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GenericDistRegression.html
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<!DOCTYPE html>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Neural network back prop, with matrix fomulation</title>
<meta name="viewport" content="width=device-width, initial-scale=1">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/normalize/3.0.3/normalize.css">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/skeleton/2.0.4/skeleton.css">
<meta name="viewport" content="width=device-width, initial-scale=1">
</head>
<script>
//---------------Matrix multiplication code
function RandomMat(inp,neurons)
{
var L = []
for(var i=0;i<neurons;i++)
{
L[i] = [];
for(var j=0;j<inp;j++)
{
L[i].push(2*Math.random()-1);
}
}
return L;
}
function PrintMat(m)
{
var str = "[";
for(var j=0;j<m.length;j++)
{
str += "[" + m[j].join(",") + "]";
}
str += "]";
return str;
}
function MulMat(m1, m2)
{
var O = [];
for(var j=0;j<m1.length;j++)
{
O[j]=[];
for(var i=0;i<m2[0].length;i++)
{
var tmp=0;
for(var k=0;k<m1[0].length;k++)
{
tmp += (m1[j][k] * m2[k][i]);
}
O[j].push( tmp);
}
}
return O;
}
function TransposeMat(m)
{
var O = [];
for(var j=0;j<m[0].length;j++)
{
O[j]=[];
for(var i=0;i<m.length;i++)
{
O[j][i] = m[i][j];
}
}
return O;
}
function AddMat(m1, m2)
{
var O = [];
for(var j=0;j<m1.length;j++)
{
O[j]=[];
for(var i=0;i<m1[0].length;i++)
{
O[j][i] = m1[j][i] + m2[j][i];
}
}
return O;
}
function SimpleMulMat(m1, m2)
{
var O = [];
for(var j=0;j<m1.length;j++)
{
O[j]=[];
for(var i=0;i<m1[0].length;i++)
{
O[j][i] = m1[j][i] * m2[j][i];
}
}
return O;
}
function SubMat(m1, m2)
{
var O = [];
for(var j=0;j<m1.length;j++)
{
O[j]=[];
for(var i=0;i<m1[0].length;i++)
{
O[j][i] = m1[j][i] - m2[j][i];
}
}
return O;
}
function funcMat(func, m )
{
var O = [];
for(var j=0;j<m.length;j++)
{
O[j]=[];
for(var i=0;i<m[0].length;i++)
{
O[j][i] = func(m[j][i]);
}
}
return O;
}
//-----------------------simple graphing code
function Graph(context, center_x, center_y, zoom)
{
this.context = context;
this.center_x = center_x;
this.center_y = center_y;
this.zoom = zoom;
this.ViewportX = function(x) { return (x*this.zoom + this.center_x); }
this.ViewportY = function(y) { return (-y*this.zoom + this.center_y); }
this.InvViewportX = function(vx) { return ((vx - this.center_x)/this.zoom); }
this.InvViewportY = function(vy) { return (-(vy - this.center_y)/this.zoom); }
this.moveTo = function(x,y) { this.context.moveTo(this.ViewportX(x),this.ViewportY(y)); }
this.lineTo = function(x,y) { this.context.lineTo(this.ViewportX(x),this.ViewportY(y)); }
this.fillText = function (str, x,y ) { this.context.fillText(str,this.ViewportX(x),this.ViewportY(y)); }
this.DrawAxis = function ()
{
this.context.beginPath();
this.context.strokeStyle="#000000";
this.moveTo( -100,0);
this.lineTo( 100,0);
this.moveTo( 0, -100);
this.lineTo( 0, 100);
this.context.closePath();
this.context.stroke();
for(var i=-30;i<30;i++)
{
this.context.font="15px ti92pluspc";
this.fillText(i,i,0);
this.fillText(i,0,i);
}
}
this.DrawLine = function (x1,y1,x2,y2)
{
this.context.beginPath();
this.moveTo(x1,y1);
this.lineTo(x2,y2);
this.context.closePath();
this.context.stroke();
}
this.DrawPlus = function (x,y,radius)
{
this.context.beginPath();
this.context.moveTo(this.ViewportX(x) - radius, this.ViewportY(y));
this.context.lineTo(this.ViewportX(x) + radius, this.ViewportY(y));
this.context.moveTo(this.ViewportX(x), this.ViewportY(y) - radius);
this.context.lineTo(this.ViewportX(x), this.ViewportY(y) + radius);
this.context.closePath();
this.context.stroke();
}
this.DrawCircle = function (x,y,radius)
{
this.context.beginPath();
this.context.arc(this.ViewportX(x), this.ViewportY(y), radius, 0 , 2 * Math.PI);
this.context.stroke();
}
}
var gfxDB, gfxAE;
//----------------------Point distribution generation and drawing
var setPoints = []
var setTarget = []
var axis_a;
var axis_b;
function RandomizeLinearF()
{
var px = Math.random()
var py = Math.random()
axis_a = (py-.5)/(px-.5);
axis_b = (1-axis_a)*.5;
}
function LinearF(x,y)
{
var dist = axis_a*x+axis_b - y;
return dist>0?1:0;
}
function SinF(x,y)
{
return y>(.4*Math.sin(x*6.28)+.5)?1:0;
}
function DiscF(x,y)
{
dist = ((x-.5)*(x-.5) + (y-.5)*(y-.5)) - .3*.3;
return dist>0?1:0;
}
function HammersleyRand(a)
{
a=(a<<16|a>>>16)>>>0;
a=((a&1431655765)<<1|(a&2863311530)>>>1)>>>0;
a=((a&858993459)<<2|(a&3435973836)>>>2)>>>0;
a=((a&252645135)<<4|(a&4042322160)>>>4)>>>0;
return(((a&16711935)<<8|(a&4278255360)>>>8)>>>0)/4294967296
}
//------------------ Compute and draw a set
function GenerateDataSet(func)
{
setPoints = []
setTarget = []
for(var i=0;i<50;i++)
{
x = i/50
y = HammersleyRand(i)
setPoints.push([[x], [y]])
setTarget.push([[func(x, y)]])
}
}
function DrawF()
{
x1 = -10; y1 = axis_a*x1+axis_b
x2 = 10; y2 = axis_a*x2+axis_b
gfx.DrawLine( x1,y1,x2,y2)
}
function DrawSetPoints(gfx, radius)
{
for(var i=0;i<setPoints.length;i++)
{
var x = setPoints[i][0];
var y = setPoints[i][1];
if (setTarget[i]==0)
{
gfx.DrawPlus(x,y,radius);
}
else
{
gfx.DrawCircle(x,y,radius);
}
}
}
//----------------------------------------------------
function Act(x)
{
return 1.0/(1.0+Math.exp(-x));
}
function DerAct(x)
{
return Act(x)*(1-Act(x));
}
function UpdateWeights(m1,m2, learningRate)
{
for(var i=0;i<m1.length;i++)
{
for(var j=0;j<m1[0].length;j++)
{
m1[i][j] += learningRate * m2[i][j];
}
}
}
//-------------------------------
// this helps taking care of the bias
function AddBiasOneT(vector)
{
return vector.concat([[1]]);
}
function DrawDecisionBoundary(gfx, tx,ty, size)
{
var canvasData = gfx.context.getImageData(0, 0, size, size);
for(var y=0;y<size;y++)
{
for(var x=0;x<size;x++)
{
var index = (x + y * size) * 4;
var xx = gfx.InvViewportX(x);
var yy = gfx.InvViewportY(y);
var o0 = AddBiasOneT([[xx],[yy]]);
var net1 = MulMat(wl_i1, o0);
var o1 = AddBiasOneT(funcMat(Act, net1));
var net2 = MulMat(wl_12, o1);
var o2 = funcMat(Act, net2);
v = o2[0][0]>.5?255:0;
canvasData.data[index + 0] = v;
canvasData.data[index + 1] = 255-v;
canvasData.data[index + 2] = 0;
canvasData.data[index + 3] = 128;
}
}
gfx.context.putImageData(canvasData, tx, ty);
}
//-------------------------------
var wl_i1 = RandomMat(2+1,4); //read from 3, ilayer is 4
var wl_12 = RandomMat(4+1,1);
var iterations = 0;
var oldFitness=1000;
var curFitness=1000;
function iterate()
{
var learningRate = 1;
var err;
var fitness=100;
var totalErr;
for(var j=0;j<10;j++)
{
totalErr = 0;
for(var i=0;i<setPoints.length;i++)
{
//forward pass
//
var o0 = AddBiasOneT(setPoints[i]);
var net1 = MulMat(wl_i1, o0);
var o1 = AddBiasOneT(funcMat(Act, net1));
var net2 = MulMat(wl_12, o1);
var o2 = funcMat(Act, net2);
//back propagate
//
// outer layer
var err = SubMat(o2, setTarget[i]);
var sp2 = SimpleMulMat(funcMat(DerAct, net2), err);
var e2 = MulMat(sp2, TransposeMat(o1));
// inner layer
var wsp2 = MulMat(TransposeMat(wl_12), sp2);
var sp1 = SimpleMulMat(funcMat(DerAct, net1), wsp2);
var e1 = MulMat(sp1, TransposeMat(o0));
//update weights
UpdateWeights(wl_12, e2, -learningRate);
UpdateWeights(wl_i1, e1, -learningRate);
totalErr += MulMat( err, TransposeMat(err))[0][0];
}
}
if (iterations%2==0)
{
DrawDecisionBoundary(gfxDB, 0,0,300)
gfxDB.DrawAxis()
DrawSetPoints(gfxDB,5);
}
if (iterations%1==0)
{
oldFitness = curFitness;
curFitness = totalErr;
gfxAE.context.beginPath();
gfxAE.context.strokeStyle="#ff0000";
gfxAE.moveTo((iterations-1)/100,oldFitness);
gfxAE.lineTo((iterations)/100,curFitness);
gfxAE.context.closePath();
gfxAE.context.stroke();
document.getElementById("text").innerHTML = "X axis, epochs: "+ iterations +"<br>Y axis, Error: " + curFitness + "<br>";
document.getElementById("text").innerHTML += " <br> "
}
iterations++;
}
function init()
{
var AbsoluteErrorCanvas = document.getElementById("AbsoluteError");
ctxAE = AbsoluteErrorCanvas.getContext('2d');
var DecisionBoundaryCanvas = document.getElementById("DecisionBoundaries");
ctxDB = DecisionBoundaryCanvas.getContext('2d');
ctxAE.clearRect(0,0,600,300);
gfxAE = new Graph(ctxAE, 10, 150-10, .5*150*.9);
gfxDB = new Graph(ctxDB, 15, 300-15, 300*.9);
ctxAE.clearRect(0,0,300,300);
setInterval(iterate,1);
RandomizeLinearF();
changeFunction(SinF);
}
function changeFunction(func)
{
gfxAE.context.clearRect(0,0,600,300);
gfxAE.DrawAxis();
iterations = 0;
wl_i1 = RandomMat(2+1,4); //read from 3, ilayer is 4
wl_12 = RandomMat(4+1,1);
GenerateDataSet(func);
}
</script>
<body onload="init()">
<a href="https://github.com/you"><img style="position: absolute; top: 0; right: 0; border: 0;" src="https://camo.githubusercontent.com/365986a132ccd6a44c23a9169022c0b5c890c387/68747470733a2f2f73332e616d617a6f6e6177732e636f6d2f6769746875622f726962626f6e732f666f726b6d655f72696768745f7265645f6161303030302e706e67" alt="Fork me on GitHub" data-canonical-src="https://s3.amazonaws.com/github/ribbons/forkme_right_red_aa0000.png"></a>
<!-- Primary Page Layout
-->
<div class="container">
<section class="header">
<h2 class="title">Neural network classifier.</h2>
<div class="row">
<div class="four columns">
<canvas id="DecisionBoundaries" class="u-max-full-width" width="300" height="300"></canvas>
</div>
<div class="eight columns">
<div>Network error:</div>
<canvas id="AbsoluteError" class="u-max-full-width" width="500" height="150"></canvas>
<div id="text"></div>
Distribution function:
<select id = "selColor" onchange = "changeFunction( [LinearF, SinF, DiscF][this.selectedIndex])">
<option >Linear</option>
<option selected="selected">Sin</option>
<option >Disc</option>
</select>
</div>
</div>
</section>
<!-- Intro -->
<div class="docs-section" id="intro">
<h4 class="docs-header">Intro</h4>
<p>This sample uses a 2x4x1 NN to classify points. </p>
<p>The network is traines using SGD(stochastic gradient descent). The point distribution can be changed using the drop down box.</p>
</div>
<div class="docs-section" id="intro">
<h4 class="docs-header">Contact/Questions</h4>
<p><my_github_account_username>[email protected]$ </p>
</div>
</div>
</body>
</html>