├── .gitignore ├── .jshintrc ├── README.md ├── gulpfile.js ├── index.js ├── package-lock.json ├── package.json ├── pca.js └── pca.min.js /.gitignore: -------------------------------------------------------------------------------- 1 | node_modules/ 2 | .vscode/ 3 | *.log* 4 | test.html 5 | nodemon.json 6 | gulpfile.js 7 | .jshintrc 8 | package-lock.json -------------------------------------------------------------------------------- /.jshintrc: -------------------------------------------------------------------------------- 1 | { 2 | "esversion": 6, 3 | "asi": true, 4 | "loopfunc": true, 5 | "eqnull": true, 6 | "curly": false 7 | } -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Principal Components Analysis in Javascript! 2 | 3 | A JS library to compute Principal Components from a given matrix of data. Use in either node.js or the browser. Look below for the API and some ideas 💡. 4 | 5 | CDN: [https://cdn.jsdelivr.net/npm/pca-js@1.0.0/pca.min.js](https://cdn.jsdelivr.net/npm/pca-js@1.0.0/pca.min.js) 6 | 7 | NPM: `npm install --save pca-js` 8 | 9 | Usage: 10 | 11 | Node 🛠: `var PCA = require('pca-js')` 12 | Browser 🌎: `PCA (global)` 13 | 14 | ## How to use the API 15 | 16 | All methods are exposed through `PCA` global variable 17 | 18 | Say you have data for marks of a class 4 students in 3 examinations on the same subject: 19 | 20 | ``` 21 | Student 1: 40,50,60 22 | Student 2: 50,70,60 23 | Student 3: 80,70,90 24 | Student 4: 50,60,80 25 | ``` 26 | 27 | You want to examine whether it is possible to come up with a single descriptive set of scores which explains performance across the class. Alternatively, whether it would make sense to replace 3 exams with just one (and reduce stress on students). 28 | 29 | 30 | First get the set of eigenvectors and eigenvalues (principal components and adjusted loadings) 31 | ```js 32 | var data = [[40,50,60],[50,70,60],[80,70,90],[50,60,80]]; 33 | var vectors = PCA.getEigenVectors(data); 34 | //Outputs 35 | // [{ 36 | // "eigenvalue": 520.0992658908312, 37 | // "vector": [0.744899700771276, 0.2849796479974595, 0.6032503924724023] 38 | // }, { 39 | // "eigenvalue": 78.10455398035167, 40 | // "vector": [0.2313199078283626, 0.7377809866160473, -0.6341689964277106] 41 | // }, { 42 | // "eigenvalue": 18.462846795484058, 43 | // "vector": [0.6257919271076777, -0.6119361208615616, -0.4836513702572988] 44 | // }] 45 | ``` 46 | 47 | Now you'd need to find a set of eigenvectors that would explain a decent amount of variance across your exams (thus telling you if 1 test or 2 tests would suffice instead of three) 48 | 49 | ```js 50 | var first = PCA.computePercentageExplained(vectors,vectors[0]) 51 | // 0.8434042149581044 52 | var topTwo = PCA.computePercentageExplained(vectors,vectors[0],vectors[1]) 53 | // 0.9700602484397556 54 | ``` 55 | 56 | So if you wanted to have 97% certainty, that someone wouldn't just flunk out accidentally, you'd take 2 exams. But let's say you just wanted to take 1, explaining 84% of variance is good enough. And instead of taking the examination again, you just wanted a normalized score 57 | 58 | ```js 59 | var adData = PCA.computeAdjustedData(data,vectors[0]) 60 | // { 61 | // "adjustedData": [ 62 | // [-22.27637101744241, -9.127781049780463, 31.316721747529886, 0.08743031969298887] 63 | // ], 64 | // "formattedAdjustedData": [ 65 | // [-22.28, -9.13, 31.32, 0.09] 66 | // ], 67 | // "avgData": [ 68 | // [-55, -62.5, -72.5], 69 | // [-55, -62.5, -72.5], 70 | // [-55, -62.5, -72.5], 71 | // [-55, -62.5, -72.5] 72 | // ], 73 | // "selectedVectors": [ 74 | // [0.744899700771276, 0.2849796479974595, 0.6032503924724023] 75 | // ] 76 | // } 77 | ``` 78 | 79 | The adjustedData is centered (mean = 0), but you could always set the mean to something like 50, to get scores of `[-22.27637101744241, -9.127781049780463, 31.316721747529886, 0.08743031969298887].map(score=>Math.round(score+50))` equal to `[28, 41, 81, 50]` , and that's how well your students would have done, in the order of students. 80 | 81 | ### Other cool stuff that's possible 82 | 83 | #### Compression (lossy): 84 | ```js 85 | var compressed = adData.formattedAdjustedData; 86 | //[ 87 | // [-22.28, -9.13, 31.32, 0.09] 88 | // ] 89 | var uncompressed = PCA.computeOriginalData(compressed,adData.selectedVectors,adData.avgData); 90 | //uncompressed.formattedOriginalData (lossy since 2 eigenvectors are removed) 91 | // [ 92 | // [38.4, 56.15, 59.06], 93 | // [48.2, 59.9, 66.99], 94 | // [78.33, 71.43, 91.39], 95 | // [55.07, 62.53, 72.55] 96 | // ] 97 | ``` 98 | 99 | Compare this to the original data to understand just how lossy the compression was 100 | ``` 101 | //Original Data 102 | [ 103 | [40, 50, 60], 104 | [50, 70, 60], 105 | [80, 70, 90], 106 | [50, 60, 80] 107 | ] 108 | //Uncompressed Data 109 | [ 110 | [38.4, 56.15, 59.06], 111 | [48.2, 59.9, 66.99], 112 | [78.33, 71.43, 91.39], 113 | [55.07, 62.53, 72.55] 114 | ] 115 | ``` 116 | ## List of Methods 117 | 118 | 119 | #### computeDeviationMatrix(data) 120 | Find centered matrix from original data 121 | 122 | #### computeDeviationScores(centeredMatrix) 123 | Find deviation from mean for values in matrix 124 | 125 | #### computeSVD(deviationScores) 126 | Singular Value Decomposition of matrix 127 | 128 | #### computePercentageExplained(allvectors, ...selected) 129 | Find percentage explained variance by selected vectors as opposed to the whole 130 | 131 | #### computeOriginalData(compressedData,selectedVectors,avgData) 132 | Get original data from the adjusted data after selecting a few eigenvectors 133 | 134 | #### computeVarianceCovariance(devSumOfSquares,isSample) 135 | Get variance covariance matrix from the data, adjust n by one if the data is from a sample 136 | 137 | #### computeAdjustedData(initialData, ...selectedVectors) 138 | Get adjusted data using principal components as selected 139 | 140 | #### getEigenVectors(initialData) 141 | Get the principal components of data using the steps outlined above. 142 | 143 | #### analyseTopResult(initialData) 144 | Same as computeAdjustedData(initialData,vectors[0]). Selecting only the top eigenvector which explains the most variance. 145 | 146 | #### transpose(A) 147 | Utility function to transpose a matrix A to A(T) 148 | 149 | #### multiply(A,B) 150 | Utility function to multiply AXB 151 | 152 | #### clone(A) 153 | Utility function to clone a matrix A 154 | 155 | #### scale(A,n) 156 | Utility function to scale all elements in A by a factor of n 157 | 158 | 159 | `LICENSE: MIT` 160 | -------------------------------------------------------------------------------- /gulpfile.js: -------------------------------------------------------------------------------- 1 | var gulp = require('gulp'), 2 | log = require('fancy-log'), 3 | minify = require('gulp-minifier'), 4 | rename = require("gulp-rename"), 5 | strip = require('gulp-strip-comments'), 6 | watch = require("gulp-watch"); 7 | 8 | 9 | gulp.task('default', function () { 10 | log('Done initializing gulp'); 11 | watch(['pca.js'],{ignoreInitial:false},()=>{ 12 | log('Reacting to changes to src files'); 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"main": "pca.js", 6 | "devDependencies": { 7 | "fancy-log": "^1.3.3", 8 | "gulp-concat": "^2.6.1", 9 | "gulp-minifier": "^1.2.2", 10 | "gulp-rename": "^1.4.0", 11 | "gulp-strip-comments": "^2.5.2", 12 | "gulp-watch": "^5.0.1" 13 | }, 14 | "scripts": { 15 | "test": "echo \"Error: no test specified\" && exit 1" 16 | }, 17 | "repository": { 18 | "type": "git", 19 | "url": "https://github.com/bitanath/pca" 20 | }, 21 | "nodemonConfig": { 22 | "ignore": [ 23 | "temp/*", 24 | "download/*", 25 | ".git", 26 | "node_modules/**/node_modules" 27 | ], 28 | "delay": "2500" 29 | }, 30 | "author": "Bitan Nath", 31 | "license": "MIT", 32 | "homepage": "https://bitanlearns.ml", 33 | "keywords": [ 34 | "principal", 35 | "components", 36 | "analysis", 37 | "pca", 38 | "machine", 39 | "learning", 40 | "ml", 41 | "data", 42 | "dimensionality" 43 | ], 44 | "dependencies": { 45 | "gulp": "^4.0.2" 46 | } 47 | } 48 | -------------------------------------------------------------------------------- /pca.js: -------------------------------------------------------------------------------- 1 | var PCA = (function () { 2 | /** 3 | * The first step is to subtract the mean and center data 4 | * 5 | * @param {Array} matrix - data in an mXn matrix format 6 | * @returns 7 | */ 8 | function computeDeviationMatrix(matrix) { 9 | var unit = unitSquareMatrix(matrix.length); 10 | return subtract(matrix, scale(multiply(unit, matrix), 1 / matrix.length)); 11 | } 12 | /** 13 | * Computes variance from deviation 14 | * 15 | * @param {Array} deviation - data minus mean as calculated from computeDeviationMatrix 16 | * @returns 17 | */ 18 | function computeDeviationScores(deviation) { 19 | var devSumOfSquares = multiply(transpose(deviation), deviation); 20 | return devSumOfSquares; 21 | } 22 | /** 23 | * Calculates the var covar square matrix using either population or sample 24 | * 25 | * @param {Array} devSumOfSquares 26 | * @param {boolean} sample - true/false whether data is from sample or not 27 | * @returns 28 | */ 29 | function computeVarianceCovariance(devSumOfSquares, sample) { 30 | var varianceCovariance; 31 | if (sample) 32 | varianceCovariance = scale(devSumOfSquares, 1 / (devSumOfSquares.length - 1)); 33 | else 34 | varianceCovariance = scale(devSumOfSquares, 1 / (devSumOfSquares.length)); 35 | return varianceCovariance; 36 | } 37 | /** 38 | * Matrix is the deviation sum of squares as computed earlier 39 | * 40 | * @param {Array} matrix - output of computeDeviationScores 41 | * @returns 42 | */ 43 | function computeSVD(matrix) { 44 | var result = svd(matrix); 45 | var eigenvectors = result.U; 46 | var eigenvalues = result.S; 47 | var results = eigenvalues.map(function (value, i) { 48 | var obj = {}; 49 | obj.eigenvalue = value; 50 | obj.vector = eigenvectors.map(function (vector, j) { 51 | return -1 * vector[i]; //HACK prevent completely negative vectors 52 | }); 53 | return obj; 54 | }); 55 | return results; 56 | } 57 | /** 58 | * Get reduced dataset after removing some dimensions 59 | * 60 | * @param {Array} data - initial matrix started out with 61 | * @param {rest} vectors - eigenvectors selected as part of process 62 | * @returns 63 | */ 64 | function computeAdjustedData(data, ...vectorObjs) { 65 | //FIXME no need to transpose vectors since they're already in row normal form 66 | var vectors = vectorObjs.map(function(v){return v.vector}); 67 | var matrixMinusMean = computeDeviationMatrix(data); 68 | var adjustedData = multiply(vectors, transpose(matrixMinusMean)); 69 | var unit = unitSquareMatrix(data.length); 70 | var avgData = scale(multiply(unit, data), -1 / data.length); //NOTE get the averages to add back 71 | 72 | var formattedAdjustData = formatData(adjustedData, 2); 73 | return { 74 | adjustedData: adjustedData, 75 | formattedAdjustedData: formattedAdjustData, 76 | avgData: avgData, 77 | selectedVectors: vectors 78 | }; 79 | } 80 | 81 | /** 82 | * Get original data set from reduced data set (decompress) 83 | * @param {*} adjustedData = formatted or unformatted adjusted data 84 | * @param {*} vectors = selectedVectors 85 | * @param {*} avgData = avgData 86 | */ 87 | function computeOriginalData(adjustedData, vectors, avgData) { 88 | var originalWithoutMean = transpose(multiply(transpose(vectors), adjustedData)); 89 | var originalWithMean = subtract(originalWithoutMean, avgData); 90 | var formattedData = formatData(originalWithMean, 2); 91 | return { 92 | originalData: originalWithMean, 93 | formattedOriginalData: formattedData 94 | } 95 | } 96 | 97 | /** 98 | * Get percentage explained, or loss 99 | * @param {*} vectors 100 | * @param {*} selected 101 | */ 102 | function computePercentageExplained(vectors, ...selected) { 103 | var total = vectors.map(function (v) { 104 | return v.eigenvalue 105 | }).reduce(function (a, b) { 106 | return a + b; 107 | }); 108 | var explained = selected.map(function (v) { 109 | return v.eigenvalue 110 | }).reduce(function (a, b) { 111 | return a + b; 112 | }); 113 | return (explained / total); 114 | } 115 | 116 | function getEigenVectors(data) { 117 | return computeSVD(computeVarianceCovariance(computeDeviationScores(computeDeviationMatrix(data)), false)); 118 | } 119 | 120 | function analyseTopResult(data) { 121 | var eigenVectors = getEigenVectors(data); 122 | var sorted = eigenVectors.sort(function (a, b) { 123 | return b.eigenvalue - a.eigenvalue; 124 | }); 125 | var selected = sorted[0].vector; 126 | return computeAdjustedData(data, selected); 127 | } 128 | 129 | function formatData(data, precision) { 130 | var TEN = Math.pow(10, precision || 2); 131 | return data.map(function (d, i) { 132 | return d.map(function (n) { 133 | return Math.round(n * TEN) / TEN; 134 | }) 135 | }) 136 | } 137 | /** 138 | * Multiplies AxB, where A and B are matrices of nXm and mXn dimensions 139 | * @param {} a 140 | * @param {*} b 141 | */ 142 | function multiply(a, b) { 143 | if (!a[0] || !b[0] || !a.length || !b.length) { 144 | throw new Error('Both A and B should be matrices'); 145 | } 146 | 147 | if (b.length !== a[0].length) { 148 | throw new Error('Columns in A should be the same as the number of rows in B'); 149 | } 150 | var product = []; 151 | 152 | for (var i = 0; i < a.length; i++) { 153 | product[i] = []; //initialize a new row 154 | for (var j = 0; j < b[0].length; j++) { 155 | for (var k = 0; k < a[0].length; k++) { 156 | (product[i])[j] = !!(product[i])[j] ? (product[i])[j] + (a[i])[k] * (b[k])[j] : (a[i])[k] * (b[k])[j]; 157 | } 158 | } 159 | } 160 | return product; 161 | } 162 | /** 163 | * Utility function to subtract matrix b from a 164 | * 165 | * @param {any} a 166 | * @param {any} b 167 | * @returns 168 | */ 169 | function subtract(a, b) { 170 | if (!(a.length === b.length && a[0].length === b[0].length)) 171 | throw new Error('Both A and B should have the same dimensions'); 172 | var result = []; 173 | for (var i = 0; i < a.length; i++) { 174 | result[i] = []; 175 | for (var j = 0; j < b[0].length; j++) { 176 | (result[i])[j] = (a[i])[j] - (b[i])[j]; 177 | } 178 | } 179 | return result; 180 | } 181 | /** 182 | * Multiplies a matrix into a factor 183 | * 184 | * @param {any} matrix 185 | * @param {any} factor 186 | * @returns 187 | */ 188 | function scale(matrix, factor) { 189 | var result = []; 190 | for (var i = 0; i < matrix.length; i++) { 191 | result[i] = []; 192 | for (var j = 0; j < matrix[0].length; j++) { 193 | (result[i])[j] = (matrix[i])[j] * factor; 194 | } 195 | } 196 | return result; 197 | } 198 | 199 | /** 200 | * Generates a unit square matrix 201 | * @param {*} rows = number of rows to fill 202 | */ 203 | function unitSquareMatrix(rows) { 204 | var result = []; 205 | for (var i = 0; i < rows; i++) { 206 | result[i] = []; 207 | for (var j = 0; j < rows; j++) { 208 | (result[i])[j] = 1; 209 | } 210 | } 211 | return result; 212 | } 213 | /** 214 | * Transposes a matrix, converts rows to columns 215 | * @param {*} matrix 216 | */ 217 | function transpose(matrix) { 218 | var operated = clone(matrix); 219 | return operated[0].map(function (m, c) { 220 | return matrix.map(function (r) { 221 | return r[c]; 222 | }); 223 | }); 224 | } 225 | /** 226 | * Deep Clones a matrix 227 | * @param {*} arr 228 | */ 229 | function clone(arr) { 230 | var string = JSON.stringify(arr); 231 | var result = JSON.parse(string); 232 | return result; 233 | } 234 | 235 | /** 236 | * Compute the thin SVD from G. H. Golub and C. Reinsch, Numer. Math. 14, 403-420 (1970) 237 | * From the Numeric JS Implementation Copyright (C) 2011 by Sébastien Loisel 238 | * The C implementation from which this has been taken may be found here: http://www.public.iastate.edu/~dicook/JSS/paper/code/svd.c 239 | * @param {*} A = m*n matrix 240 | */ 241 | function svd(A) { 242 | var temp; 243 | var prec = Math.pow(2, -52) // assumes double prec 244 | var tolerance = 1.e-64 / prec; 245 | var itmax = 50; 246 | var c = 0; 247 | var i = 0; 248 | var j = 0; 249 | var k = 0; 250 | var l = 0; 251 | var u = clone(A); 252 | var m = u.length; 253 | var n = u[0].length; 254 | 255 | if (m < n) throw "Need more rows than columns" 256 | 257 | var e = new Array(n); //vector1 258 | var q = new Array(n); //vector2 259 | for (i = 0; i < n; i++) e[i] = q[i] = 0.0; 260 | var v = rep([n, n], 0); 261 | 262 | function pythag(a, b) { 263 | a = Math.abs(a) 264 | b = Math.abs(b) 265 | if (a > b) 266 | return a * Math.sqrt(1.0 + (b * b / a / a)) 267 | else if (b == 0.0) 268 | return a 269 | return b * Math.sqrt(1.0 + (a * a / b / b)) 270 | } 271 | 272 | //rep function 273 | function rep(s, v, k) { 274 | if (typeof k === "undefined") { 275 | k = 0; 276 | } 277 | var n = s[k], 278 | ret = Array(n), 279 | i; 280 | if (k === s.length - 1) { 281 | for (i = n - 2; i >= 0; i -= 2) { 282 | ret[i + 1] = v; 283 | ret[i] = v; 284 | } 285 | if (i === -1) { 286 | ret[0] = v; 287 | } 288 | return ret; 289 | } 290 | for (i = n - 1; i >= 0; i--) { 291 | ret[i] = rep(s, v, k + 1); 292 | } 293 | return ret; 294 | } 295 | 296 | //Householder's reduction to bidiagonal form 297 | 298 | var f = 0.0; 299 | var g = 0.0; 300 | var h = 0.0; 301 | var x = 0.0; 302 | var y = 0.0; 303 | var z = 0.0; 304 | var s = 0.0; 305 | 306 | for (i = 0; i < n; i++) { 307 | e[i] = g; //vector 308 | s = 0.0; //sum 309 | l = i + 1; //stays i+1 310 | for (j = i; j < m; j++) 311 | s += (u[j][i] * u[j][i]); 312 | if (s <= tolerance) 313 | g = 0.0; 314 | else { 315 | f = u[i][i]; 316 | g = Math.sqrt(s); 317 | if (f >= 0.0) g = -g; 318 | h = f * g - s 319 | u[i][i] = f - g; 320 | for (j = l; j < n; j++) { 321 | s = 0.0 322 | for (k = i; k < m; k++) 323 | s += u[k][i] * u[k][j] 324 | f = s / h 325 | for (k = i; k < m; k++) 326 | u[k][j] += f * u[k][i] 327 | } 328 | } 329 | q[i] = g 330 | s = 0.0 331 | for (j = l; j < n; j++) 332 | s = s + u[i][j] * u[i][j] 333 | if (s <= tolerance) 334 | g = 0.0 335 | else { 336 | f = u[i][i + 1] 337 | g = Math.sqrt(s) 338 | if (f >= 0.0) g = -g 339 | h = f * g - s 340 | u[i][i + 1] = f - g; 341 | for (j = l; j < n; j++) e[j] = u[i][j] / h 342 | for (j = l; j < m; j++) { 343 | s = 0.0 344 | for (k = l; k < n; k++) 345 | s += (u[j][k] * u[i][k]) 346 | for (k = l; k < n; k++) 347 | u[j][k] += s * e[k] 348 | } 349 | } 350 | y = Math.abs(q[i]) + Math.abs(e[i]) 351 | if (y > x) 352 | x = y 353 | } 354 | 355 | // accumulation of right hand transformations 356 | for (i = n - 1; i != -1; i += -1) { 357 | if (g != 0.0) { 358 | h = g * u[i][i + 1] 359 | for (j = l; j < n; j++) 360 | v[j][i] = u[i][j] / h //u is array, v is square of columns 361 | for (j = l; j < n; j++) { 362 | s = 0.0 363 | for (k = l; k < n; k++) 364 | s += u[i][k] * v[k][j] 365 | for (k = l; k < n; k++) 366 | v[k][j] += (s * v[k][i]) 367 | } 368 | } 369 | for (j = l; j < n; j++) { 370 | v[i][j] = 0; 371 | v[j][i] = 0; 372 | } 373 | v[i][i] = 1; 374 | g = e[i] 375 | l = i 376 | } 377 | 378 | // accumulation of left hand transformations 379 | for (i = n - 1; i != -1; i += -1) { 380 | l = i + 1 381 | g = q[i] 382 | for (j = l; j < n; j++) 383 | u[i][j] = 0; 384 | if (g != 0.0) { 385 | h = u[i][i] * g 386 | for (j = l; j < n; j++) { 387 | s = 0.0 388 | for (k = l; k < m; k++) s += u[k][i] * u[k][j]; 389 | f = s / h 390 | for (k = i; k < m; k++) u[k][j] += f * u[k][i]; 391 | } 392 | for (j = i; j < m; j++) u[j][i] = u[j][i] / g; 393 | } else 394 | for (j = i; j < m; j++) u[j][i] = 0; 395 | u[i][i] += 1; 396 | } 397 | 398 | // diagonalization of the bidiagonal form 399 | prec = prec * x 400 | for (k = n - 1; k != -1; k += -1) { 401 | for (var iteration = 0; iteration < itmax; iteration++) { // test f splitting 402 | var test_convergence = false 403 | for (l = k; l != -1; l += -1) { 404 | if (Math.abs(e[l]) <= prec) { 405 | test_convergence = true 406 | break 407 | } 408 | if (Math.abs(q[l - 1]) <= prec) 409 | break 410 | } 411 | if (!test_convergence) { // cancellation of e[l] if l>0 412 | c = 0.0 413 | s = 1.0 414 | var l1 = l - 1 415 | for (i = l; i < k + 1; i++) { 416 | f = s * e[i] 417 | e[i] = c * e[i] 418 | if (Math.abs(f) <= prec) 419 | break 420 | g = q[i] 421 | h = pythag(f, g) 422 | q[i] = h 423 | c = g / h 424 | s = -f / h 425 | for (j = 0; j < m; j++) { 426 | y = u[j][l1] 427 | z = u[j][i] 428 | u[j][l1] = y * c + (z * s) 429 | u[j][i] = -y * s + (z * c) 430 | } 431 | } 432 | } 433 | // test f convergence 434 | z = q[k] 435 | if (l == k) { //convergence 436 | if (z < 0.0) { //q[k] is made non-negative 437 | q[k] = -z 438 | for (j = 0; j < n; j++) 439 | v[j][k] = -v[j][k] 440 | } 441 | break //break out of iteration loop and move on to next k value 442 | } 443 | if (iteration >= itmax - 1) 444 | throw 'Error: no convergence.' 445 | // shift from bottom 2x2 minor 446 | x = q[l] 447 | y = q[k - 1] 448 | g = e[k - 1] 449 | h = e[k] 450 | f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y) 451 | g = pythag(f, 1.0) 452 | if (f < 0.0) 453 | f = ((x - z) * (x + z) + h * (y / (f - g) - h)) / x 454 | else 455 | f = ((x - z) * (x + z) + h * (y / (f + g) - h)) / x 456 | // next QR transformation 457 | c = 1.0 458 | s = 1.0 459 | for (i = l + 1; i < k + 1; i++) { 460 | g = e[i] 461 | y = q[i] 462 | h = s * g 463 | g = c * g 464 | z = pythag(f, h) 465 | e[i - 1] = z 466 | c = f / z 467 | s = h / z 468 | f = x * c + g * s 469 | g = -x * s + g * c 470 | h = y * s 471 | y = y * c 472 | for (j = 0; j < n; j++) { 473 | x = v[j][i - 1] 474 | z = v[j][i] 475 | v[j][i - 1] = x * c + z * s 476 | v[j][i] = -x * s + z * c 477 | } 478 | z = pythag(f, h) 479 | q[i - 1] = z 480 | c = f / z 481 | s = h / z 482 | f = c * g + s * y 483 | x = -s * g + c * y 484 | for (j = 0; j < m; j++) { 485 | y = u[j][i - 1] 486 | z = u[j][i] 487 | u[j][i - 1] = y * c + z * s 488 | u[j][i] = -y * s + z * c 489 | } 490 | } 491 | e[l] = 0.0 492 | e[k] = f 493 | q[k] = x 494 | } 495 | } 496 | 497 | for (i = 0; i < q.length; i++) 498 | if (q[i] < prec) q[i] = 0 499 | 500 | //sort eigenvalues 501 | for (i = 0; i < n; i++) { 502 | for (j = i - 1; j >= 0; j--) { 503 | if (q[j] < q[i]) { 504 | c = q[j] 505 | q[j] = q[i] 506 | q[i] = c 507 | for (k = 0; k < u.length; k++) { 508 | temp = u[k][i]; 509 | u[k][i] = u[k][j]; 510 | u[k][j] = temp; 511 | } 512 | for (k = 0; k < v.length; k++) { 513 | temp = v[k][i]; 514 | v[k][i] = v[k][j]; 515 | v[k][j] = temp; 516 | } 517 | i = j 518 | } 519 | } 520 | } 521 | 522 | return { 523 | U: u, 524 | S: q, 525 | V: v 526 | } 527 | } 528 | 529 | return { 530 | computeDeviationScores: computeDeviationScores, 531 | computeDeviationMatrix: computeDeviationMatrix, 532 | computeSVD: computeSVD, 533 | computePercentageExplained: computePercentageExplained, 534 | computeOriginalData: computeOriginalData, 535 | computeVarianceCovariance: computeVarianceCovariance, 536 | computeAdjustedData: computeAdjustedData, 537 | getEigenVectors: getEigenVectors, 538 | analyseTopResult: analyseTopResult, 539 | transpose: transpose, 540 | multiply: multiply, 541 | clone: clone, 542 | scale: scale 543 | } 544 | })(); 545 | 546 | if(typeof module !== 'undefined') 547 | module.exports = PCA; -------------------------------------------------------------------------------- /pca.min.js: -------------------------------------------------------------------------------- 1 | var PCA=function(){function r(r){return i(r,c(u(l(r.length),r),1/r.length))}function n(r){return u(h(r),r)}function t(r,n){return c(r,n?1/(r.length-1):1/r.length)}function e(r){var n=function(r){var n,t=Math.pow(2,-52),e=1e-64/t,o=0,a=0,f=0,u=0,i=0,c=s(r),l=c.length,h=c[0].length;if(l=0;o-=2)f[o+1]=t,f[o]=t;return-1===o&&(f[0]=t),f}for(o=a-1;o>=0;o--)f[o]=r(n,t,e+1);return f}([h,h],0);function d(r,n){return r=Math.abs(r),n=Math.abs(n),r>n?r*Math.sqrt(1+n*n/r/r):0==n?r:n*Math.sqrt(1+r*r/n/n)}var p=0,M=0,w=0,b=0,A=0,D=0,y=0;for(a=0;a=0&&(M=-M),w=p*M-y,c[a][a]=p-M,f=i;f=0&&(M=-M),w=p*M-y,c[a][a+1]=p-M,f=i;fb&&(b=A)}for(a=h-1;-1!=a;a+=-1){if(0!=M){for(w=M*c[a][a+1],f=i;f=49)throw"Error: no convergence.";for(b=v[i],A=v[u-1],M=g[u-1],w=g[u],M=d(p=((A-D)*(A+D)+(M-w)*(M+w))/(2*w*A),1),p=p<0?((b-D)*(b+D)+w*(A/(p-M)-w))/b:((b-D)*(b+D)+w*(A/(p+M)-w))/b,o=1,y=1,a=i+1;a=0;f--)if(v[f]