<?php
/**
* file: class.BackPropagationScale.php
*
* Using artificial intelligence and NN (neuronal networks)
* to solve the multiplication table problem.
*
* It uses a technique called back propagation, that is
* the network learns by calculating the errors going
* backwards: from the output, through the first hidden layers.
*
* The learning unit is called the perceptron: a neuron capable
* of learning, connected to layers and adjusting the weights.
*
* Data needs to be scaled/unscaled to adjust the values common to
* the neural network
*
* Free for educational purposes
* Copyright © 2010
*
* @author freedelta ( http://freedelta.free.fr )
*/
error_reporting(E_ERROR);
define("_RAND_MAX",32767);
define("HI",0.9);
define("LO",0.1);
class BackPropagationScale
{
/* Output of each neuron */
public $output=null;
/* Last calcualted output value */
public $vectorOutput=null;
/* delta error value for each neuron */
public $delta=null;
/* Array of weights for each neuron */
public $weight=null;
/* Num of layers in the net, including input layer */
public $numLayers=null;
/* Array num elments containing size for each layer */
public $layersSize=null;
/* Learning rate */
public $beta=null;
/* Momentum */
public $alpha=null;
/* Storage for weight-change made in previous epoch (three-dimensional array) */
public $prevDwt=null;
/* Data */
public $data=null;
/* Test Data */
public $testData=null;
/* N lines of Data */
public $NumPattern=null;
/* N columns in Data */
public $NumInput=null;
/* Minimum value in data set */
public $minX=0;
/* Maximum value in data set */
public $maxX=1;
/* Stores ann scale calculated parameters */
public $normalizeMax=null;
public $normalizeMin=null;
/* Holds all output data in one array */
public $output_vector=null;
public function __construct($numLayers,$layersSize,$beta,$alpha,$minX,$maxX)
{
$this->alpha=$alpha;
$this->beta=$beta;
$this->minX=$minX;
$this->maxX=$maxX;
// Set no of layers and their sizes
$this->numLayers=$numLayers;
$this->layersSize=$layersSize;
// seed and assign random weights
for($i=1;$i<$this->numLayers;$i++)
{
for($j=0;$j<$this->layersSize[$i];$j++)
{
for($k=0;$k<$this->layersSize[$i-1]+1;$k++)
{
$this->weight[$i][$j][$k]=$this->rando();
}
// bias in the last neuron
$this->weight[$i][$j][$this->layersSize[$i-1]]=-1;
}
}
// initialize previous weights to 0 for first iteration
for($i=1;$i<$this->numLayers;$i++)
{
for($j=0;$j<$this->layersSize[$i];$j++)
{
for($k=0;$k<$this->layersSize[$i-1]+1;$k++)
{
$this->prevDwt[$i][$j][$k]=(double)0.0;
}
}
}
}
public function rando()
{
$randValue = LO + (HI - LO) * mt_rand(0, _RAND_MAX)/_RAND_MAX;
return $randValue;//32767
}
/* --- sigmoid function */
public function sigmoid($inputSource)
{
return (double)(1.0 / (1.0 + exp(-$inputSource)));
}
/* --- mean square error */
public function mse($target)
{
$mse=0;
for($i=0;$i<$this->layersSize[$this->numLayers-1];$i++)
{
$mse+=($target-$this->output[$this->numLayers-1][$i])*($target-$this->output[$this->numLayers-1][$i]);
}
return $mse/2;
}
/* --- returns i'th outputput of the net */
public function Out($i)
{
return $this->output[$this->numLayers-1][$i];
}
/* ---
* Feed forward one set of input
* to update the output values for each neuron. This function takes the input
* to the net and finds the output of each neuron
*/
public function ffwd($inputSource)
{
$sum=0.0;
$numElem=count($inputSource);
// assign content to input layer
for($i=0;$i<$numElem;$i++)
{
$this->output[0][$i]=$inputSource[$i]; // outputput_from_neuron(i,j) Jth neuron in Ith Layer
}
// assign output (activation) value to each neuron usng sigmoid func
for($i=1;$i<$this->numLayers;$i++) // For each layer
{
for($j=0;$j<$this->layersSize[$i];$j++) // For each neuron in current layer
{
$sum=0.0;
for($k=0;$k<$this->layersSize[$i-1];$k++) // For each input from each neuron in preceeding layer
{
$sum+=$this->output[$i-1][$k]*$this->weight[$i][$j][$k]; // Apply weight to inputs and add to sum
}
// Apply bias
$sum+=$this->weight[$i][$j][$this->layersSize[$i-1]];
// Apply sigmoid function
$this->output[$i][$j]=$this->sigmoid($sum);
}
}
}
/* --- Backpropagate errors from outputput layer back till the first hidden layer */
public function bpgt($inputSource,$target)
{
/* --- Update the output values for each neuron */
$this->ffwd($inputSource);
///////////////////////////////////////////////
/// FIND DELTA FOR OUPUT LAYER (Last Layer) ///
///////////////////////////////////////////////
for($i=0;$i<$this->layersSize[$this->numLayers-1];$i++)
{
$this->delta[$this->numLayers-1][$i]=$this->output[$this->numLayers-1][$i]*(1-$this->output[$this->numLayers-1][$i])*($target-$this->output[$this->numLayers-1][$i]);
}
/////////////////////////////////////////////////////////////////////////////////////////////
/// FIND DELTA FOR HIDDEN LAYERS (From Last Hidden Layer BACKWARDS To First Hidden Layer) ///
/////////////////////////////////////////////////////////////////////////////////////////////
for($i=$this->numLayers-2;$i>0;$i--)
{
for($j=0;$j<$this->layersSize[$i];$j++)
{
$sum=0.0;
for($k=0;$k<$this->layersSize[$i+1];$k++)
{
$sum+=$this->delta[$i+1][$k]*$this->weight[$i+1][$k][$j];
}
$this->delta[$i][$j]=$this->output[$i][$j]*(1-$this->output[$i][$j])*$sum;
}
}
////////////////////////
/// MOMENTUM (Alpha) ///
////////////////////////
for($i=1;$i<$this->numLayers;$i++)
{
for($j=0;$j<$this->layersSize[$i];$j++)
{
for($k=0;$k<$this->layersSize[$i-1];$k++)
{
$this->weight[$i][$j][$k]+=$this->alpha*$this->prevDwt[$i][$j][$k];
}
$this->weight[$i][$j][$this->layersSize[$i-1]]+=$this->alpha*$this->prevDwt[$i][$j][$this->layersSize[$i-1]];
}
}
///////////////////////////////////////////////
/// ADJUST WEIGHTS (Using Steepest Descent) ///
///////////////////////////////////////////////
for($i=1;$i<$this->numLayers;$i++)
{
for($j=0;$j<$this->layersSize[$i];$j++)
{
for($k=0;$k<$this->layersSize[$i-1];$k++)
{
$this->prevDwt[$i][$j][$k]=$this->beta*$this->delta[$i][$j]*$this->output[$i-1][$k];
$this->weight[$i][$j][$k]+=$this->prevDwt[$i][$j][$k];
}
/* --- Apply the corrections */
$this->prevDwt[$i][$j][$this->layersSize[$i-1]]=$this->beta*$this->delta[$i][$j];
$this->weight[$i][$j][$this->layersSize[$i-1]]+=$this->prevDwt[$i][$j][$this->layersSize[$i-1]];
}
}
}
///////////////////////////////
/// SCALING FUNCTIONS BLOCK ///
///////////////////////////////
/* --- Set scaling parameters */
public function setScaleOutput($data)
{
$oldMin=$data[0][0];
$oldMax=$oldMin;
$numElem=count($data[0]);
/* --- First calcualte minimum and maximum */
for($i=0;$i<$this->NumPattern;$i++)
{
$oldMin=$data[$i][0];
$oldMax=$oldMin;
for($j=1;$j<$numElem;$j++)
{
// Min
if($oldMin > $data[$i][$j])
{
$oldMin=$data[$i][$j];
}
// Max
if($oldMax < $data[$i][$j])
{
$oldMax=$data[$i][$j];
}
}
$this->normalizeMin[$i]=$oldMin;
$this->normalizeMax[$i]=$oldMax;
}
}
/* --- Scale input data to range before feeding it to the network */
/*
x - Min
t = (HI -LO) * (---------) + LO
Max-Min
*/
public function scale($data)
{
$this->setScaleOutput($data);
$numElem=count($data[0]);
$temp=0.0;
for( $i=0; $i < $this->NumPattern; $i++ )
{
for($j=0;$j<$numElem;$j++)
{
$temp=(HI-LO)*(($data[$i][$j] - $this->normalizeMin[$i]) / ($this->normalizeMax[$i] - $this->normalizeMin[$i])) + LO;
$data[$i][$j]=$temp;
}
}
return $data;
}
/* --- Unscale output data to original range */
/*
x - LO
t = (Max-Min) * (---------) + Min
HI-LO
*/
public function unscaleOutput($output_vector)
{
$temp=0.0;
for( $i=0; $i < $this->NumPattern; $i++ )
{
$temp=($this->normalizeMax[$i]-$this->normalizeMin[$i]) * (($output_vector[$i] - LO) / (HI-LO)) + $this->normalizeMin[$i] ;
$unscaledVector[$i] =$temp;
}
return $unscaledVector;
}
public function Run($dataX,$testDataX)
{
/* --- Threshhold - thresh (value of target mse, training stops once it is achieved) */
$Thresh = 0.00001;
$numEpoch = 200000;
$MSE=0.0;
$this->NumPattern=count($dataX);
$this->NumInput=count($dataX[0]);
/* --- Pre-process data: Scale input and test values */
$data=$this->scale($dataX);
/* --- Test data=(data-1 column) */
for($i=0;$i<$this->NumPattern;$i++)
{
for($j=0;$j<$this->NumInput-1;$j++)
{
$testData[$i][$j]=$data[$i][$j];
}
}
/* --- Start training: looping through epochs and exit when MSE error < Threshold */
echo "\nNow training the network....";
for($e=0;$e<$numEpoch;$e++)
{
/* -- Backpropagate */
$this->bpgt($data[$e%$this->NumPattern],$data[$e%$this->NumPattern][$this->NumInput-1]);
$MSE=$this->mse($data[$e%$this->NumPattern][$this->NumInput-1]);
if($e==0)
{
echo "\nFirst epoch Mean Square Error: $MSE";
}
if( $MSE < $Thresh)
{
echo "\nNetwork Trained. Threshold value achieved in ".$e." iterations.";
echo "\nMSE: ".$MSE;
break;
}
}
echo "\nLast epoch Mean Square Error: $MSE";
echo "\nNow using the trained network to make predictions on test data....\n";
for ($i = 0 ; $i < $this->NumPattern; $i++ )
{
$this->ffwd($testData[$i]);
$this->vectorOutput[]=(double)$this->Out(0);
}
$out=$this->unscaleOutput($this->vectorOutput);
for($col=1;$col<$this->NumInput;$col++)
{
echo "Input$col\t";
}
echo "Predicted \n";
for ($i = 0 ; $i < $this->NumPattern; $i++ )
{
for($j=0;$j<$this->NumInput-1;$j++)
{
echo " ".$testDataX[$i][$j]." \t\t";
}
echo " " .abs($out[$i])."\n";
}
}
}
/* --- Sample use */
// Mutliplication data: 1 x 1 = 1, 1 x 2 = 2,.. etc
$data=array(0=>array(1,1,1),
1=>array(1,2,2),
2=>array(1,3,3),
3=>array(1,4,4),
4=>array(1,5,5),
5=>array(2,1,2),
6=>array(2,2,4),
7=>array(2,3,6),
8=>array(2,4,8),
9=>array(2,5,10),
10=>array(3,1,3),
11=>array(3,2,6),
12=>array(3,3,9),
13=>array(3,4,12),
14=>array(3,5,15),
15=>array(4,1,4),
16=>array(4,2,8),
17=>array(4,3,12),
18=>array(4,4,16),
19=>array(4,5,20),
20=>array(5,1,5),
21=>array(5,2,10),
22=>array(5,3,15),
23=>array(5,4,20),
24=>array(5,5,25)
);
// 1 x 1 =?
$testData=array(0=>array(1,1),
1=>array(1,2),
2=>array(1,3),
3=>array(1,4),
4=>array(1,5),
5=>array(2,1),
6=>array(2,2),
7=>array(2,3),
8=>array(2,4),
9=>array(2,5),
10=>array(3,1),
11=>array(3,2),
12=>array(3,3),
13=>array(3,4),
14=>array(3,5),
15=>array(4,1),
16=>array(4,2),
17=>array(4,3),
18=>array(4,4),
19=>array(4,5),
20=>array(5,1),
21=>array(5,2),
22=>array(5,3),
23=>array(5,4),
24=>array(5,5)
);
$layersSize=array(3,2,1);
$numLayers = count($layersSize);
// Learing rate - beta
// momentum - alpha
$beta = 0.3;
$alpha = 0.1;
$minX=1;
$maxX=25;
// Creating the net
$bp=new BackPropagationScale($numLayers,$layersSize,$beta,$alpha,$minX,$maxX);
$bp->Run($data,$testData);
?>
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