Using Sylvester to run gradient decent in Node.

ex1data.txt

6.1101,17.592
5.5277,9.1302
8.5186,13.662
7.0032,11.854
5.8598,6.8233
8.3829,11.886
7.4764,4.3483
8.5781,12
6.4862,6.5987
5.0546,3.8166
5.7107,3.2522
14.164,15.505
5.734,3.1551
8.4084,7.2258
5.6407,0.71618
5.3794,3.5129
6.3654,5.3048
5.1301,0.56077
6.4296,3.6518
7.0708,5.3893
6.1891,3.1386
20.27,21.767
5.4901,4.263
6.3261,5.1875
5.5649,3.0825
18.945,22.638
12.828,13.501
10.957,7.0467
13.176,14.692
22.203,24.147
5.2524,-1.22
6.5894,5.9966
9.2482,12.134
5.8918,1.8495
8.2111,6.5426
7.9334,4.5623
8.0959,4.1164
5.6063,3.3928
12.836,10.117
6.3534,5.4974
5.4069,0.55657
6.8825,3.9115
11.708,5.3854
5.7737,2.4406
7.8247,6.7318
7.0931,1.0463
5.0702,5.1337
5.8014,1.844
11.7,8.0043
5.5416,1.0179
7.5402,6.7504
5.3077,1.8396
7.4239,4.2885
7.6031,4.9981
6.3328,1.4233
6.3589,-1.4211
6.2742,2.4756
5.6397,4.6042
9.3102,3.9624
9.4536,5.4141
8.8254,5.1694
5.1793,-0.74279
21.279,17.929
14.908,12.054
18.959,17.054
7.2182,4.8852
8.2951,5.7442
10.236,7.7754
5.4994,1.0173
20.341,20.992
10.136,6.6799
7.3345,4.0259
6.0062,1.2784
7.2259,3.3411
5.0269,-2.6807
6.5479,0.29678
7.5386,3.8845
5.0365,5.7014
10.274,6.7526
5.1077,2.0576
5.7292,0.47953
5.1884,0.20421
6.3557,0.67861
9.7687,7.5435
6.5159,5.3436
8.5172,4.2415
9.1802,6.7981
6.002,0.92695
5.5204,0.152
5.0594,2.8214
5.7077,1.8451
7.6366,4.2959
5.8707,7.2029
5.3054,1.9869
8.2934,0.14454
13.394,9.0551
5.4369,0.61705

gradient_decent.js

var Vector = require('./node_modules/sylvester').Vector;
var Matrix = require('./node_modules/sylvester').Matrix;


/*
 - Here is my Octive
 
 hyp = X* theta;
 n = hyp - y;
 x = n'*n;
 J = n'*n/(2*m); 
 
*/
var computeCost = function(X, y, theta) {
  var J = 0;
  var m = y.dimensions();
  
  y = y.transpose();
  var hyp = X.multiply(theta);
  var n = hyp.subtract(y);
  var n1 = n.transpose();
  var n2 = n1.multiply(n)

  J = n2.e(1,1) / (2*m);

  return J;
}

/*
 - Here is my Octive
 - Approch one
 	%temp0 = theta(1,1) - alpha/m * (n' * X(:,1));
	%temp1 = theta(2,1) - alpha/m * (n' * X(:,2));

	%theta(1,1) = temp0;
	%theta(2,1) = temp1;

 - Approch two - Vectorized (used below)
	hyp = X * theta;
	n = hyp - y;
	theta = theta - (alpha/m * (n' * X))';

*/
var gradientDescent = function(X, y, theta, alpha, num_iters) {
  
  var m = y.dimensions();  
    
  for (var i = 1; i <= num_iters; i++) {
    
    var hyp = X.multiply(theta);
    var yT = y.transpose();
    var n = hyp.subtract(yT);
    var nTmX = (n.transpose()).multiply(X);
    var amT = nTmX.multiply(alpha/m).transpose();

    theta = theta.subtract(amT)
  }
  
  return theta;
}

// Starting point.

var data = Matrix.loadFile('./ex1data.txt');
var m = data.rows(); // number of training examples
var X = data.col(1); 
var y = data.col(2);

var ones = Matrix.Ones(m, 1);
X1 = ones.augment(X.transpose()); // Add a column of ones to x
X = X1;
theta = Matrix.Zero(2, 1); // initialize fitting parameters

// Some gradient descent settings
var iterations = 1500;
var alpha = 0.01;

var J = computeCost(X, y, theta);
theta = gradientDescent(X, y, theta, alpha, iterations);

console.log('Theta found by gradient descent: ');
console.log(theta.e(1,1), theta.e(2,1));

// Predict values for population sizes of 35,000 and 70,000
var predict1 = $V([1,3.5]);
predict1 = predict1.dot(theta);
var predict2 = $V([1, 7]);
predict2 = predict2.dot(theta);
// 
console.log('For population = 35,000, we predict a profit of', predict1 * 10000, "\n");
console.log('For population = 70,000, we predict a profit of', predict2 * 10000, "\n");