Gradient descent

Linear regression using gradient descent method

<!DOCTYPE html>
<meta charset="utf-8">
<style>

body {
  font: 10px sans-serif;
}

.axis path,
.axis line {
  fill: none;
  stroke: #000;
  shape-rendering: crispEdges;
}

.line {
  fill: none;
  stroke: black;
  stroke-width: 1px;
}

</style>
<body>
<script src="https://d3js.org/d3.v3.min.js"></script>
<script>

var margin = {top: 20, right: 20, bottom: 30, left: 40},
    width = 960 - margin.left - margin.right,
    height = 500 - margin.top - margin.bottom;

var format = d3.format(".3f");

var x = d3.scale.linear()
    .range([0, width]);

var y = d3.scale.linear()
    .range([height, 0]);

var xAxis = d3.svg.axis()
    .scale(x)
    .orient("bottom");

var yAxis = d3.svg.axis()
    .scale(y)
    .orient("left");

var svg = d3.select("body").append("svg")
    .attr("width", width + margin.left + margin.right)
    .attr("height", height + margin.top + margin.bottom)
  .append("g")
    .attr("transform", "translate(" + margin.left + "," + margin.top + ")");

d3.csv("data.csv", function(error, data) {
  data.forEach(function(d) {
    d.population = +d.population;
    d.profit = +d.profit;
  });

x.domain(d3.extent(data, function(d) { return d.population; })).nice();
  y.domain(d3.extent(data, function(d) { return d.profit; })).nice();

var xMin = x.domain()[0],
      xMax = x.domain()[1],
      yMin = y.domain()[0],
      yMax = y.domain()[1];

svg.append("g")
      .attr("class", "x axis")
      .attr("transform", "translate(0," + height + ")")
      .call(xAxis)
    .append("text")
      .attr("class", "label")
      .attr("x", width)
      .attr("y", -6)
      .style("text-anchor", "end")
      .style("font-weight","bold")
      .text("Population of City in 10,000s");

svg.append("g")
      .attr("class", "y axis")
      .call(yAxis)
    .append("text")
      .attr("class", "label")
      .attr("transform", "rotate(-90)")
      .attr("y", 6)
      .attr("dy", ".71em")
      .style("font-weight","bold")
      .style("text-anchor", "end")
      .text("Profit in $10,000s")

svg.selectAll(".dot")
      .data(data)
    .enter().append("circle")
      .attr("class", "dot")
      .attr("r", 3.5)
      .attr("cx", function(d) { return x(d.population); })
      .attr("cy", function(d) { return y(d.profit); })
      .style("fill","#d73027");

// Some gradient descent settings
  var iteration = 0,
      iterationNumber = 1500,
      m = data.length,
      alpha = 0.01;
      theta0 = 0,
      theta1 = 0;

var line = svg.append("line")
    .attr("class", "line")
    .attr("x1",x( xMin ))
    .attr("y1",y( theta1 * xMin + theta0 ))
    .attr("x2",x( xMax ))
    .attr("y2",y( theta1 * xMax + theta0 ));

var hyp = svg.append("text")
    .attr("x", width/2)
    .attr("y", 40)
    .style("text-anchor","middle")
    .style("font-size","35px")
    .text("hθ(x) = 0 + 0x");

function computeCost (data, theta0, theta1) {
    var cost = 0;
    data.forEach(function(d) {
      cost += Math.pow((theta1 * d.population + theta0 - d.profit),2);
    });
    return cost/(2 * m);
  };

d3.timer(function() {

var temp0 = theta0 - alpha * (1/m) * d3.sum(data.map(function(d) { return ((theta1 * d.population + theta0) - d.profit); }));
    var temp1 = theta1 - alpha * (1/m) * d3.sum(data.map(function(d) { return ((theta1 * d.population + theta0) - d.profit) * d.population ; }));

theta0 = temp0;
    theta1 = temp1;

line.attr("x1",x( xMin ))
    .attr("y1",y( theta1 * xMin + theta0 ))
    .attr("x2",x( xMax ))
    .attr("y2",y( theta1 * xMax + theta0 ));
  
    hyp.text("hθ(x) = " + format(theta0) + " + " + format(theta1) + "x");

return ++iteration > iterationNumber;
  },200);

});

</script>

https://d3js.org/d3.v3.min.js