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t-SNE mock
Raw
.block
license: gpl-3.0
Raw
README.md
Raw
index.html
<!DOCTYPE html>
<head>
<meta charset="utf-8">
<script src="https://d3js.org/d3.v3.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
<style>
body { margin:0;position:fixed;top:0;right:0;bottom:0;left:0; }
</style>
<script>
// create main global object
var tsnejs = tsnejs || { REVISION: 'ALPHA' };
(function(global) {
"use strict";
// utility function
var assert = function(condition, message) {
if (!condition) { throw message || "Assertion failed"; }
}
// syntax sugar
var getopt = function(opt, field, defaultval) {
if(opt.hasOwnProperty(field)) {
return opt[field];
} else {
return defaultval;
}
}
// return 0 mean unit standard deviation random number
var return_v = false;
var v_val = 0.0;
var gaussRandom = function() {
if(return_v) {
return_v = false;
return v_val;
}
var u = 2*Math.random()-1;
var v = 2*Math.random()-1;
var r = u*u + v*v;
if(r == 0 || r > 1) return gaussRandom();
var c = Math.sqrt(-2*Math.log(r)/r);
v_val = v*c; // cache this for next function call for efficiency
return_v = true;
return u*c;
}
// return random normal number
var randn = function(mu, std){ return mu+gaussRandom()*std; }
// utilitity that creates contiguous vector of zeros of size n
var zeros = function(n) {
if(typeof(n)==='undefined' || isNaN(n)) { return []; }
if(typeof ArrayBuffer === 'undefined') {
// lacking browser support
var arr = new Array(n);
for(var i=0;i<n;i++) { arr[i]= 0; }
return arr;
} else {
return new Float64Array(n); // typed arrays are faster
}
}
// utility that returns 2d array filled with random numbers
// or with value s, if provided
var randn2d = function(n,d,s) {
var uses = typeof s !== 'undefined';
var x = [];
for(var i=0;i<n;i++) {
var xhere = [];
for(var j=0;j<d;j++) {
if(uses) {
xhere.push(s);
} else {
xhere.push(randn(0.0, 1e-4));
}
}
x.push(xhere);
}
return x;
}
// compute L2 distance between two vectors
var L2 = function(x1, x2) {
var D = x1.length;
var d = 0;
for(var i=0;i<D;i++) {
var x1i = x1[i];
var x2i = x2[i];
d += (x1i-x2i)*(x1i-x2i);
}
return d;
}
// compute pairwise distance in all vectors in X
var xtod = function(X) {
var N = X.length;
var dist = zeros(N * N); // allocate contiguous array
for(var i=0;i<N;i++) {
for(var j=i+1;j<N;j++) {
var d = L2(X[i], X[j]);
dist[i*N+j] = d;
dist[j*N+i] = d;
}
}
return dist;
}
// compute (p_{i|j} + p_{j|i})/(2n)
var d2p = function(D, perplexity, tol) {
var Nf = Math.sqrt(D.length); // this better be an integer
var N = Math.floor(Nf);
assert(N === Nf, "D should have square number of elements.");
var Htarget = Math.log(perplexity); // target entropy of distribution
var P = zeros(N * N); // temporary probability matrix
var prow = zeros(N); // a temporary storage compartment
for(var i=0;i<N;i++) {
var betamin = -Infinity;
var betamax = Infinity;
var beta = 1; // initial value of precision
var done = false;
var maxtries = 50;
// perform binary search to find a suitable precision beta
// so that the entropy of the distribution is appropriate
var num = 0;
while(!done) {
//debugger;
// compute entropy and kernel row with beta precision
var psum = 0.0;
for(var j=0;j<N;j++) {
var pj = Math.exp(- D[i*N+j] * beta);
if(i===j) { pj = 0; } // we dont care about diagonals
prow[j] = pj;
psum += pj;
}
// normalize p and compute entropy
var Hhere = 0.0;
for(var j=0;j<N;j++) {
var pj = prow[j] / psum;
prow[j] = pj;
if(pj > 1e-7) Hhere -= pj * Math.log(pj);
}
// adjust beta based on result
if(Hhere > Htarget) {
// entropy was too high (distribution too diffuse)
// so we need to increase the precision for more peaky distribution
betamin = beta; // move up the bounds
if(betamax === Infinity) { beta = beta * 2; }
else { beta = (beta + betamax) / 2; }
} else {
// converse case. make distrubtion less peaky
betamax = beta;
if(betamin === -Infinity) { beta = beta / 2; }
else { beta = (beta + betamin) / 2; }
}
// stopping conditions: too many tries or got a good precision
num++;
if(Math.abs(Hhere - Htarget) < tol) { done = true; }
if(num >= maxtries) { done = true; }
}
// console.log('data point ' + i + ' gets precision ' + beta + ' after ' + num + ' binary search steps.');
// copy over the final prow to P at row i
for(var j=0;j<N;j++) { P[i*N+j] = prow[j]; }
} // end loop over examples i
// symmetrize P and normalize it to sum to 1 over all ij
var Pout = zeros(N * N);
var N2 = N*2;
for(var i=0;i<N;i++) {
for(var j=0;j<N;j++) {
Pout[i*N+j] = Math.max((P[i*N+j] + P[j*N+i])/N2, 1e-100);
}
}
return Pout;
}
// helper function
function sign(x) { return x > 0 ? 1 : x < 0 ? -1 : 0; }
var tSNE = function(opt) {
var opt = opt || {};
this.perplexity = getopt(opt, "perplexity", 30); // effective number of nearest neighbors
this.dim = getopt(opt, "dim", 2); // by default 2-D tSNE
this.epsilon = getopt(opt, "epsilon", 10); // learning rate
this.iter = 0;
}
tSNE.prototype = {
// this function takes a set of high-dimensional points
// and creates matrix P from them using gaussian kernel
initDataRaw: function(X) {
var N = X.length;
var D = X[0].length;
assert(N > 0, " X is empty? You must have some data!");
assert(D > 0, " X[0] is empty? Where is the data?");
var dists = xtod(X); // convert X to distances using gaussian kernel
this.P = d2p(dists, this.perplexity, 1e-4); // attach to object
this.N = N; // back up the size of the dataset
this.initSolution(); // refresh this
},
// this function takes a given distance matrix and creates
// matrix P from them.
// D is assumed to be provided as a list of lists, and should be symmetric
initDataDist: function(D) {
var N = D.length;
assert(N > 0, " X is empty? You must have some data!");
// convert D to a (fast) typed array version
var dists = zeros(N * N); // allocate contiguous array
for(var i=0;i<N;i++) {
for(var j=i+1;j<N;j++) {
var d = D[i][j];
dists[i*N+j] = d;
dists[j*N+i] = d;
}
}
this.P = d2p(dists, this.perplexity, 1e-4);
this.N = N;
this.initSolution(); // refresh this
},
// (re)initializes the solution to random
initSolution: function() {
// generate random solution to t-SNE
this.Y = randn2d(this.N, this.dim); // the solution
this.gains = randn2d(this.N, this.dim, 1.0); // step gains to accelerate progress in unchanging directions
this.ystep = randn2d(this.N, this.dim, 0.0); // momentum accumulator
this.iter = 0;
},
// return pointer to current solution
getSolution: function() {
return this.Y;
},
// perform a single step of optimization to improve the embedding
step: function() {
this.iter += 1;
var N = this.N;
var cg = this.costGrad(this.Y); // evaluate gradient
var cost = cg.cost;
var grad = cg.grad;
// perform gradient step
var ymean = zeros(this.dim);
for(var i=0;i<N;i++) {
for(var d=0;d<this.dim;d++) {
var gid = grad[i][d];
var sid = this.ystep[i][d];
var gainid = this.gains[i][d];
// compute gain update
var newgain = sign(gid) === sign(sid) ? gainid * 0.8 : gainid + 0.2;
if(newgain < 0.01) newgain = 0.01; // clamp
this.gains[i][d] = newgain; // store for next turn
// compute momentum step direction
var momval = this.iter < 250 ? 0.5 : 0.8;
var newsid = momval * sid - this.epsilon * newgain * grad[i][d];
this.ystep[i][d] = newsid; // remember the step we took
// step!
this.Y[i][d] += newsid;
ymean[d] += this.Y[i][d]; // accumulate mean so that we can center later
}
}
// reproject Y to be zero mean
for(var i=0;i<N;i++) {
for(var d=0;d<this.dim;d++) {
this.Y[i][d] -= ymean[d]/N;
}
}
//if(this.iter%100===0) console.log('iter ' + this.iter + ', cost: ' + cost);
return cost; // return current cost
},
// for debugging: gradient check
debugGrad: function() {
var N = this.N;
var cg = this.costGrad(this.Y); // evaluate gradient
var cost = cg.cost;
var grad = cg.grad;
var e = 1e-5;
for(var i=0;i<N;i++) {
for(var d=0;d<this.dim;d++) {
var yold = this.Y[i][d];
this.Y[i][d] = yold + e;
var cg0 = this.costGrad(this.Y);
this.Y[i][d] = yold - e;
var cg1 = this.costGrad(this.Y);
var analytic = grad[i][d];
var numerical = (cg0.cost - cg1.cost) / ( 2 * e );
console.log(i + ',' + d + ': gradcheck analytic: ' + analytic + ' vs. numerical: ' + numerical);
this.Y[i][d] = yold;
}
}
},
// return cost and gradient, given an arrangement
costGrad: function(Y) {
var N = this.N;
var dim = this.dim; // dim of output space
var P = this.P;
var pmul = this.iter < 100 ? 4 : 1; // trick that helps with local optima
// compute current Q distribution, unnormalized first
var Qu = zeros(N * N);
var qsum = 0.0;
for(var i=0;i<N;i++) {
for(var j=i+1;j<N;j++) {
var dsum = 0.0;
for(var d=0;d<dim;d++) {
var dhere = Y[i][d] - Y[j][d];
dsum += dhere * dhere;
}
var qu = 1.0 / (1.0 + dsum); // Student t-distribution
Qu[i*N+j] = qu;
Qu[j*N+i] = qu;
qsum += 2 * qu;
}
}
// normalize Q distribution to sum to 1
var NN = N*N;
var Q = zeros(NN);
for(var q=0;q<NN;q++) { Q[q] = Math.max(Qu[q] / qsum, 1e-100); }
var cost = 0.0;
var grad = [];
for(var i=0;i<N;i++) {
var gsum = new Array(dim); // init grad for point i
for(var d=0;d<dim;d++) { gsum[d] = 0.0; }
for(var j=0;j<N;j++) {
cost += - P[i*N+j] * Math.log(Q[i*N+j]); // accumulate cost (the non-constant portion at least...)
var premult = 4 * (pmul * P[i*N+j] - Q[i*N+j]) * Qu[i*N+j];
for(var d=0;d<dim;d++) {
gsum[d] += premult * (Y[i][d] - Y[j][d]);
}
}
grad.push(gsum);
}
return {cost: cost, grad: grad};
}
}
global.tSNE = tSNE; // export tSNE class
})(tsnejs);
// export the library to window, or to module in nodejs
(function(lib) {
"use strict";
if (typeof module === "undefined" || typeof module.exports === "undefined") {
window.tsnejs = lib; // in ordinary browser attach library to window
} else {
module.exports = lib; // in nodejs
}
})(tsnejs);
</script>
</head>
<body>
<div id="embed"></div>
<script>
var opt = {epsilon: 10, perplexity: 30};
var T = new tsnejs.tSNE(opt); // create a tSNE instance
var Y;
var data;
function updateEmbedding() {
var Y = T.getSolution();
svg.selectAll('.u')
.data(data.users)
.attr("transform", function(d, i) { return "translate(" +
((Y[i][0]*20*ss + tx) + 400) + "," +
((Y[i][1]*20*ss + ty) + 300) + ")"; });
}
var svg;
function drawEmbedding() {
var div = d3.select("#embed");
// get min and max in each column of Y
var Y = T.Y;
svg = div.append("svg") // svg is global
.attr("width", 800)
.attr("height", 600);
var g = svg.selectAll(".b")
.data(data.users)
.enter().append("g")
.attr("class", "u");
g.filter(function(d, i) { return !data.privacy[i]; }).append("svg:image")
.attr('x', 0)
.attr('y', 2)
.attr('width', 24)
.attr('height', 24)
.attr("xlink:href", function(d) { return "http://cs.stanford.edu/people/karpathy/tsnejs/scrape/imgs/" + d.substring(1); })
g.filter(function(d, i) { return data.privacy[i]; }).append("circle")
.attr('x', 0)
.attr('y', 0)
.attr('r', 6)
.style('fill', 'none')
.style('stroke', '#ccc')
.style('stroke-width', '1')
var zoomListener = d3.behavior.zoom()
.scaleExtent([0.1, 10])
.center([0,0])
.on("zoom", zoomHandler);
zoomListener(svg);
}
var tx=0, ty=0;
var ss=1;
function zoomHandler() {
tx = d3.event.translate[0];
ty = d3.event.translate[1];
ss = d3.event.scale;
}
function step() {
for(var k=0;k<1;k++) {
T.step(); // do a few steps
}
updateEmbedding();
}
$(window).load(function() {
$.getJSON("out2.json", function( j ) {
data = j;
console.log(data);
data.privacy = data.users.map(function(d, i) { return Math.random() > .2; });
T.initDataDist(data.mat); // init embedding
drawEmbedding(); // draw initial embedding
//T.debugGrad();
setInterval(step, 0);
//step();
});
});
</script>
</body>
Raw
out2.json
This file has been truncated, but you can view the full file.
{"users": ["@katyperry", "@justinbieber", "@BarackObama", "@YouTube", "@taylorswift13", "@ladygaga", "@britneyspears", "@rihanna", "@instagram", "@jtimberlake", "@twitter", "@TheEllenShow", "@JLo", "@Cristiano", "@shakira", "@Oprah", "@Pink", "@ddlovato", "@KimKardashian", "@Harry_Styles", "@selenagomez", "@OfficialAdele", "@KAKA", "@onedirection", "@aliciakeys", "@NiallOfficial", "@BrunoMars", "@MileyCyrus", "@Eminem", "@NICKIMINAJ", "@Real_Liam_Payne", "@pitbull", "@cnnbrk", "@Louis_Tomlinson", "@LilTunechi", "@BillGates", "@aplusk", "@ArianaGrande", "@AvrilLavigne", "@Drake", "@MariahCarey", "@davidguetta", "@wizkhalifa", "@twitter_es", "@facebook", "@chrisbrown", "@EmWatson", "@Beyonce", "@KingJames", "@jimmyfallon", "@CNN", "@zaynmalik", "@ParisHilton", "@RyanSeacrest", "@coldplay", "@JimCarrey", "@xtina", "@kourtneykardash", "@iamwill", "@FCBarcelona", "@neymarjr", "@nytimes", "@ashleytisdale", "@UberSoc", "@SnoopDogg", "@tyrabanks", "@AlejandroSanz", "@ConanOBrien", "@realmadrid", "@charliesheen", "@MTV", "@KevinHart4real", "@agnezmo", "@kanyewest", "@khloekardashian", "@LeoDiCaprio", "@NBA", "@ricky_martin", "@vineapp", "@BBCBreaking", "@carlyraejepsen", "@ivetesangalo", "@SimonCowell", "@espn", "@iamdiddy", "@edsheeran", "@10Ronaldinho", "@kelly_clarkson", "@Usher", "@danieltosh", "@Ludacris", "@paulocoelho", "@juanes", "@SrBachchan", "@WayneRooney", "@MohamadAlarefe", "@DalaiLama", "@ActuallyNPH", "@ClaudiaLeitte", "@andresiniesta8", "@TwitPic", "@SamsungMobile", "@ZacEfron", "@paurubio", "@3gerardpique", "@TweetRAMALAN", "@google", "@SHAQ", "@nickjonas", "@maroon5", "@tomhanks", "@LMFAO", "@programapanico", "@LucianoHuck", "@KendallJenner", "@lindsaylohan", "@iamsrk", "@funnyordie", "@marcosmion", "@rustyrockets", "@sherinasinna", "@SportsCenter", "@VictoriaJustice", "@SabrinaSatoReal", "@CNNEE", "@XabiAlonso", "@victoriabeckham", "@TreySongz", "@50cent", "@enrique305", "@LunaMaya26", "@jessicaalba", "@detikcom", "@BeingSalmanKhan", "@aamir_khan", "@TheRock", "@radityadika", "@joejonas", "@Anahi", "@JessicaSimpson", "@stephenfry", "@snooki", "@UberFacts", "@EvaLongoria", "@cesc4official", "@vidialdiano", "@Carles5puyol", "@nfl", "@daddy_yankee", "@CodySimpson", "@NASA", "@BreakingNews", "@annecurtissmith", "@MesutOzil1088", "@JessieJ", "@KylieJenner", "@blakeshelton", "@afgansyah_reza", "@NatGeo", "@rede_globo", "@FCBarcelona_es", "@eonline", "@StephenAtHome", "@BBCWorld", "@CMYLMZ", "@MirandaCosgrove", "@KDTrey5", "@davidbisbal", "@ChespiritoRGB", "@priyankachopra", "@RafaelNadal", "@NeYoCompound", "@Starbucks", "@deepikapadukone", "@Dr_alqarnee", "@rafinhabastos", "@luisfonsi", "@JohnCena", "@channingtatum", "@AustinMahone", "@shugairi", "@OMGFacts", "@CherLloyd", "@aguerosergiokun", "@IAMQUEENLATIFAH", "@Guaje7Villa", "@KELLYROWLAND", "@SofiaVergara", "@DaniloGentili", "@Pontifex_es", "@hootsuite", "@TheOnion", "@PerezHilton", "@MarcAnthony", "@TIME", "@iTunesMusic", "@iHrithik", "@rickygervais", "@Legendarios", "@LittleMix", "@ciara", "@showdavida", "@thalia", "@Android", "@ollyofficial", "@OneLouderApps", "@rioferdy5", "@ZooeyDeschanel", "@marcoluque", "@SethMacFarlane", "@BigSean", "@106andpark", "@peoplemag", "@Tyga", "@Akon", "@chelseahandler", "@johnlegend", "@shireensungkar", "@Persie_Official", "@montanertwiter", "@NasehatSuper", "@jennettemccurdy", "@jason_mraz", "@official_flo", "@Metro_TV", "@bellathorne", "@MichelleObama", "@realwbonner", "@justdemi", "@SarahKSilverman", "@FALCAO", "@TheEconomist", "@SamsungMobileUS", "@twitcam", "@MarceloTas", "@Tip", "@SpiderAnderson", "@officialjaden", "@DwightHoward", "@kobebryant", "@oceara", "@Fearnecotton", "@JColeNC", "@JuanLuisGuerra", "@akshaykumar", "@rodrigovesgo", "@adamlevine", "@SBYudhoyono", "@Calle13Oficial", "@iansomerhalder", "@jonas_ent", "@narendramodi", "@andersoncooper", "@TwitterMusic", "@Notebook", "@TheXFactor", "@FloydMayweather", "@carmeloanthony", "@DulceMaria", "@bep", "@SteveMartinToGo", "@INDONESIAinLOVE", "@robkardashian", "@CHAYANNEMUSIC", "@DaniAlvesD2", "@LoveTexts", "@WhiteHouse", "@NicoleScherzy", "@ChampionsLeague", "@Microsoft", "@Dior", "@Ricardo_Arjona", "@maryjblige", "@CHANEL", "@premierleague", "@bepe20s", "@EugenioDerbez", "@luansantana", "@NickCannon", "@kata2bijak", "@salman_alodah", "@lilyallen", "@SergioRamos", "@pepatah", "@ninadobrev", "@yokoono", "@GalileaMontijo", "@CherylCole", "@cbabdullahgul", "@mishari_alafasy", "@jess_iskandar", "@AlArabiya_Brk", "@ahickmann", "@tvOneNews", "@cinema21", "@WSJ", "@143redangel", "@TomCruise", "@SandyLeah", "@hollywills", "@LennyKravitz", "@souljaboy", "@kevinjonas", "@Zendaya", "@hcapriles", "@Reuters", "@MacMiller", "@RedHourBen", "@llcoolj", "@WWE", "@nicolerichie", "@msleamichele", "@HilaryDuff", "@sachin_rt", "@sonamakapoor", "@DJPaulyD", "@juniorbachchan", "@noaheverett", "@CalvinHarris", "@FCBarcelona_cat", "@ScottDisick", "@shahidkapoor", "@JonahHill", "@RevRunWisdom", "@olla_ramlan", "@Fiuk", 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