工神经网络（ANN）是用于人工智能的算法来模拟人类的思维。该网络的工作方式类似于人的大脑，它是由神经元彼此沟通，并提供有价值的产出。虽然只是一个模型 – 甚至还没有接近人类的思维 – 人工神经网络已经被用于预测，分类和决策支持系统，以及光学字符识别和许多其他应用程序中。
人工神经网络的发展主要集中在高层次的编程语言，如C或C + +，但你也可以在PHP 中实现神经网络，这也许是在Web应用程序中使用人工智能最方便的方式。在这篇文章中，我将解释如何建立一个最常见的神经网络拓扑结构，多层次的感知，并通过使用一个PHP神经网络类在PHP中创建第一个神经网络。
类似人类思维过程，神经网络：
接收一些（数据）输入分析，并处理它
提供输出值（即，计算的结果）
这就是为什么在这个例子中拓扑结构有三层（多层感知）：
输入层
隐藏层
输出层
根据您的需要，每一层都有一个特定的神经元数量。每一个神经元将被连接到下一层中所有神经元。神经元通过调整输出（即它们之间的权重系数）处理给定的任务。当然，它们可以应用到实际使用的情况下之前，神经网络往往需要去学习任务。但是，之前的一切，你要准备好你的数据网络。
在PHP中输入神经网络 – 准备数据
由于神经网络是复杂的数学模型，你可以不发送任何数据类型到输入神经元。之前的网络必须将数据标准化才可以使用它。这意味着，数据应被缩放到-1到1的范围内。不幸的是，在PHP中没有正常化函数，所以你必须自己做，但是可以我给你的公式：
I = Imin + (Imax-Imin)*(D-Dmin)/(Dmax-Dmin)
Imin 和 Imax代表的是神经网络的范围内（-1至1），Dmin和Dmax是数据的最小值和最大值。
正常处理数据后，你必须选择输入神经元的数量。例如，如果你有RGB颜色，你要确定红色或蓝色是主色，你将有4个输入神经元（红，绿，蓝值是神经元，第四个是偏见 – 通常等于1 ）。下面是这样计算的PHP代码：
<?php
require_once``(``"class_neuralnetwork.php"``);
$n = ``new``NeuralNetwork(4, 4, 1); ``// the number of neurons in each layer of the network -- 4 input, 4 hidden and 1 output neurons
$n``->setVerbose(false); ``// do not display error messages
//test data
// First array is input data, and the second is the expected output value (1 means blue and 0 means red)
$n``->addTestData( ``array (0, 0, 255, 1), ``array (1));
$n``->addTestData( ``array (0, 0, 192, 1), ``array (1));
$n``->addTestData( ``array (208, 0, 49, 1), ``array (0));
$n``->addTestData( ``array ( 228, 105, 116, 1), ``array (0));
$n``->addTestData( ``array (128, 80, 255, 1), ``array (1));
$n``->addTestData( ``array ( 248, 80, 68, 1), ``array (0));
?>
只有一个输出神经元，因为你只有两种可能性结果。对于更复杂的问题，你可以使用一个以上的神经元网络输出，因此有许多的0和1作为可能的输出组合。
在PHP中训练神经网络
在能够解决问题之前，人工神经网络需要学习如何解决它，想像这个网络为一个公式。您已添加测试数据和预期的输出，并且该网络具有通过寻找输入和输出之间的连接来求解方程。这个过程被称为训练。在神经网络中，这些连接是神经元的权重。这几个算法可用于网络的训练，但反向传播算法是最常用的。BP算法实际上是指向后传播的错误。
初始化随机网络中的权重后，接下来的步骤是：
通过测试数据循环
1.计算实际输出
2.计算误差（所需的输出 – 当前网络输出）
3.向后计算增量的权重
4.更新权重
该过程继续进行，直到所有的测试数据已被正确地分类或算法已经达到停止标准。一般程序员试图使用最多三次的网络，而训练弹（时期）的最大数目为1000。另外，每个学习算法需要的激活功能。反向传播算法，激活函数是双曲正切（双曲正切）
让我们来看看如何在PHP中训练一个神经网络：
<?php
$max = 3;
// train the network in max 1000 epochs, with a max squared error of 0.01
while (!(``$success``=``$n``->train(1000, 0.01)) && ``$max``-->0) {
// training failed -- re-initialize the network weights
$n``->initWeights();
}
//training successful
if (``$success``) {
$epochs = ``$n``->getEpoch(); ``// get the number of epochs needed for training
}
?>
平均平方误差（mse）的错误，也被称为标准偏差的平方的平均值。默认的平均平方误差值通常为0.01，如果小于0.01，这意味着平均平方误差训练成功。
在来看下在PHP中工作的人工神经网络例子，这其实是一种很好的做法，可以节省您的神经网络文件或SQL数据库。如果你不保存它，你将不得不每次培训人来执行你的应用。简单的任务是很容易学的，但训练是一个更复杂的问题，需要更长的时间，你希望你的用户尽量少等待， 幸运的是，在这个PHP类例子中有保存和加载功能：
<?php
$n``->save(``'my_network.ini'``);
?>
请注意，文件扩展名必须是 .ini.
关于我们神经网络的PHP代码
让我们来看看在正在运行的应用程序中接收红，绿，蓝的值，并计算是否是蓝色或红色占主导地位的的PHP代码：
<?php
require_once``(``"class_neuralnetwork.php"``);
$r = ``$_POST``[``'red'``];
$g = ``$_POST``[``'green'``];
$b = ``$_POST``[``'blue'``];
$n = ``new NeuralNetwork(4, 4, 1); ``//initialize the neural network
$n``->setVerbose(false);
$n``->load(``'my_network.ini'``); ``// load the saved weights into the initialized neural network. This way you won't need to train the network each time the application has been executed
$input``= ``array``(normalize(``$r``),normalize(``$g``),normalize(``$b``)); ``//note that you will have to write a normalize function, depending on your needs
$result = ``$n``->calculate(``$input``);
If(``$result``>0.5) {
// the dominant color is blue
}
else {
// the dominant color is red
}
?>
神经网络的限制
神经网络的主要限制是，它们只能解决线性可分的问题，很多问题不是线性可分。因此，非线性可分问题需要另一种人工智能算法。然而，神经网络可以解决很多的问题，需要计算机智能赚取的人工智能算法中占有重要地位。
附class_neuralnetwork.php :
<?php
/**
* <b>Multi-layer Neural Network in PHP</b>
*
* Loosely based on source code by {@link [http://www.philbrierley.com](http://www.philbrierley.com) Phil Brierley},
* that was translated into PHP by ‘dspink’ in sep 2005
*
* Algorithm was obtained from the excellent introductory book
* “{@link [http://www.amazon.com/link/dp/0321204662](http://www.amazon.com/link/dp/0321204662) Artificial Intelligence – a guide to intelligent systems}”
* by Michael Negnevitsky (ISBN 0-201-71159-1)
*
* <b>Example: learning the ‘XOR’-function</b>
* <code>
* require_once(“class_neuralnetwork.php”);
*
* // Create a new neural network with 3 input neurons,
* // 4 hidden neurons, and 1 output neuron
* $n = new NeuralNetwork(3, 4, 1);
* $n->setVerbose(false);
*
* // Add test-data to the network. In this case,
* // we want the network to learn the ‘XOR’-function.
* // The third input-parameter is the ‘bias’.
* $n->addTestData( array (-1, -1, 1), array (-1));
* $n->addTestData( array (-1, 1, 1), array ( 1));
* $n->addTestData( array ( 1, -1, 1), array ( 1));
* $n->addTestData( array ( 1, 1, 1), array (-1));
*
* // we try training the network for at most $max times
* $max = 3;
*
* // train the network in max 1000 epochs, with a max squared error of 0.01
* while (!($success=$n->train(1000, 0.01)) && $max–>0) {
* // training failed:
* // 1\. re-initialize the weights in the network
* $n->initWeights();
*
* // 2\. display message
* echo “Nothing found…<hr />”;
* }
*
* // print a message if the network was succesfully trained
* if ($success) {
* $epochs = $n->getEpoch();
* echo “Success in $epochs training rounds!<hr />”;
* }
*
* // in any case, we print the output of the neural network
* for ($i = 0; $i < count($n->trainInputs); $i ++) {
* $output = $n->calculate($n->trainInputs[$i]);
* print “<br />Testset $i; “;
* print “expected output = (“.implode(“, “, $n->trainOutput[$i]).”) “;
* print “output from neural network = (“.implode(“, “, $output).”)n”;
* }
* </code>
*
* The resulting output could for example be something along the following lines:
*
* <code>
* Success in 719 training rounds!
* Testset 0; expected output = (-1) output from neural network = (-0.986415991978)
* Testset 1; expected output = (1) output from neural network = (0.992121412998)
* Testset 2; expected output = (1) output from neural network = (0.992469534962)
* Testset 3; expected output = (-1) output from neural network = (-0.990224120384)
* </code>
*
* …which indicates the network has learned the task.
*
* @author ir. E. Akerboom
* @author {@link [http://www.tremani.nl/](http://www.tremani.nl/) Tremani}, {@link [http://maps.google.com/maps?f=q&hl=en&q=delft%2C+the+netherlands&ie=UTF8&t=k&om=1&ll=53.014783%2C4.921875&spn=36.882665%2C110.566406&z=4](http://maps.google.com/maps?f=q&hl=en&q=delft%2C+the+netherlands&ie=UTF8&t=k&om=1&ll=53.014783%2C4.921875&spn=36.882665%2C110.566406&z=4) Delft}, The Netherlands
* @since feb 2007
* @version 1.0
* @license [http://opensource.org/licenses/bsd-license.php](http://opensource.org/licenses/bsd-license.php) BSD License
*/
class NeuralNetwork {
/**#@+
* @access private
*/
var $nodecount = array ();
var $nodevalue = array ();
var $nodethreshold = array ();
var $edgeweight = array ();
var $learningrate = array (0.1);
var $layercount = 0;
var $previous_weightcorrection = array ();
var $momentum = 0.8;
var $is_verbose = true;
var $trainInputs = array ();
var $trainOutput = array ();
var $trainDataID = array ();
var $controlInputs = array ();
var $controlOutput = array ();
var $controlDataID = array ();
var $weightsInitialized = false;
var $epoch;
var $error_trainingset;
var $error_controlset;
var $success;
/**#@-*/
/**
* Creates a neural network.
*
* Example:
* <code>
* // create a network with 4 input nodes, 10 hidden nodes, and 4 output nodes
* $n = new NeuralNetwork(4, 10, 4);
*
* // create a network with 4 input nodes, 1 hidden layer with 10 nodes,
* // another hidden layer with 10 nodes, and 4 output nodes
* $n = new NeuralNetwork(4, 10, 10, 4);
*
* // alternative syntax
* $n = new NeuralNetwork(array(4, 10, 10, 4));
* </code>
*
* @param array $nodecount The number of nodes in the consecutive layers.
*/
function NeuralNetwork($nodecount) {
if (!is_array($nodecount)) {
$nodecount = func_get_args();
}
$this->nodecount = $nodecount;
// store the number of layers
$this->layercount = count($this->nodecount);
}
/**
* Sets the learning rate between the different layers.
*
* @param array $learningrate An array containing the learning rates [range 0.0 – 1.0].
* The size of this array is ‘layercount – 1′. You might also provide a single number. If that is
* the case, then this will be the learning rate for the whole network.
*/
function setLearningRate($learningrate) {
if (!is_array($learningrate)) {
$learningrate = func_get_args();
}
$this->learningrate = $learningrate;
}
/**
* Gets the learning rate for a specific layer
*
* @param int $layer The layer to obtain the learning rate for
* @return float The learning rate for that layer
*/
function getLearningRate($layer) {
if (array_key_exists($layer, $this->learningrate)) {
return $this->learningrate[$layer];
}
return $this->learningrate[0];
}
/**
* Sets the ‘momentum’ for the learning algorithm. The momentum should
* accelerate the learning process and help avoid local minima.
*
* @param float $momentum The momentum. Must be between 0.0 and 1.0; Usually between 0.5 and 0.9
*/
function setMomentum($momentum) {
$this->momentum = $momentum;
}
/**
* Gets the momentum.
*
* @return float The momentum
*/
function getMomentum() {
return $this->momentum;
}
/**
* Calculate the output of the neural network for a given input vector
*
* @param array $input The vector to calculate
* @return mixed The output of the network
*/
function calculate($input) {
// put the input vector on the input nodes
foreach ($input as $index => $value) {
$this->nodevalue[0][$index] = $value;
}
// iterate the hidden layers
for ($layer = 1; $layer < $this->layercount; $layer ++) {
$prev_layer = $layer -1;
// iterate each node in this layer
for ($node = 0; $node < ($this->nodecount[$layer]); $node ++) {
$node_value = 0.0;
// each node in the previous layer has a connection to this node
// on basis of this, calculate this node’s value
for ($prev_node = 0; $prev_node < ($this->nodecount[$prev_layer]); $prev_node ++) {
$inputnode_value = $this->nodevalue[$prev_layer][$prev_node];
$edge_weight = $this->edgeweight[$prev_layer][$prev_node][$node];
$node_value = $node_value + ($inputnode_value * $edge_weight);
}
// apply the threshold
$node_value = $node_value – $this->nodethreshold[$layer][$node];
// apply the activation function
$node_value = $this->activation($node_value);
// remember the outcome
$this->nodevalue[$layer][$node] = $node_value;
}
}
// return the values of the last layer (the output layer)
return $this->nodevalue[$this->layercount – 1];
}
/**
* Implements the standard (default) activation function for backpropagation networks,
* the ‘tanh’ activation function.
*
* @param float $value The preliminary output to apply this function to
* @return float The final output of the node
*/
function activation($value) {
return tanh($value);
// return (1.0 / (1.0 + exp(- $value)));
}
/**
* Implements the derivative of the activation function. By default, this is the
* inverse of the ‘tanh’ activation function: 1.0 – tanh($value)*tanh($value);
*
* @param float $value ‘X’
* @return $float
*/
function derivative_activation($value) {
$tanh = tanh($value);
return 1.0 – $tanh * $tanh;
//return $value * (1.0 – $value);
}
/**
* Add a test vector and its output
*
* @param array $input An input vector
* @param array $output The corresponding output
* @param int $id (optional) An identifier for this piece of data
*/
function addTestData($input, $output, $id = null) {
$index = count($this->trainInputs);
foreach ($input as $node => $value) {
$this->trainInputs[$index][$node] = $value;
}
foreach ($output as $node => $value) {
$this->trainOutput[$index][$node] = $value;
}
$this->trainDataID[$index] = $id;
}
/**
* Returns the identifiers of the data used to train the network (if available)
*
* @return array An array of identifiers
*/
function getTestDataIDs() {
return $this->trainDataID;
}
/**
* Add a set of control data to the network.
*
* This set of data is used to prevent ‘overlearning’ of the network. The
* network will stop training if the results obtained for the control data
* are worsening.
*
* The data added as control data is not used for training.
*
* @param array $input An input vector
* @param array $output The corresponding output
* @param int $id (optional) An identifier for this piece of data
*/
function addControlData($input, $output, $id = null) {
$index = count($this->controlInputs);
foreach ($input as $node => $value) {
$this->controlInputs[$index][$node] = $value;
}
foreach ($output as $node => $value) {
$this->controlOutput[$index][$node] = $value;
}
$this->controlDataID[$index] = $id;
}
/**
* Returns the identifiers of the control data used during the training
* of the network (if available)
*
* @return array An array of identifiers
*/
function getControlDataIDs() {
return $this->controlDataID;
}
/**
* Shows the current weights and thresholds
*
* @param boolean $force Force the output, even if the network is {@link setVerbose() not verbose}.
*/
function showWeights($force = false) {
if ($this->isVerbose() || $force) {
echo “<hr>”;
echo “<br />Weights: <pre>”.serialize($this->edgeweight).”</pre>”;
echo “<br />Thresholds: <pre>”.serialize($this->nodethreshold).”</pre>”;
}
}
/**
* Determines if the neural network displays status and error messages. By default, it does.
*
* @param boolean $is_verbose ‘true’ if you want to display status and error messages, ‘false’ if you don’t
*/
function setVerbose($is_verbose) {
$this->is_verbose = $is_verbose;
}
/**
* Returns whether or not the network displays status and error messages.
*
* @return boolean ‘true’ if status and error messages are displayed, ‘false’ otherwise
*/
function isVerbose() {
return $this->is_verbose;
}
/**
* Loads a neural network from a file saved by the ‘save()’ function. Clears
* the training and control data added so far.
*
* @param string $filename The filename to load the network from
* @return boolean ‘true’ on success, ‘false’ otherwise
*/
function load($filename) {
if (file_exists($filename)) {
$data = parse_ini_file($filename);
if (array_key_exists(“edges”, $data) && array_key_exists(“thresholds”, $data)) {
// make sure all standard preparations performed
$this->initWeights();
// load data from file
$this->edgeweight = unserialize($data[‘edges’]);
$this->nodethreshold = unserialize($data[‘thresholds’]);
$this->weightsInitialized = true;
// load IDs of training and control set
if (array_key_exists(“training_data”, $data) && array_key_exists(“control_data”, $data)) {
// load the IDs
$this->trainDataID = unserialize($data[‘training_data’]);
$this->controlDataID = unserialize($data[‘control_data’]);
// if we do not reset the training and control data here, then we end up
// with a bunch of IDs that do not refer to the actual data we’re training
// the network with.
$this->controlInputs = array ();
$this->controlOutput = array ();
$this->trainInputs = array ();
$this->trainOutput = array ();
}
return true;
}
}
<iframe id="iframeu2288174_0" name="iframeu2288174_0" src="https://pos.baidu.com/acpm?conwid=468&conhei=60&rdid=2288174&dc=3&di=u2288174&dri=0&dis=0&dai=2&ps=10678x393&enu=encoding&dcb=___adblockplus&dtm=HTML_POST&dvi=0.0&dci=-1&dpt=none&tsr=0&tpr=1516673778004&ti=PHP%E7%A5%9E%E7%BB%8F%E7%BD%91%E7%BB%9C%20%7C%20%E9%99%88%E9%B9%8F%E4%B8%AA%E4%BA%BA%E5%8D%9A%E5%AE%A2&ari=2&dbv=2&drs=1&pcs=1887x955&pss=1887x10729&cfv=0&cpl=4&chi=1&cce=true&cec=UTF-8&tlm=1516673778&prot=2&rw=955&ltu=file%3A%2F%2F%2FC%3A%2FUsers%2Fn%2FAppData%2FLocal%2FTemp%2FWeiyunDisk%2Ftencent_weiyun_open_file_temp%2F%257BBBC9F2F2-5890-493B-81C9-4471E78E6909%257D%2FPHP%25E7%25A5%259E%25E7%25BB%258F%25E7%25BD%2591%25E7%25BB%259C.html&ecd=1&uc=1920x1040&pis=-1x-1&sr=1920x1080&tcn=1516673778&qn=93c7ca2aac11bc8b&tt=1516673777759.428.634.634" width="468" height="60" align="center,center" vspace="0" hspace="0" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" allowtransparency="true" style="box-sizing: border-box; max-width: 100%; border: 0px; vertical-align: bottom; margin: 0px; width: 468px; height: 60px;"></iframe>
return false;
}
/**
* Saves a neural network to a file
*
* @param string $filename The filename to save the neural network to
* @return boolean ‘true’ on success, ‘false’ otherwise
*/
function save($filename) {
$f = fopen($filename, “w”);
if ($f) {
fwrite($f, “[weights]”);
fwrite($f, “rnedges = “”.serialize($this->edgeweight).”””);
fwrite($f, “rnthresholds = “”.serialize($this->nodethreshold).”””);
fwrite($f, “rn”);
fwrite($f, “[identifiers]”);
fwrite($f, “rntraining_data = “”.serialize($this->trainDataID).”””);
fwrite($f, “rncontrol_data = “”.serialize($this->controlDataID).”””);
fclose($f);
return true;
}
return false;
}
/**
* Start the training process
*
* @param int $maxEpochs The maximum number of epochs
* @param float $maxError The maximum squared error in the training data
* @return bool ‘true’ if the training was successful, ‘false’ otherwise
*/
function train($maxEpochs = 500, $maxError = 0.01) {
if (!$this->weightsInitialized) {
$this->initWeights();
}
if ($this->isVerbose()) {
echo “<table>”;
echo “<tr><th>#</th><th>error(trainingdata)</th><th>error(controldata)</th><th>slope(error(controldata))</th></tr>”;
}
$epoch = 0;
$errorControlSet = array ();
$avgErrorControlSet = array ();
define(‘SAMPLE_COUNT’, 10);
do {
// echo “<tr><td colspan=10><b>epoch $epoch</b></td></tr>”;
for ($i = 0; $i < count($this->trainInputs); $i ++) {
// select a training pattern at random
$index = mt_rand(0, count($this->trainInputs) – 1);
// determine the input, and the desired output
$input = $this->trainInputs[$index];
$desired_output = $this->trainOutput[$index];
// calculate the actual output
$output = $this->calculate($input);
// echo “<tr><td></td><td>Training set $i</td><td>input = (” . implode(“, “, $input) . “)</td>”;
// echo “<td>desired = (” . implode(“, “, $desired_output) . “)</td>”;
// echo “<td>output = (” . implode(“, “, $output) .”)</td></tr>”;
// change network weights
$this->backpropagate($output, $desired_output);
}
// buy some time
set_time_limit(300);
//display the overall network error after each epoch
$squaredError = $this->squaredErrorEpoch();
if ($epoch % 2 == 0) {
$squaredErrorControlSet = $this->squaredErrorControlSet();
$errorControlSet[] = $squaredErrorControlSet;
if (count($errorControlSet) > SAMPLE_COUNT) {
$avgErrorControlSet[] = array_sum(array_slice($errorControlSet, -SAMPLE_COUNT)) / SAMPLE_COUNT;
}
list ($slope, $offset) = $this->fitLine($avgErrorControlSet);
$controlset_msg = $squaredErrorControlSet;
} else {
$controlset_msg = “”;
}
if ($this->isVerbose()) {
echo “<tr><td><b>$epoch</b></td><td>$squaredError</td><td>$controlset_msg”;
echo “<script type=’text/javascript’>window.scrollBy(0,100);</script>”;
echo “</td><td>$slope</td></tr>”;
echo “</td></tr>”;
flush();
ob_flush();
}
// conditions for a ‘successful’ stop:
// 1\. the squared error is now lower than the provided maximum error
$stop_1 = $squaredError <= $maxError || $squaredErrorControlSet <= $maxError;
// conditions for an ‘unsuccessful’ stop
// 1\. the maximum number of epochs has been reached
$stop_2 = $epoch ++ > $maxEpochs;
// 2\. the network’s performance on the control data is getting worse
$stop_3 = $slope > 0;
} while (!$stop_1 && !$stop_2 && !$stop_3);
$this->setEpoch($epoch);
$this->setErrorTrainingSet($squaredError);
$this->setErrorControlSet($squaredErrorControlSet);
$this->setTrainingSuccessful($stop_1);
if ($this->isVerbose()) {
echo “</table>”;
}
return $stop_1;
}
/**
* After training, this function is used to store the number of epochs the network
* needed for training the network. An epoch is defined as the number of times
* the complete trainingset is used for training.
*
* @access private
* @param int $epoch
*/
function setEpoch($epoch) {
$this->epoch = $epoch;
}
/**
* Gets the number of epochs the network needed for training.
*
* @access private
* @return int The number of epochs.
*/
function getEpoch() {
return $this->epoch;
}
/**
* After training, this function is used to store the squared error between the
* desired output and the obtained output of the training data.
*
* @access private
* @param float $error The squared error of the training data
*/
function setErrorTrainingSet($error) {
$this->error_trainingset = $error;
}
/**
* Gets the squared error between the desired output and the obtained output of
* the training data.
*
* @access private
* @return float The squared error of the training data
*/
function getErrorTrainingSet() {
return $this->error_trainingset;
}
/**
* After training, this function is used to store the squared error between the
* desired output and the obtained output of the control data.
*
* @access private
* @param float $error The squared error of the control data
*/
function setErrorControlSet($error) {
$this->error_controlset = $error;
}
/**
* Gets the squared error between the desired output and the obtained output of
* the control data.
*
* @access private
* @return float The squared error of the control data
*/
function getErrorControlSet() {
return $this->error_controlset;
}
/**
* After training, this function is used to store whether or not the training
* was successful.
*
* @access private
* @param bool $success ‘true’ if the training was successful, ‘false’ otherwise
*/
function setTrainingSuccessful($success) {
$this->success = $success;
}
/**
* Determines if the training was successful.
*
* @access private
* @return bool ‘true’ if the training was successful, ‘false’ otherwise
*/
function getTrainingSuccessful() {
return $this->success;
}
/**
* Finds the least square fitting line for the given data.
*
* This function is used to determine if the network is overtraining itself. If
* the line through the controlset’s most recent squared errors is going ‘up’,
* then it’s time to stop training.
*
* @access private
* @param array $data The points to fit a line to. The keys of this array represent
* the ‘x’-value of the point, the corresponding value is the
* ‘y’-value of the point.
* @return array An array containing, respectively, the slope and the offset of the fitted line.
*/
function fitLine($data) {
// based on
// [http://mathworld.wolfram.com/LeastSquaresFitting.html](http://mathworld.wolfram.com/LeastSquaresFitting.html)
$n = count($data);
if ($n > 1) {
$sum_y = 0;
$sum_x = 0;
$sum_x2 = 0;
$sum_xy = 0;
foreach ($data as $x => $y) {
$sum_x += $x;
$sum_y += $y;
$sum_x2 += $x * $x;
$sum_xy += $x * $y;
}
// implementation of formula (12)
$offset = ($sum_y * $sum_x2 – $sum_x * $sum_xy) / ($n * $sum_x2 – $sum_x * $sum_x);
// implementation of formula (13)
$slope = ($n * $sum_xy – $sum_x * $sum_y) / ($n * $sum_x2 – $sum_x * $sum_x);
return array ($slope, $offset);
} else {
return array (0.0, 0.0);
}
}
/**
* Gets a random weight between [-0.25 .. 0.25]. Used to initialize the network.
*
* @return float A random weight
*/
function getRandomWeight($layer) {
return ((mt_rand(0, 1000) / 1000) – 0.5) / 2;
}
/**
* Randomise the weights in the neural network
*
* @access private
*/
function initWeights() {
// assign a random value to each edge between the layers, and randomise each threshold
//
// 1\. start at layer ‘1’ (so skip the input layer)
for ($layer = 1; $layer < $this->layercount; $layer ++) {
$prev_layer = $layer -1;
// 2\. in this layer, walk each node
for ($node = 0; $node < $this->nodecount[$layer]; $node ++) {
// 3\. randomise this node’s threshold
$this->nodethreshold[$layer][$node] = $this->getRandomWeight($layer);
// 4\. this node is connected to each node of the previous layer
for ($prev_index = 0; $prev_index < $this->nodecount[$prev_layer]; $prev_index ++) {
// 5\. this is the ‘edge’ that needs to be reset / initialised
$this->edgeweight[$prev_layer][$prev_index][$node] = $this->getRandomWeight($prev_layer);
// 6\. initialize the ‘previous weightcorrection’ at 0.0
$this->previous_weightcorrection[$prev_layer][$prev_index] = 0.0;
}
}
}
}
/**
* Performs the backpropagation algorithm. This changes the weights and thresholds of the network.
*
* @access private
* @param array $output The output obtained by the network
* @param array $desired_output The desired output
*/
function backpropagate($output, $desired_output) {
$errorgradient = array ();
$outputlayer = $this->layercount – 1;
$momentum = $this->getMomentum();
// Propagate the difference between output and desired output through the layers.
for ($layer = $this->layercount – 1; $layer > 0; $layer –) {
for ($node = 0; $node < $this->nodecount[$layer]; $node ++) {
// step 1: determine errorgradient
if ($layer == $outputlayer) {
// for the output layer:
// 1a. calculate error between desired output and actual output
$error = $desired_output[$node] – $output[$node];
// 1b. calculate errorgradient
$errorgradient[$layer][$node] = $this->derivative_activation($output[$node]) * $error;
} else {
// for hidden layers:
// 1a. sum the product of edgeweight and errorgradient of the ‘next’ layer
$next_layer = $layer +1;
$productsum = 0;
for ($next_index = 0; $next_index < ($this->nodecount[$next_layer]); $next_index ++) {
$_errorgradient = $errorgradient[$next_layer][$next_index];
$_edgeweight = $this->edgeweight[$layer][$node][$next_index];
$productsum = $productsum + $_errorgradient * $_edgeweight;
}
// 1b. calculate errorgradient
$nodevalue = $this->nodevalue[$layer][$node];
$errorgradient[$layer][$node] = $this->derivative_activation($nodevalue) * $productsum;
}
// step 2: use the errorgradient to determine a weight correction for each node
$prev_layer = $layer -1;
$learning_rate = $this->getLearningRate($prev_layer);
for ($prev_index = 0; $prev_index < ($this->nodecount[$prev_layer]); $prev_index ++) {
// 2a. obtain nodevalue, edgeweight and learning rate
$nodevalue = $this->nodevalue[$prev_layer][$prev_index];
$edgeweight = $this->edgeweight[$prev_layer][$prev_index][$node];
// 2b. calculate weight correction
$weight_correction = $learning_rate * $nodevalue * $errorgradient[$layer][$node];
// 2c. retrieve previous weight correction
$prev_weightcorrection = $this->previous_weightcorrection[$layer][$node];
// 2d. combine those (‘momentum learning’) to a new weight
$new_weight = $edgeweight + $weight_correction + $momentum * $prev_weightcorrection;
// 2e. assign the new weight to this edge
$this->edgeweight[$prev_layer][$prev_index][$node] = $new_weight;
// 2f. remember this weightcorrection
$this->previous_weightcorrection[$layer][$node] = $weight_correction;
}
// step 3: use the errorgradient to determine threshold correction
$threshold_correction = $learning_rate * -1 * $errorgradient[$layer][$node];
$new_threshold = $this->nodethreshold[$layer][$node] + $threshold_correction;
$this->nodethreshold[$layer][$node] = $new_threshold;
}
}
}
/**
* Calculate the root-mean-squared error of the output, given the
* trainingdata.
*
* @access private
* @return float The root-mean-squared error of the output
*/
function squaredErrorEpoch() {
$RMSerror = 0.0;
for ($i = 0; $i < count($this->trainInputs); $i ++) {
$RMSerror += $this->squaredError($this->trainInputs[$i], $this->trainOutput[$i]);
}
$RMSerror = $RMSerror / count($this->trainInputs);
return sqrt($RMSerror);
}
/**
* Calculate the root-mean-squared error of the output, given the
* controldata.
*
* @access private
* @return float The root-mean-squared error of the output
*/
function squaredErrorControlSet() {
if (count($this->controlInputs) == 0) {
return 1.0;
}
$RMSerror = 0.0;
for ($i = 0; $i < count($this->controlInputs); $i ++) {
$RMSerror += $this->squaredError($this->controlInputs[$i], $this->controlOutput[$i]);
}
$RMSerror = $RMSerror / count($this->controlInputs);
return sqrt($RMSerror);
}
/**
* Calculate the root-mean-squared error of the output, given the
* desired output.
*
* @access private
* @param array $input The input to test
* @param array $desired_output The desired output
* @return float The root-mean-squared error of the output compared to the desired output
*/
function squaredError($input, $desired_output) {
$output = $this->calculate($input);
$RMSerror = 0.0;
foreach ($output as $node => $value) {
//calculate the error
$error = $output[$node] – $desired_output[$node];
$RMSerror = $RMSerror + ($error * $error);
}
return $RMSerror;
}
}
?>
