, GTM, (Growing) Neural gas, Growing cell structures, LVQ, ART, SVC, CAST, NMF, Autoencoder |
+| clustering | k-means, k-means++, k-medois, k-medians, x-means, G-means, LBG, ISODATA, Soft k-means, Fuzzy c-means, Possibilistic c-means, Kernel k-means, Agglomerative (complete linkage, single linkage, group average, Ward's, centroid, weighted average, median), DIANA, Monothetic, Mean shift, DBSCAN, OPTICS, HDBSCAN, PAM, CLARA, CLARANS, BIRCH, CURE, ROCK, PLSA, Latent dirichlet allocation, GMM, VBGMM, Affinity propagation, Spectral clustering, Mountain, SOM, GTM, (Growing) Neural gas, Growing cell structures, LVQ, ART, SVC, CAST, NMF, Autoencoder |
 | classification | Linear discriminant (FLD, LDA), Quadratic discriminant, Mixture discriminant, Least squares, Ridge, (Complement / Negation / Universal-set / Selective) Naive Bayes (gaussian), AODE, k-nearest neighbor, Radius neighbor, Fuzzy k-nearest neighbor, Nearest centroid, DANN, Decision tree, Random forest, Extra trees, GBDT, XGBoost, ALMA, ROMMA, Online gradient descent, Passive aggressive, RLS, Second order perceptron, AROW, NAROW, Confidence weighted, CELLIP, IELLIP, Normal herd, (Multinomial) Logistic regression, (Multinomial) Probit, SVM, Gaussian process, HMM, CRF, Bayesian Network, LVQ, Perceptron, ADALINE, MLP, LMNN |
 | semi-supervised classification | k-nearest neighbor, Radius neighbor, Label propagation, Label spreading, k-means, GMM, Ladder network |
 | regression | Least squares, Ridge, Lasso, Elastic net, RLS, Bayesian linear, Poisson, Least absolute deviations, Huber, Tukey, Least trimmed squares, Least median squares, Lp norm linear, SMA, Deming, Segmented, LOWESS, spline, Gaussian process, Principal components, Partial least squares, Projection pursuit, Quantile regression, k-nearest neighbor, Radius neighbor, IDW, Nadaraya Watson, Priestley Chao, Gasser Muller, RBF Network, RVM, Decision tree, Random forest, Extra trees, GBDT, XGBoost, SVR, MLP, GMR, Isotonic, Ramer Douglas Peucker, Theil-Sen, Passing-Bablok, Repeated median |

js/model_selector.js

@@ -74,6 +74,7 @@ const AIMethods = [
 				{ value: 'cure', title: 'CURE' },
 				{ value: 'rock', title: 'ROCK' },
 				{ value: 'diana', title: 'DIANA' },
+				{ value: 'monothetic', title: 'Monothetic' },
 			],
 			Distribution: [
 				{ value: 'gmm', title: 'Gaussian mixture model' },

js/view/monothetic.js

@@ -0,0 +1,40 @@
+import MonotheticClustering from '../../lib/model/monothetic.js'
+
+var dispMonothetic = function (elm, platform) {
+	let model = null
+
+	const fitModel = cb => {
+		platform.fit((tx, ty, pred_cb) => {
+			if (!model) {
+				model = new MonotheticClustering()
+				model.init(tx)
+			}
+			model.fit()
+			const pred = model.predict()
+			pred_cb(pred.map(v => v + 1))
+			elm.select('[name=clusters]').text(model.size)
+			cb && cb()
+		})
+	}
+
+	elm.append('input')
+		.attr('type', 'button')
+		.attr('value', 'Initialize')
+		.on('click', () => {
+			model = null
+			elm.select('[name=clusters]').text(0)
+		})
+	elm.append('input')
+		.attr('type', 'button')
+		.attr('value', 'Step')
+		.on('click', () => {
+			fitModel()
+		})
+	elm.append('span').text(' Clusters: ')
+	elm.append('span').attr('name', 'clusters')
+}
+
+export default function (platform) {
+	platform.setting.ml.usage = 'Click and add data point. Then, click "Step" button repeatedly.'
+	dispMonothetic(platform.setting.ml.configElement, platform)
+}

lib/model/monothetic.js

@@ -0,0 +1,136 @@
+/**
+ * Monothetic Clustering
+ */
+export default class MonotheticClustering {
+	// https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.106.2839&rep=rep1&type=pdf
+	// https://cran.r-project.org/web/packages/monoClust/vignettes/monoclust.html
+	constructor() {}
+
+	/**
+	 * Number of clusters
+	 *
+	 * @type {number}
+	 */
+	get size() {
+		return this._leafs().length
+	}
+
+	/**
+	 * Initialize model.
+	 *
+	 * @param {Array<Array<number>>} datas
+	 */
+	init(datas) {
+		this._x = datas
+		this._d = datas[0].length
+		const idx = []
+		for (let i = 0; i < datas.length; idx[i] = i++);
+		this._c = { index: idx, values: this._x, children: [] }
+	}
+
+	_leafs() {
+		let leafs = [this._c]
+		while (true) {
+			const stk = []
+			for (let i = 0; i < leafs.length; i++) {
+				if (leafs[i].children.length > 0) {
+					stk.push(...leafs[i].children)
+				} else {
+					stk.push(leafs[i])
+				}
+			}
+			if (leafs.length === stk.length) {
+				return leafs
+			}
+			leafs = stk
+		}
+	}
+
+	_distance2(a, b) {
+		return a.reduce((s, v, i) => s + (v - b[i]) ** 2, 0)
+	}
+
+	_inertia(c) {
+		const m = c[0].concat()
+		for (let i = 1; i < c.length; i++) {
+			for (let d = 0; d < this._d; d++) {
+				m[d] += c[i][d]
+			}
+		}
+		for (let d = 0; d < this._d; d++) {
+			m[d] /= c.length
+		}
+
+		let v = 0
+		for (let i = 0; i < c.length; i++) {
+			v += this._distance2(c[i], m)
+		}
+		return v
+	}
+
+	/**
+	 * Fit model.
+	 */
+	fit() {
+		const leafs = this._leafs()
+
+		let max_d = -Infinity
+		let best_f = -1
+		let best_t = -1
+		let best_leaf = null
+		for (let k = 0; k < leafs.length; k++) {
+			const x = leafs[k].values
+			const ck = this._inertia(x)
+			for (let d = 0; d < this._d; d++) {
+				const xd = x.map(v => v[d])
+				xd.sort((a, b) => a - b)
+				for (let i = 0; i < xd.length - 1; i++) {
+					const t = (xd[i] + xd[i + 1]) / 2
+					const x1 = x.filter(v => v[d] <= t)
+					const x2 = x.filter(v => v[d] > t)
+					const ck1 = this._inertia(x1)
+					const ck2 = this._inertia(x2)
+
+					const dck = ck - ck1 - ck2
+					if (max_d < dck) {
+						max_d = dck
+						best_f = d
+						best_t = t
+						best_leaf = leafs[k]
+					}
+				}
+			}
+		}
+
+		best_leaf.feature = best_f
+		best_leaf.threshold = best_t
+		best_leaf.children = [
+			{
+				index: best_leaf.index.filter((v, i) => best_leaf.values[i][best_f] <= best_t),
+				values: best_leaf.values.filter(v => v[best_f] <= best_t),
+				children: [],
+			},
+			{
+				index: best_leaf.index.filter((v, i) => best_leaf.values[i][best_f] > best_t),
+				values: best_leaf.values.filter(v => v[best_f] > best_t),
+				children: [],
+			},
+		]
+	}
+
+	/**
+	 * Returns predicted categories.
+	 *
+	 * @returns {number[]}
+	 */
+	predict() {
+		const leafs = this._leafs()
+		const p = []
+		for (let k = 0; k < leafs.length; k++) {
+			for (let i = 0; i < leafs[k].index.length; i++) {
+				p[leafs[k].index[i]] = k
+			}
+		}
+		return p
+	}
+}

tests/lib/model/monothetic.test.js

@@ -0,0 +1,22 @@
+import Matrix from '../../../lib/util/matrix.js'
+import MonotheticClustering from '../../../lib/model/monothetic.js'
+
+import { randIndex } from '../../../lib/evaluate/clustering.js'
+
+test('clustering', () => {
+	const model = new MonotheticClustering()
+	const n = 50
+	const x = Matrix.randn(n, 2, 0, 0.1).concat(Matrix.randn(n, 2, 5, 0.1)).toArray()
+
+	model.init(x)
+	model.fit()
+	const y = model.predict()
+	expect(y).toHaveLength(x.length)
+
+	const t = []
+	for (let i = 0; i < x.length; i++) {
+		t[i] = Math.floor(i / n)
+	}
+	const ri = randIndex(y, t)
+	expect(ri).toBeGreaterThan(0.9)
+})