A kernel is any smooth function K such that K(x) >= 0 and
The boxcar kernel is 0 across the domain of X, except for at a specified distance from x. We can use the boxcar kernel to take local averages for nonparametric estimation. Here the bandwidth parameter controls the specified distance. As
| <!DOCTYPE html> | |
| <meta charset="utf-8"> | |
| <head> | |
| <style> | |
| .axis { | |
| font: 10px sans-serif; | |
| } | |
| path { | |
| stroke: steelblue; | |
| stroke-width: 2; | |
| fill: none; | |
| } | |
| .axis path, | |
| .axis line { | |
| fill: none; | |
| stroke: #000; | |
| shape-rendering: crispEdges; | |
| } | |
| </style> | |
| </head> | |
| <body> | |
| <div id="BandSelect" align=center></div> | |
| <script src="http://d3js.org/d3.v3.min.js"></script> | |
| <script> | |
| var data = [] | |
| for (var i = 0; i < 20; i++){ | |
| var a = 6 * Math.random(); | |
| data.push({'x': a,'y': 0.9 * Math.sin(a) + (0.25 * Math.random()) - 0.125}); | |
| } | |
| var sliderLabel = d3.select("#BandSelect") | |
| .append("label") | |
| .attr("for", "fader") | |
| .text("bandwidth"); | |
| var slider = d3.select("#BandSelect").append("input") | |
| .attr("id","slider2").attr("type","range") | |
| .attr("min","0.5").attr("max","6") | |
| .attr("step","0.25").attr("value","1") | |
| .attr("oninput","outputUpdate(value)"); | |
| var sliderOutput = d3.select("#BandSelect") | |
| .append("output").attr("for","fader") | |
| .attr("id","band") | |
| .text("1"); | |
| var margin = {top: 80, right: 180, bottom: 80, left: 180}, | |
| width = 960 - margin.left - margin.right, | |
| height = 500 - margin.top - margin.bottom; | |
| 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 + ")"); | |
| var y = d3.scale.linear() | |
| .domain([-1, 1]) | |
| .range([height, 0]); | |
| var x = d3.scale.linear() | |
| .domain([0, 6]) | |
| .range([0, width]) | |
| var xAxis = d3.svg.axis() | |
| .scale(x) | |
| .orient("bottom"); | |
| var yAxis = d3.svg.axis() | |
| .scale(y) | |
| .orient("left"); | |
| var line = d3.svg.line() | |
| .x(function(d) { return x(d.x); }) | |
| .y(function(d) { return y(d.y); }); | |
| svg.append("g") | |
| .attr("class", "x axis") | |
| .attr("transform", "translate(0," + height + ")") | |
| .call(xAxis) | |
| svg.append("g") | |
| .attr("class", "y axis") | |
| .call(yAxis); | |
| svg.selectAll(".dot") | |
| .data(data) | |
| .enter().append("circle") | |
| .attr("class", "dot") | |
| .attr("r", 3.5) | |
| .attr("cx", function(d){ | |
| return x(d.x); | |
| }) | |
| .attr("cy", function(d){ | |
| return y(d.y) | |
| }) | |
| .style("fill", "black"); | |
| var smoothed = boxcarSmoother(data, 1, 0, 6, 1000); | |
| svg.append("path") | |
| .datum(smoothed) | |
| .attr("class", "line") | |
| .attr("d", line); | |
| slider.on("change", function(d){ | |
| band = ChangeReg(); | |
| var smoothed = boxcarSmoother(data, band, 0, 6, 1000); | |
| svg.selectAll(".line") | |
| .datum(smoothed) | |
| .transition() | |
| .attr("class", "line") | |
| .attr("d", line); | |
| }); | |
| function boxcarSmoother(data, bandwidth, rangeMin, rangeMax, samples){ | |
| //Takes a dataset and a bandwith parameter and performs a loess | |
| var support = []; | |
| var step = (rangeMax - rangeMin) / samples; | |
| //generate support set for given resolution | |
| for (var i = 0; i < samples; i++){ | |
| support.push(step * i); | |
| } | |
| var smoothData = []; | |
| for (var i = 0; i < samples; i++){ | |
| var activePoints = data.filter(function(d){ | |
| return ((support[i] >= d.x - bandwidth) && (support[i] <= d.x + bandwidth)); | |
| }).map(function(d){ | |
| return d.y; | |
| }); | |
| if (activePoints.length == 0){ | |
| activePoints.push(0); | |
| } | |
| var estimateY = activePoints.reduce(function(a, b){ | |
| return a + b; | |
| }); | |
| smoothData.push({'x': support[i], 'y': estimateY / activePoints.length}); | |
| } | |
| return smoothData; | |
| } | |
| function ChangeReg() { | |
| var e = document.getElementById("band"); | |
| var selection = +e.value; | |
| return selection; | |
| } | |
| function outputUpdate(vol) { | |
| document.querySelector('#band').value = vol; | |
| } | |
| </script> | |
| </body> |
