L2 Regularization

README.md

l2 Regularization is applied to previous regression parameter values, the strength of the coefficient lambda can be manually adjusted.

Data source: Auto MPG Data Set, Lichman, M. (2013). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science.

AutoMpg.json

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index.html

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

.axis text {
  font: 10px sans-serif;
}

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

.axis path {
  display: none;
}

.tile {
  shape-rendering: crispEdges;
}

.dot {
  stroke: #000;
}

</style>
<body>
<div id="RegSelect"></div>
<script src="http://d3js.org/d3.v3.min.js"></script>
<script type="text/javascript"
  src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
  tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}
});
</script>
<script>
var margin = {top: 20, right: 20, bottom: 30, left: 30},
    width = 960 - margin.left - margin.right,
    height = 500 - margin.top - margin.bottom;

var gridX = d3.scale.linear()
    .domain([0, 100])
    .range([-5, 5]);

var gridY = d3.scale.linear()
    .domain([0, 100])
    .range([-50, 200]);

var x = d3.scale.linear()
    .domain([-5, 5])
    .range([0, width]);

var y = d3.scale.linear()
    .domain([-50, 200])
    .range([height, 0]);

var lambda = 0;

var sliderLabel = d3.select("#RegSelect")
    .append("label")
    .attr("for", "fader")
    .text("lambda");

var slider = d3.select("#RegSelect").append("input")
    .attr("id","slider2").attr("type","range")
    .attr("min","0").attr("max","10")
    .attr("step","0.05").attr("value","0")
    .attr("oninput","outputUpdate(value)");

var sliderOutput = d3.select("#RegSelect")
    .append("output").attr("for","fader")
    .attr("id","reg")
    .text("0");

var color = d3.scale.quantize()
    .domain([0, 1])
    .range(['rgb(255,255,217)','rgb(237,248,177)',
      'rgb(199,233,180)','rgb(127,205,187)',
      'rgb(65,182,196)','rgb(29,145,192)',
      'rgb(34,94,168)','rgb(37,52,148)',
      'rgb(8,29,88)']);

var xAxis = d3.svg.axis()
    .scale(x)
    .orient("bottom")
    .ticks(10);

var yAxis = d3.svg.axis()
    .scale(y)
    .orient("left")
    .ticks(10);

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.json("AutoMpg.json", function(error, data){

  var surface = [];

  for (var i = 0; i < 100; i ++){
    for (var j = 0; j < 100; j++){
      surface.push(
        {'x': gridX(i),'y': gridY(j),
         'e': calculateError(gridX(i), gridY(j)),
         'r': Math.pow(gridX(i), 2) + Math.pow(gridY(j), 2)
        });
    }
  }
  var minimum = d3.min(surface, function(d){ return d.e + lambda * d.r;}),
  maximum = d3.max(surface, function(d){ return d.e + lambda * d.r;});

  mapping = d3.scale.log()
    .domain([minimum, maximum])
    .range([0, 1]);

  svg.selectAll(".tile")
      .data(surface)
      .enter().append("rect")
      .attr("class","tile")
      .attr("x", function(d) { return x(d.x); })
      .attr("y", function(d) { return y(d.y); })
      .attr("width", width/20)
      .attr("height", height/20)
      .style("fill", function(d) { 
          return color(mapping(d.e + lambda * d.r));
      });

  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");

  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("text-anchor", "end");

  slider.on("change", function(d){
          lambda = ChangeReg();
          // minimum = d3.min(surface, function(d){ return d.e + lambda * d.r;});
          // maximum = d3.max(surface, function(d){ return d.e + lambda * d.r;});
          svg.selectAll(".tile")
             .style("fill", function(d){
                return color(mapping(d.e + lambda * d.r));
             });
      });

  function calculateError(b1, b0){
      var error = 0.0;
      for (var i = 0; i < data.length; i++){
        error += Math.pow(data[i].mpg - ((b1 * data[i].horsepower) + b0), 2);
      }
      return error / data.length;

  }
});
function ChangeReg() {
        var e = document.getElementById("reg");
        var selection = +e.value;
        return selection;
  }
function outputUpdate(vol) {
    document.querySelector('#reg').value = vol;
  }
</script>

thumbnail.png