Mocking t-SNE with some data not visible
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t-SNE mock
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| license: gpl-3.0 |
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| <!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> |
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| {"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", 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