Learning rate

Cost function J(θ) convergence for different learning rate α values.

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

body {
  font: 10px sans-serif;
}

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

.axis text {
  font-weight: bold;
}
.line {
  fill: none;
  stroke: #000;
  stroke-width: 1.2px;
  stroke-linejoin: round;
}
</style>
<body>
<script src="https://d3js.org/d3.v3.min.js"></script>
<script>

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

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

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

var xAxis = d3.svg.axis()
    .scale(x)
    .tickSize(-height)
    .tickPadding(8)
    .orient("bottom");

var yAxis = d3.svg.axis()
    .scale(y)
    .tickSize(-width)
    .tickPadding(8)
    .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) {
  
  // Some gradient descent settings
  var iterationNumber = 150,
    m = data.length,
    alpha = [0.01,0.001,0.0005,0.0001],
    theta0 = 0,
    theta1 = 0;

data.forEach(function(d) {
    d.population = +d.population;
    d.profit = +d.profit;
  });

var values = alpha.map(function(alphaValue) {
    
    var costHistory = [];
    theta0 = 0;
    theta1 = 0;

for(i=0;i<iterationNumber;i++) {

costHistory.push({iteration: i, cost: computeCost(data, theta0, theta1) });

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

theta0 = temp0;
      theta1 = temp1;

};

return {alpha: alphaValue, data: costHistory};
  })

x.domain([0,iterationNumber]);
  var yMin = d3.min(values, function(alphaValue) { return d3.min(alphaValue.data, function(d) { return d.cost; }); });
  var yMax = d3.max(values, function(alphaValue) { return d3.max(alphaValue.data, function(d) { return d.cost; }); });

y.domain([yMin,yMax]).nice();

var line = d3.svg.line()
      .interpolate("basis")
      .x(function(d) { return x(d.iteration); })
      .y(function(d) { return y(d.cost); });

svg.append("rect")
    .attr("class", "background")
    .attr("width", width)
    .attr("height", height)
    .style("fill","#e7e7e7");

svg.append("g")
      .attr("class", "x axis")
      .attr("transform", "translate(0," + height + ")")
      .call(xAxis)
    .append("text")
      .attr("class", "label")
      .attr("x", width-5)
      .attr("y", -6)
      .style("text-anchor", "end")
      .style("font-weight","bold")
      .text("Number of iterations");

svg.append("g")
      .attr("class", "y axis")
      .call(yAxis)
    .append("text")
      .attr("class", "label")
      .attr("transform", "rotate(-90)")
      .attr("dx","-.71em")
      .attr("y", 6)
      .attr("dy", ".71em")
      .style("font-weight","bold")
      .style("text-anchor", "end")
      .text("J(θ)")

var path = svg.selectAll(".line")
      .data(values).enter()
      
  path.append("path")
      .attr("id", function(d) { console.log(d); return d.alpha; })
      .attr("class","line")
      .attr("d", function(d) { return line(d.data); });

path.append("text")
    .attr("dy", "-3px")
    .append("textPath")
    .attr("xlink:href", function(d) { return "#" + d.alpha; })
    .attr("startOffset", "24%")
    .style("font-weight","bold")
    .text(function(d) { return "α = " + d.alpha; });

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);
  };
});

</script>

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