A t-SNE inspired visualization of a BigML G-means clustering built from a varient of the UCI Covertype dataset. Mouse over a cluster to see the centroid.
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June 29, 2017 01:58
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t-SNE Layout of Forest Cover Clusters
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| Set.prototype.union = function(setB) { | |
| var union = new Set(this); | |
| for (var elem of setB) { | |
| union.add(elem); | |
| } | |
| return union; | |
| } | |
| Set.prototype.intersection = function(setB) { | |
| var intersection = new Set(); | |
| for (var elem of setB) { | |
| if (this.has(elem)) { | |
| intersection.add(elem); | |
| } | |
| } | |
| return intersection; | |
| } | |
| function termDist(set1, set2) { | |
| if (set1.size == 0 && set2.size == 0) { | |
| return 0; | |
| } else if (set1.size == 0 || set2.size == 0) { | |
| return 1; | |
| } else { | |
| return 1 - set1.intersection(set2).size / Math.sqrt(set1.size * set2.size); | |
| } | |
| } | |
| /* | |
| Given a BigML cluster resource, will return a function that computes | |
| the distance between two clusters (referenced by their index) | |
| */ | |
| function clusterDistFn(resource) { | |
| var clusters = resource.clusters.clusters; | |
| for (var i in clusters) { | |
| var center = clusters[i].center; | |
| for (k in center) { | |
| if (typeof center[k] == 'object') { | |
| center[k] = new Set(center[k]); | |
| } | |
| } | |
| } | |
| var scales = resource.scales; | |
| return function (a, b) { | |
| var sum = 0; | |
| var clusterA = clusters[a]; | |
| var clusterB = clusters[b]; | |
| for (var k in clusterA.center) { | |
| var aVal = clusterA.center[k]; | |
| var bVal = clusterB.center[k]; | |
| var diff; | |
| switch (typeof aVal) { | |
| case 'number': | |
| diff = aVal - bVal; | |
| break; | |
| case 'string': | |
| diff = aVal == bVal ? 0 : 1; | |
| break; | |
| case 'object': | |
| diff = termDist(aVal, bVal); | |
| break; | |
| } | |
| diff *= scales[k]; | |
| sum += diff * diff; | |
| } | |
| /* console.log(clusterA.center, clusterB.center, a, b, Math.sqrt(sum)); */ | |
| return Math.sqrt(sum); | |
| }; | |
| } | |
| /* | |
| Given a BigML cluster resource, returns a distance matrix for the | |
| clusters | |
| */ | |
| function distMatrix (resource) { | |
| var clusterCount = Object.keys(resource.clusters.clusters).length; | |
| var distFn = clusterDistFn(resource); | |
| var matrix = new Array(clusterCount); | |
| for (var a = 0; a < clusterCount; a++) { | |
| matrix[a] = new Array(clusterCount); | |
| for (var b = 0; b < clusterCount; b++) { | |
| if (a == b) { | |
| matrix[a][b] = 0; | |
| } else if (a > b) { | |
| matrix[a][b] = matrix[b][a]; | |
| } else { | |
| matrix[a][b] = distFn(a, b); | |
| } | |
| } | |
| } | |
| console.log(matrix); | |
| return matrix; | |
| } |
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| {"balance_fields": true, "category": 0, "cluster_datasets": {}, "cluster_models": {}, "cluster_seed": "2c249dda00fbf54ab4cdd850532a584f286af5b6", "clusters": {"between_ss": 259549.60913, "clusters": [{"center": {"000000": 2784.11367, "000001": 83.58594, "000002": 8.78962, "000003": 218.48279, "000004": 19.26321, "000005": 1541.41577, "000006": 227.65007, "000007": 227.65401, "000008": 132.59869, "000009": 1938.91012, "00000a": "Rawah", "00000b": "Montane + subalpine", "00000c": "Igneous", "00000d": "Lodgepole Pine"}, "count": 39564, "distance": {"bins": [[0.10988, 5], [0.1473, 156], [0.17798, 206], [0.20169, 336], [0.22631, 563], [0.24922, 820], [0.27179, 1303], [0.30484, 3719], [0.33307, 2713], [0.35536, 3381], [0.3783, 3910], [0.40066, 3865], [0.42292, 3651], [0.44509, 3896], [0.47576, 5355], [0.51345, 3079], [0.54865, 1485], [0.58199, 697], [0.61704, 264], [0.65167, 60], [0.67741, 26], [0.70679, 18], [0.73283, 3], [0.75459, 6], [0.78119, 6], [0.81538, 6], [0.84654, 9], [0.87611, 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| <script src="//d3js.org/d3.v3.min.js" charset="utf-8"></script> | |
| <script src="//cdnjs.cloudflare.com/ajax/libs/seedrandom/2.4.0/seedrandom.min.js"></script> | |
| <script src="cluster-dist.js" charset="utf-8"></script> | |
| <script src="tsne.js" charset="utf-8"></script> | |
| </head> | |
| <body> | |
| <svg width="850" height="500"></svg> | |
| <div id="words"></div> | |
| <script> | |
| var width = 850; | |
| var height = 500; | |
| var colors = d3.scale.category20(); | |
| d3.json("clustered-cover.json", function(error, resource) { | |
| var fields = resource.clusters.fields; | |
| var coords = tsneLayout(resource, "defaultseed"); | |
| var clusters = resource.clusters.clusters; | |
| var clusterCount = Object.keys(clusters).length; | |
| var range = Array.apply(null, Array(clusterCount)).map(function (_, i) {return i;}); | |
| // scale the tsne coordinates relative to the svg size | |
| coords = scaleDimension(width, width/10, 0, coords); | |
| coords = scaleDimension(height, height/10, 1, coords); | |
| var words = d3.select("#words"); | |
| var colorFn = function (i, lightness) { | |
| return d3.lab(lightness, | |
| (200 * coords[i][0] / width) - 100, | |
| (200 * coords[i][1] / height) - 100); | |
| }; | |
| var svg = d3.select("svg"); | |
| svg.style("width", width); | |
| svg.style("height", height); | |
| svg.selectAll(".dot").data(range).enter() | |
| .append("circle") | |
| .attr("class", "dot") | |
| .attr("r", function (i) { | |
| // set topic radius relative to the 'topic_means' score | |
| var area = clusters[i].count / resource.rows; | |
| r = Math.sqrt(area) * 60; | |
| return r; | |
| }) | |
| .on("mouseenter", function (i) { | |
| words.selectAll(".word").remove(); | |
| var cluster = clusters[i]; | |
| for (var k in cluster.center) { | |
| var name = fields[k].name; | |
| var val; | |
| if (typeof cluster.center[k] == 'object') { | |
| name += "(tokens)"; | |
| val = Array.from(cluster.center[k]); | |
| } else { | |
| val = cluster.center[k]; | |
| } | |
| name += " : "; | |
| words.append("text") | |
| .attr("class", "word") | |
| .text(name + val); | |
| } | |
| words.append("text").attr("class", "word") | |
| .text("Cluster Size : " + cluster.count); | |
| }) | |
| .on("mouseleave", function (i) { | |
| words.selectAll(".word").remove(); | |
| }) | |
| .attr("cx", function (i) {return coords[i][0];}) | |
| .attr("cy", function (i) {return coords[i][1];}) | |
| .style("fill", function (i) { return colorFn(i, 80); }) | |
| .style("stroke", function (i) { return colorFn(i, 65); }); | |
| }); | |
| function scaleDimension(dimSize, buffer, dimIndex, coords) { | |
| var minDim = coords[0][dimIndex]; | |
| var maxDim = coords[0][dimIndex]; | |
| for (var i in coords) { | |
| minDim = Math.min(minDim, coords[i][dimIndex]); | |
| maxDim = Math.max(maxDim, coords[i][dimIndex]); | |
| } | |
| var diff = maxDim - minDim; | |
| var dimScale = dimSize - 2 * buffer; | |
| for (var i in coords) { | |
| coords[i][dimIndex] = (((coords[i][dimIndex] - minDim) / diff) * dimScale) + buffer; | |
| } | |
| return coords; | |
| } | |
| function tsneLayout(resource, seed) { | |
| Math.seedrandom(seed); | |
| var clusterCount = resource.clusters.clusters.length; | |
| var perplexity = Math.round(clusterCount / 10); | |
| perplexity = Math.max(perplexity, 2); | |
| console.log(perplexity); | |
| var tsne = new tsnejs.tSNE({epsilon: 10, perplexity: perplexity}); | |
| tsne.initDataDist(distMatrix(resource)); | |
| for (var k = 0; k < 300; k++) { | |
| tsne.step(); | |
| } | |
| return tsne.getSolution(); | |
| } | |
| </script> | |
| </body> | |
| </html> |
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| // from https://github.com/karpathy/tsnejs | |
| // 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); |
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