Add Brahmagupta's interpolation

Author: ishii-norimi

README.md

@@ -21,7 +21,7 @@ This is a site where you can easily try out AI in your browser.
 | classification | Linear discriminant (FLD, LDA), Quadratic discriminant, Mixture discriminant, Least squares, Ridge, Naive bayes (gaussian), AODE, k nearest neighbor, Nearest centroid, Decision tree, Random forest, 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, LVQ, Perceptron, ADALINE, MLP |
 | semi-supervised classification | k nearest neighbor, Label propagation, Label spreading, k-means, GMM |
 | 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, RBF Network, RVM, Decision tree, Random forest, GBDT, XGBoost, SVR, MLP, GMR, Isotonic, Ramer Douglas Peucker |
-| interpolation | Nearest neighbor, IDW, Linear, Logarithmic, Cosine, (Inverse) Smoothstep, Cubic, (Centripetal) Catmull-Rom, Hermit, Polynomial, Lagrange, Trigonometric, Spline, RBF Network, Akima |
+| interpolation | Nearest neighbor, IDW, Linear, Brahmagupta, Logarithmic, Cosine, (Inverse) Smoothstep, Cubic, (Centripetal) Catmull-Rom, Hermit, Polynomial, Lagrange, Trigonometric, Spline, RBF Network, Akima |
 | anomaly detection | Percentile, MAD, 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 |
 | dimension reduction | Random projection, PCA (kernel), 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 |
 | feature selection | Mutual information, Ridge, Lasso, Elastic net, Decision tree, NCA |

js/model_selector.js

@@ -196,6 +196,7 @@ const AIMethods = [
 			{ value: "knearestneighbor", title: "nearest neighbor" },
 			{ value: "inverse_distance_weighting", title: "IDW" },
 			{ value: "lerp", title: "Linear" },
+			{ value: "brahmagupta_interpolation", title: "Brahmagupta" },
 			// { value: "slerp", title: "Slerp" },
 			{ value: "logarithmic_interpolation", title: "Logarithmic" },
 			{ value: "cosine_interpolation", title: "Cosine" },

model/brahmagupta_interpolation.js

@@ -0,0 +1,55 @@
+class BrahmaguptaInterpolation {
+	// https://en.wikipedia.org/wiki/Brahmagupta%27s_interpolation_formula
+	constructor() {}
+
+	fit(x, y) {
+		const d = x.map((v, i) => [v, y[i]])
+		d.sort((a, b) => a[0] - b[0])
+		this._x = d.map((v) => v[0])
+		this._y = d.map((v) => v[1])
+	}
+
+	predict(target) {
+		const n = this._x.length
+		return target.map((t) => {
+			if (t <= this._x[0]) {
+				return this._y[0]
+			} else if (t >= this._x[n - 1]) {
+				return this._y[n - 1]
+			}
+			for (let i = 1; i < n; i++) {
+				if (t <= this._x[i]) {
+					const p = (t - this._x[i - 1]) / (this._x[i] - this._x[i - 1])
+					const y0 = i > 1 ? this._y[i - 2] : this._y[i - 1] * 2 - this._y[i]
+					const d1 = this._y[i] - this._y[i - 1]
+					const d0 = this._y[i - 1] - y0
+					return ((d1 - d0) / 2) * p ** 2 + ((d1 + d0) / 2) * p + this._y[i - 1]
+				}
+			}
+			return this._y[n - 1]
+		})
+	}
+}
+
+var dispBrahmagupta = function (elm, platform) {
+	const calcBrahmagupta = function () {
+		platform.fit((tx, ty) => {
+			const model = new BrahmaguptaInterpolation()
+			model.fit(
+				tx.map((v) => v[0]),
+				ty.map((v) => v[0])
+			)
+			platform.predict((px, cb) => {
+				const pred = model.predict(px.map((v) => v[0]))
+				cb(pred)
+			}, 1)
+		})
+	}
+
+	elm.append('input').attr('type', 'button').attr('value', 'Calculate').on('click', calcBrahmagupta)
+}
+
+export default function (platform) {
+	platform.setting.ml.usage = 'Click and add data point. Then, click "Calculate".'
+	dispBrahmagupta(platform.setting.ml.configElement, platform)
+}