add tsne.js by Andrej Karpathy (https://github.com/karpathy/tsnejs)

browser/index.html

@@ -31,8 +31,6 @@
         <link id="palette" rel="stylesheet" type="text/css" href="css/light.css" /> 
 
         <script data-main="js/app.js" src="js/lib/require.js"></script>
-        <script src="js/numeric-1.2.6.js"></script>
-        <script src="js/tsne.js"></script>
 
     </head>
 

browser/js/app.js

@@ -20,6 +20,7 @@ require(["jquery",
         "underscore",
         "rgbcolor",
         "file",
+        "tsne",
         "../compare", 
         "../menu", 
         "../dbscan", 

browser/js/lib/tsne.js

+/* tsne.JS
+ * AUTHOR : Andrej Karpathy 
+ * https://github.com/karpathy/tsnejs
+ * license : MIT
+ * */
+
+
+// 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(gainid < 0.01) gainid = 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);