fcmeans

Implementation of Fuzzy-C-means clustering algorithm for JavaScript/TypeScript

WARNING

This repository is still in development. The API of this module could change until there is a real first release. I do not guarantee the correctness of this module. Please review und participate if you have suggestions. Please think about giving a star to this repository to reach more people.

Motivation

Why using Fuzzy-C-means clustering algorithms in JavaScript/TypeScript? Yes, JavaScript is not a typical language for data science methods but JavaScript is still the language for browsers. So if you want to create an application for web and want to calculate the clusters on clientside, you need an implementation for JavaScript. The k-means algorithm exists widely in JavaScript-space but unfortunately not the (n-dimensional, ) C-means algorithm.

Get started

Installing

You can add this module to your project by this github repository while it's not published on npm.

npm install https://github.com/durek1337/fcmeans

or

yarn add https://github.com/durek1337/fcmeans

Importing

Simply import the module to use it.

ES6

import fcmeans from 'fcmeans'

CommonJS

const fcmeans = require('fcmeans')

Example

import fcmeans, {calculateFuzzifier} from 'fcmeans'
var amount = 50
var dimensions = 3
var max = 10
var min = 1
var data_vectors = (new Array(amount)).fill(0).map((e,i) => (new Array(dimensions)).fill(0).map((e) => Math.round((max-min)*Math.random())+min))
var clusters = Math.floor(Math.sqrt(amount))
var fuzzifier = calculateFuzzifier(dimensions,amount) // you could also use a value of 2 but some people write it's not a good habbit. Inform yourself before you use this provided function. The fuzzifier in this example is far too high. In literature (example: doi 10.1109/TALE.2017.8252307 p76) the range of fuzzifier was suggested between 1.5 and 4 and came to the conclusion that the value of 2 is sufficient in most times.
var result = fcmeans({k : clusters, vectors : data_vectors, epsilon : 0.0001, fuzziness : fuzzifier})
console.log("fuzzifier",fuzzifier,"result",JSON.stringify(result))

Results for one execution

fuzzifier 6.964152032076 result {"centroids":[[6.32818075403257,4.645920074604211,6.104947524131507],[4.4165881209614355,5.750511348130167,4.971218575506165],[3.716478703947623,5.768237395462908,3.6774287921482816],[5.911578846963853,6.524336740532647,6.5796632970456885],[5.88850532588595,6.062890654099869,5.385919464774966],[7.660864679991841,8.3838885365249,7.84442448271217],[6.314048466841104,4.40610461995109,6.1568155759328596]],"membershipMatrix":{"rows":50,"cols":7,"mtx":[[0.14101754863046384,0.13254955690293205,0.12094363838588558,0.16218906783865972,0.1411503374711683,0.16256312932041894,0.1395867214504716],[0.14219970919606614,0.1513714154040498,0.16142248215517424,0.13622622230125675,0.1426326829799189,0.12357548853254588,0.14257199943098833],[0.1353810947026932,0.13038409472196238,0.12412486741706753,0.1466060272330747,0.13869952677244995,0.1906203165292354,0.13418407262351684],[0.14007960207059666,0.1488418878529835,0.14312007349672595,0.14822209141440781,0.142729956806541,0.1373326276892769,0.13967376066946818],[0.15089068244926107,0.1276830440855284,0.11511254116132892,0.16476788093512082,0.14306556344441757,0.1497674811469817,0.14871280677736146],[0.14514314472656636,0.16130530089813724,0.15114721127148237,0.13854315718869956,0.14224427923106023,0.11575813719345791,0.14585876949059629],[0.15351348151558109,0.13412695740647979,0.12718402513272822,0.14467785521517412,0.14186150721181012,0.1441312545178399,0.15450491900038676],[0.16419126224651395,0.1332911504142122,0.12337400547584614,0.14264583748369333,0.1400248430223517,0.1282635479763638,0.1682093533810189],[0.1395250953901285,0.1517269113748468,0.1607292442947358,0.13667206532570705,0.15154186190915794,0.1216349564736846,0.13816986523173924],[0.16057721498483493,0.13304928720404186,0.12536192117808356,0.14203623600502321,0.14254607107889425,0.13388363414892807,0.16254563540019415],[0.135895484965127,0.15701319584658216,0.17505097825164254,0.13524618444629993,0.1409253771397269,0.12021172944766048,0.13565704990296099],[0.13415724522774203,0.13896952848698302,0.13155359309343637,0.15402632928820859,0.1431302494673293,0.1655269099526127,0.13263614448368802],[0.14037859991902446,0.15511941580764158,0.14445382895091197,0.13839193048914533,0.171397489462739,0.113015474859835,0.1372432605107027],[0.133332378411552,0.15472311231040906,0.16136972520349188,0.14270971621519574,0.14487861658073092,0.13080975763497354,0.13217669364364687],[0.1260622082426908,0.12086801625678051,0.11346895139508101,0.1419085807732672,0.13125836199826085,0.2419664751637602,0.12446740617015944],[0.15249366490686206,0.14325392095459955,0.13376491532933843,0.14540285210831722,0.14130600513291683,0.12952003131534642,0.1542586102526195],[0.13622612759459232,0.13005320915671004,0.12273771070213045,0.14836937598827896,0.1378702463192367,0.18959532520132238,0.13514800503772914],[0.13494856070581285,0.15369448325268678,0.1725206144629411,0.13667538100507767,0.14326496545074338,0.12465219413213445,0.13424380099060382],[0.13477747957755096,0.13279821035124478,0.12205591668376385,0.16351561251835278,0.15362777837884495,0.16147411249388177,0.13175088999636086],[0.1298855749908411,0.1701131437019896,0.16848258474927666,0.14043144296982876,0.14469160944025347,0.11793147234736226,0.12846417180044814],[0.1405898061058232,0.12859549996752534,0.11811219294276479,0.1576170986611352,0.13931762760449165,0.1766147090371766,0.13915306568108324],[0.13451830787307925,0.12829250398577124,0.12148314266758112,0.14700105772778094,0.14031579465416238,0.1955799084838096,0.13280928460781544],[0.13203304067404292,0.15625799275231317,0.1901368164636317,0.13205937459921363,0.14135563524891603,0.1168834710347602,0.1312736692271224],[0.13333446528895265,0.12644366135578686,0.11950491912786741,0.14543368971605106,0.1371027665979166,0.20631491345782935,0.13186558445559607],[0.14841548947478667,0.1498493238770946,0.13897498001688627,0.1456632420232866,0.14224596435105014,0.12552551652287527,0.1493254837340204],[0.14514314472656636,0.16130530089813724,0.15114721127148237,0.13854315718869956,0.14224427923106023,0.11575813719345791,0.14585876949059629],[0.1335939279883504,0.1298838079259363,0.12320010272413459,0.14724714418835427,0.13786737658774473,0.1959045484460027,0.13230309213947705],[0.13913338385850857,0.14672689441402273,0.15127020471089536,0.14126030913825394,0.14988508928136224,0.1339156938052588,0.1378084247916983],[0.15614717604089245,0.13620372841613815,0.1307502924401399,0.14109036023846908,0.1435908247053882,0.13462757266918376,0.15759004548978842],[0.15361293044491697,0.14220749526826457,0.1405614235890519,0.13749661885439185,0.14568742362962928,0.12568002769298842,0.154754080520757],[0.1356093187757044,0.1252888040205525,0.11753676984139853,0.14673555215785822,0.13746625709558574,0.20329272388293285,0.13407057422596777],[0.1436013221235592,0.15198421040876298,0.16120228016459817,0.13525494662133797,0.1426669439530464,0.12107546798162054,0.14421482874707472],[0.1335939279883504,0.1298838079259363,0.12320010272413459,0.14724714418835427,0.13786737658774473,0.1959045484460027,0.13230309213947705],[0.19107872218351163,0.12258801847975057,0.10894620995383743,0.13946190071127015,0.14758889647023565,0.11064348080408609,0.17969277139730844],[0.1493166356956151,0.1464905514430538,0.148895991441338,0.13657347183777982,0.1442872626515104,0.12404031858759114,0.15039576834311175],[0.1494275791975214,0.14958229286863103,0.15249338092466758,0.13474029543837568,0.1439589937312348,0.11907368932169274,0.1507237685178768],[0.14931691480547524,0.13906498415537655,0.1324628590935595,0.14390407528446192,0.158345187964712,0.13012749999523165,0.14677847870118313],[0.1329586211396854,0.15085731132621188,0.15011630267431542,0.14737177342215602,0.1519658196628791,0.13573156537620767,0.13099860639854452],[0.15089068244926107,0.1276830440855284,0.11511254116132892,0.16476788093512082,0.14306556344441757,0.1497674811469817,0.14871280677736146],[0.1367773388114423,0.14131626045211337,0.1329198818702521,0.15482752447806175,0.14287643733220573,0.15571498210302678,0.13556757495289795],[0.1351999414762904,0.1805511217698245,0.1415361238879008,0.14782894519436582,0.14975930096123705,0.11186720862409638,0.13325735808628514],[0.1347341723409316,0.1394288565353767,0.1346597792818697,0.1503722696399123,0.1486439457423991,0.15938084178094614,0.1327801346785645],[0.16414534902707714,0.13714447858825352,0.12972352565251344,0.13694344915119788,0.14146182117674425,0.12163585193828777,0.16894552446592606],[0.1498780245713282,0.1514850663915002,0.1431095117593948,0.14091081784906556,0.14176358882056583,0.12133639120624531,0.15151659940190007],[0.15776297492650576,0.13805883151238293,0.13113920321128036,0.14110927808812462,0.1411223427577865,0.130003100699182,0.16080426880473786],[0.13563175868905175,0.15261802313606232,0.1662281572173008,0.13872433743084875,0.14352518480819784,0.12833708156295232,0.13493545715558616],[0.1400521280384631,0.1395889346632645,0.1345799610734666,0.14818630556038734,0.1548952731683631,0.14496446200669091,0.13773293548936447],[0.15897898081286577,0.1445718189163398,0.1370799375056675,0.1366568661830124,0.14137201018260775,0.1182656293900611,0.16307475700944568],[0.13898852914497115,0.15555253500964683,0.15161207464966409,0.14452648823607486,0.1427046641418887,0.12797448583293392,0.1386412229848205],[0.14461959876875924,0.1443369114248193,0.14491872602240838,0.14041681322694954,0.15205655398507598,0.1303259420278532,0.14332545454413442]]}}

The assignments in result.membershipMatrix.mtx has a length of 7 (which is also stored in result.membershipMatrix.cols). This amount was calculated and stored in variable clusters. The values of result.membershipMatrix.mtx are between 0 and 1 but the values scatter around 1/clusters. The sum of all elements of one membership array is 1 (negleted computation errors which could lead to a little bit more or less). This example has the following sums calculated by JSON.stringify(result.membershipMatrix.mtx.map(arr => arr.reduce((pr,c) => pr+c))):

Sums

[1,1,0.9999999999999999,1,0.9999999999999999,1,1,1.0000000000000002,1,1,1,1.0000000000000002,1,1,1,1,1,1,0.9999999999999999,1,0.9999999999999999,0.9999999999999998,1,1.0000000000000002,0.9999999999999999,1,1,1,1,1,1,1,1,1,1,1,0.9999999999999999,1,0.9999999999999999,1,1,1,1,1,1,1,1,1,1,1]

Sources

• Algorithm implementation took in snippets from https://github.com/nantunes/figue
• Fuzzier-Finder: A simple and fast method to determine the parameters for fuzzy c–means cluster analysis doi:10.1093/bioinformatics/btq534
• Homogeneous group formation in collaborative learning using fuzzy C-means doi:10.1109/TALE.2017.8252307