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Last active March 24, 2016 16:07
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Learning rate
Raw
README.md

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

Raw
data.csv
population profit
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
Raw
index.html
<!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>
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