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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 | 42x 42x 17243x 17243x 1x 17242x 1x 17243x 2448x 2448x 2448x 2448x 2448x 2448x 36x 36x 36x 36x 36x 36x 36x 36x 36x 36x 36x 36x 36x 36x 36x 36x 36x 36x 2448x 2448x 2448x 2448x 2448x 2412x 2412x 2412x 36x 2412x 2412x 36x 36x 36x 39x 72x 452x 17x 1x 16x 16x 36x 36x 16x 36x 36x 36x 36x 36x 42x 42x 42x 42x 42x | /* * Copyright (c) AXA Group Operations Spain S.A. * * Permission is hereby granted, free of charge, to any person obtaining * a copy of this software and associated documentation files (the * "Software"), to deal in the Software without restriction, including * without limitation the rights to use, copy, modify, merge, publish, * distribute, sublicense, and/or sell copies of the Software, and to * permit persons to whom the Software is furnished to do so, subject to * the following conditions: * * The above copyright notice and this permission notice shall be * included in all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION * WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ const Vector = require('./vector'); const Matrix = require('./matrix'); class Mathops { /** * Calculates the sigmoid defined as: * S(x) = 1/(1+e^(-x)) * @param {Number} x Input value. * @returns {Number} Sigmoid of x. */ static sigmoid(x) { let result = 1.0 / (1 + Math.exp(-x)); if (result === 1) { result = 0.99999999999999; } else if (result === 0) { result = 1e-14; } return result; } /** * Calculate the hypothesis from the observations. * @param {Matrix} theta Theta matrix. * @param {Matrix} observations Observations. * @returns {Matrix} Hypothesis result. */ static hypothesis(theta, observations) { return observations.multiply(theta, Mathops.sigmoid); } /** * Cost function * @param {Matrix} theta Theta matrix. * @param {Matrix} observations Observations. * @param {Matrix} classifications Classification matrix. * @param {Matrix} srcHypothesis Hypothesis. If not provided is calculated. * @return {number} Calculated cost based on the hypothesis. */ static cost(theta, observations, classifications, srcHypothesis) { const hypothesis = srcHypothesis || Mathops.hypothesis(theta, observations); const ones = Vector.one(observations.rowCount()); const costOne = Vector.zero(observations.rowCount()) .subtract(classifications) .elementMultiply(hypothesis.log()); const costZero = ones .subtract(classifications) .elementMultiply(ones.subtract(hypothesis).log()); return (1 / observations.rowCount()) * costOne.subtract(costZero).sum(); } /** * Descend the gradient based on the cost function. * @param {Matrix} srcTheta Theta matrix. * @param {Vector} srcExamples Examples. * @param {Matrix} classifications Classification matrix. * @param {Object} srcOptions Settings for the descend. */ static descendGradient(srcTheta, srcExamples, classifications, srcOptions) { return new Promise((resolve, reject) => { const options = srcOptions || {}; const maxIterationFactor = options.maxIterationFactor || Mathops.maxIterationFactor; const learningRateStart = options.learningRateStart || Mathops.learningRateStart; const maxCostDelta = options.maxCostDelta || Mathops.maxCostDelta; const learningRateDivisor = options.learningRateDivisor || Mathops.learningRateDivisor; const maxIterations = maxIterationFactor * srcExamples.rowCount(); const examples = Matrix.one(srcExamples.rowCount(), 1).augment( srcExamples ); const examplesRowCountInverse = 1 / examples.rowCount(); const transposed = examples.transpose(); let learningRate = learningRateStart; let multiplyFactor = examplesRowCountInverse * learningRate; let learningRateFound = false; let theta = srcTheta.augment([0]); while (!learningRateFound || learningRate === 0) { let i = 0; let lastCost = null; while (i < maxIterations) { const hypothesis = Mathops.hypothesis(theta, examples); theta = theta.subtract( transposed .multiply(hypothesis.subtract(classifications)) .multiply(multiplyFactor) ); const currentCost = Mathops.cost( theta, examples, classifications, hypothesis ); i += 1; if (lastCost) { Iif (currentCost >= lastCost) { break; } learningRateFound = true; if (lastCost - currentCost < maxCostDelta) { break; } } Iif (i >= maxIterations) { return reject(new Error('Unable to find minimum')); } lastCost = currentCost; } learningRate /= learningRateDivisor; multiplyFactor = examplesRowCountInverse * learningRate; } return resolve(theta.chomp(1)); }); } /** * Return a vector representing x. * @param {Number[]} x Input array. * @returns {Vector} Vector representing x. */ static asVector(x) { return new Vector(x); } /** * Returns a matrix representing x. * @param {Number[][]} x Input array. * @return {Matrix} Matrix representing x. */ static asMatrix(x) { return new Matrix(x); } /** * Function returning 0. * @returns {number} Returns 0. */ static zero() { return 0; } /** * Compute the thetas of the examples and classifications. * @param {Vector} srcExamples Vector of examples. * @param {Matrix} srcClassifications Matrix of classifications. */ static async computeThetas(srcExamples, srcClassifications) { if (!srcClassifications || srcClassifications.length === 0) { return []; } const result = []; await Promise.all( srcClassifications[0].map(async (_, i) => { const item = await Mathops.computeThetasHelper( srcExamples, srcClassifications, i ); result.push(item); }) ); return result; } static async computeThetasHelper(srcExamples, srcClassifications, num) { const examples = this.asMatrix(srcExamples); const classifications = this.asMatrix(srcClassifications); const row = examples.row(0); const theta = row.map(this.zero); return this.descendGradient(theta, examples, classifications.column(num)); } } Mathops.learningRateStart = 3; Mathops.learningRateDivisor = 3; Mathops.maxIterationFactor = 500; Mathops.maxCostDelta = 0.0001; module.exports = Mathops; |