Merge pull request #61 from mateogianolio/logistic-regression

add logistic regression example

README.md

@@ -62,7 +62,8 @@ At the moment, Google Chrome seems to offer the best TypedArray support.
 
 **Machine learning**
 * [**Backpropagation**](https://github.com/mateogianolio/vectorious/tree/master/examples/neural-network.js) (by [@lucidrains](https://github.com/lucidrains))
-* [**Gradient descent**](https://github.com/mateogianolio/vectorious/tree/master/examples/neural-network.js)
+* [**Gradient descent**](https://github.com/mateogianolio/vectorious/tree/master/examples/gradient-descent.js)
+* [**Logistic regression**](https://github.com/mateogianolio/vectorious/tree/master/examples/logistic-regression.js)
 
 ### Documentation
 

examples/backpropagation.js

@@ -5,7 +5,6 @@
 
   var Matrix = require('../vectorious').Matrix;
 
-  // aliases
   var add = Matrix.add,
       subtract = Matrix.subtract,
       random = Matrix.random;
@@ -26,15 +25,14 @@
     };
   }
 
-  // inputs and outputs
+  // input and output
   var X = new Matrix([[0, 0, 1], [0, 1, 1], [1, 0, 1], [1, 1, 1]]),
       y = new Matrix([[0, 1, 1, 0]]).T;
 
   // initialize weights with a standard deviation of 2 and mean -1
   var syn0 = random.apply(null, X.T.shape, 2, -1),
       syn1 = random.apply(null, y.shape, 2, -1);
 
-  // layers and deltas
   var l0,
       l1,
       l0_delta,

examples/gradient-descent.js

@@ -5,7 +5,6 @@
 
   var Matrix = require('../vectorious').Matrix;
 
-  // aliases
   var subtract = Matrix.subtract,
       random = Matrix.random;
 
@@ -25,7 +24,7 @@
     };
   }
 
-  // inputs and outputs
+  // input and output
   var X = new Matrix([[0, 0, 1], [0, 1, 1], [1, 0, 1], [1, 1, 1]]),
       y = new Matrix([[0, 1, 1, 0]]).T;
 
@@ -36,7 +35,6 @@
   var syn0 = random(X.T.shape[0], hidden_dim, 2, -1),
       syn1 = random(hidden_dim, 1, 2, -1);
 
-  // layers and deltas
   var l0,
       l1,
       l0_delta,

examples/logistic-regression.js

@@ -0,0 +1,93 @@
+(function () {
+  // logistic regression example based on https://github.com/junku901/dnn
+  'use strict';
+
+  var v = require('../vectorious'),
+      Matrix = v.Matrix,
+      Vector = v.Vector;
+
+  var subtract = Matrix.subtract;
+
+  // perform row-wise softmax on matrix
+  function softmax(m) {
+    var c = m.shape[1],
+        max = new Vector(m).max(),
+        sum;
+
+    return m.map(function (x, i, j) {
+      if (j === 0) {
+        sum = 0;
+        for (var k = 0; k < c; k++)
+          sum += Math.exp(m.get(i, k) - max);
+      }
+
+      return Math.exp(x - max) / sum;
+    });
+  }
+
+  // get col-wise mean of matrix as vector
+  function mean(m) {
+    var c = m.shape[1],
+        v = Vector.zeros(c),
+        sum;
+
+    return v.map(function (x, i) {
+      sum = 0;
+      for (var j = 0; j < c; j++)
+        sum += m.get(i, j);
+
+      return sum / c;
+    });
+  }
+
+  // row-wise add vector to matrix
+  function addMatVec(m, v) {
+    return m.map(function (x, r, c) {
+      return x + v.get(c);
+    });
+  }
+
+  var X = new Matrix([
+    [1, 1, 1, 0, 0, 0],
+    [1, 0, 1, 0, 0, 0],
+    [1, 1, 1, 0, 0, 0],
+    [0, 0, 1, 1, 1, 0],
+    [0, 0, 1, 0, 1, 0],
+    [0, 0, 1, 1, 1, 0]
+  ]);
+
+  var y = new Matrix([
+    [1, 0],
+    [1, 0],
+    [1, 0],
+    [0, 1],
+    [0, 1],
+    [0, 1]
+  ]);
+
+  var W = Matrix.zeros(X.shape[0], y.shape[1]),
+      b = Vector.zeros(y.shape[1]);
+
+  var rate = 0.01,
+      prob,
+      delta;
+
+  // train
+  for (var i = 0; i < 800; i++) {
+    prob = softmax(addMatVec(X.multiply(W), b));
+    delta = subtract(y, prob);
+
+    W.add(X.T.multiply(delta).scale(rate));
+    b.add(mean(delta).scale(rate));
+  }
+
+  // predict
+  var x = new Matrix([
+    [1, 1, 0, 0, 0, 0],
+    [0, 0, 0, 1, 1, 0],
+    [1, 1, 1, 1, 1, 0]
+  ]);
+
+  console.log(softmax(addMatVec(x.multiply(W), b)).toArray());
+  // prediction should be close to [[1, 0], [0, 1], [0.5, 0.5]]
+}());