An example of a Multi Layer Perception (MLP) Artificial Neural Network (ANN) for reading handwritten numbers (OCR).
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February 13, 2017 23:07
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MLP Neural Network for O.C.R.
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<!DOCTYPE html> | |
<html> | |
<style> | |
body { | |
margin: 0; | |
font-family: Helvetica; | |
font-weight: 100; | |
} | |
svg { | |
shape-rendering: crispEdges; | |
cursor: pointer; | |
} | |
.controls { | |
position: absolute; | |
left: 410px; | |
top: 10px; | |
font-size: 20px; | |
} | |
</style> | |
<body> | |
<div class="controls"> | |
Draw a number (0 to 9) in the grid. Then see the neural networks guess below. <br /> | |
<button class="clear"> Clear </button> | |
<div>Guess <span class="prediction"> ?? </span> </div> | |
Confidence | |
<div class="confidences"> | |
</div> | |
</div> | |
<script src="http://d3js.org/d3.v3.min.js" charset="utf-8"></script> | |
<script> | |
'use strict' | |
// Create the grid the user will use to draw numbers. | |
var dim = 400, bN = 8, bD = dim / bN | |
var svg = d3.select('body').append('svg').attr({width: dim, height: dim}) | |
var data = d3.range(bN * bN).map(function(d) { | |
return { i: d % bN, j: Math.floor( d / bN ), id: d, active: 0 } | |
}) | |
var blocks = svg.append('g').attr('class', 'blocks') | |
.selectAll('rect').data(data).enter().append('rect') | |
.attr({width: bD, height: bD}) | |
.attr('x', function(d) { return bD * d.i }) | |
.attr('y', function(d) { return bD * d.j }) | |
.style('stroke', 'rgba(255, 255, 255, 0.2)') | |
function updateBlock(g) { | |
g.style('fill', function(d) { | |
return d.active ? 'rgba(255, 255, 255, 1)' : 'black' | |
}) | |
} | |
var conf = d3.select('.confidences').selectAll('div') | |
.data(d3.range(10)).enter() | |
.append('div').text(function(d) { return d + ': ' }) | |
var bar = conf.append('div').attr('class', 'bg') | |
.style({ | |
width: '60px', | |
height: '20px', | |
display: 'inline-block' | |
}) | |
bar.append('div').attr('class', 'fg') | |
.style({ | |
width: '20%', | |
height: '100%', | |
'background-color': 'rgba(0, 0, 0, 0.8)' | |
}) | |
svg.on('mousedown', function() { | |
svg.on('mousemove', function() { | |
var p = d3.mouse(this) | |
var i = Math.floor(p[0] / bD) | |
var j = Math.floor(p[1] / bD) | |
blocks.filter(function(d) { return d.i === i && d.j === j }) | |
.each(function(d) { d.active = 1 }) | |
.call(updateBlock) | |
updateStats() | |
}) | |
}).on('mouseup', function() { | |
svg.on('mousemove', null) | |
updateStats() | |
}) | |
function updateStats() { | |
var x = data.map(function(d) { return d.active }) | |
var max = -1, maxId = -1 | |
var res = net(x) | |
res.forEach(function(d, i) { if (d > max) max = d, maxId = i }) | |
console.log('maxId', maxId) | |
console.log('confidences', max) | |
conf.data(res).select('.fg') | |
.style('width', function(d) { return d3.round(d * 100, 2) + '%' }) | |
d3.select('.prediction').text(maxId) | |
d3.select('.confidence').text(max) | |
} | |
d3.select('button.clear').on('click', resetBlocks) | |
function resetBlocks() { | |
blocks.each(function(d) { d.active = 0 }).call(updateBlock) | |
} | |
// The MLP code. | |
// [-0.5, 0.5) | |
var rand = function() { return Math.random() - 0.5 } | |
// input layer -> [0, 63] or 8x8 image. | |
var iLen = 64 | |
// Let's have a single hidden layer with 25 nodes. | |
var hLen = 25 | |
// Matrix of hidden layer weights. The plus + 1 is for the input bias term. | |
var hW = d3.range(hLen).map(function() { return d3.range(iLen + 1).map(rand) }) | |
// We'll also have 10 output nodes, one for each digit [0, 9]. | |
var oLen = 10 | |
// Matrix of output layer weights. The plus + 1 is for the input bias term. | |
var oW = d3.range(oLen).map(function() { return d3.range(hLen + 1).map(rand) }) | |
// The sigmoid function. Our activation function. | |
function sig(x) { return 1 / (1 + Math.pow(Math.E, -x)) } | |
// The derivative of the sigmoid function. This function isn't actually used | |
// directly since we've already computed `sig` by the time we need `sig_prime`. | |
// We leave it here simply for reference. | |
function sig_prime(x) { return sig(x) * ( 1 - sig(x) ) } | |
function dot(a, b) { | |
var res = 0, l = a.length | |
for(var i = 0; i < l; i++) res = res + a[i] * b[i] | |
return res | |
} | |
// Perform a forward pass of the network. | |
function forward(x) { | |
// Calculate the hidden layer activations. | |
var hA = [] // Activations for each hidden layer node. | |
// For each hidden layer node... | |
for(var i = 0; i < hW.length; i++) { | |
// Calculate the activation. | |
hA[i] = sig(dot(x, hW[i]) + hW[i][iLen] /* bias weight */) | |
} | |
var oA = [] | |
// Calculate the output layer activations. | |
for(var i = 0; i < oW.length; i++) { | |
// Calculate the activation. | |
oA[i] = sig(dot(hA, oW[i]) + oW[i][hLen] /* bias weight */) | |
} | |
return { hA: hA, oA: oA } | |
} | |
// Update the weights by training the network. | |
function train(x, t, n) { | |
// The node activations. | |
var r = forward(x), hA = r.hA, oA = r.oA | |
// Deltas for the output nodes. | |
var oDel = [] | |
// For each output node... | |
for(var i = 0; i < oLen; i++) { | |
// Calculate the deltas from the errors. | |
oDel[i] = (t[i] - oA[i]) * oA[i] * (1 - oA[i]) | |
} | |
// Deltas for hidden layer. | |
var hDel = [] | |
// For each hidden layer node... | |
for(var i = 0; i < hLen; i++) { | |
hDel[i] = 0 | |
// For each output layer node... | |
// Collect all the deltas that fed out of this hidden layer node. | |
for(var j = 0; j < oLen; j++) hDel[i] += oDel[j] * oW[j][i] | |
hDel[i] = hDel[i] * hA[i] * ( 1 - hA[i] ) | |
} | |
// Update the weights. | |
// For each output node... | |
for(var i = 0; i < oLen; i++) { | |
for(var j = 0; j < hLen; j++) oW[i][j] += n * oDel[i] * hA[j] | |
oW[i][hLen] += n * oDel[i] // Bias. | |
} | |
for(var i = 0; i < hLen; i++) { | |
for(var j = 0; j < iLen; j++) hW[i][j] += n * hDel[i] * x[j] | |
hW[i][iLen] += n * hDel[i] // Bias. | |
} | |
} | |
function net(x) { return forward(x).oA } | |
d3.text('training-data.csv', function(err, data) { | |
if (err) throw err | |
var ts, te, idx | |
data = d3.csv.parseRows(data, function(row) { return row.map(Number) }) | |
.map(function(d) { | |
// Expected output. | |
var t = d3.range(10).map(function() { return 0 }) | |
t[d[0]] = 1 | |
return { x: d.slice(1), t: t, label: d[0] } | |
}) | |
ts = Date.now() | |
for(var i = 0; i < 1e4; i++) { | |
idx = i % data.length | |
train(data[idx].x, data[idx].t, 0.1) | |
} | |
te = Date.now() | |
console.log('time to train', te - ts) | |
}) | |
</script> | |
</body> | |
</html> |
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0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | |
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3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | |
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7 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
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9 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | |
0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | |
1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | |
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