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A simple example of logistic regression via gradient descent in PHP.
<?php
error_reporting(E_ALL);
define('NUM_FEATURES', 3);
// My dataset describes cities around the world where I might consider living.
// Each sample (city) consists of 3 features:
// * Feature 1: average low winter temperature in the city
// * Feature 2: city population, in millions
// * Feature 3: does the city have an airport I can fly to from USA directly?
//
// The labels (categories) are 1 (yes) and 0 (no).
// All the data is floating-point.
$training = array(
array(-11., 2.6, 1.),
array( 8., 0.78, 1.),
array( 15., 4.2, 0.),
array(-16., 0.18, 0.),
array( 3., 1.1, 0.),
array( 7., 1.4, 1.),
array( -3., 1.44, 1.),
array( -7., 0.52, 0.),
array( 30., 0.82, 1.),
array( 20., 1.32, 0.),
);
$labels = array(
0.,
1.,
0.,
0.,
1.,
1.,
1.,
0.,
0.,
1
);
$NUM_SAMPLES = sizeof($training);
// Initialize the weights array to random starting values.
// There are always 1+NUM_FEATURES weights, because the first weight
// does not correspond to a feature value, since:
// weights * features = weight0 + weight1 * feature1 + weight2 * feature2 + ...
$weights = array();
for ($j=0; $j < NUM_FEATURES+1; $j++)
$weights[$j] = mt_rand()/mt_getrandmax()*5.0;
// Calculate the data we need for feature scaling (mean/variance)
$scaling = calc_feature_scaling($training);
$learning_rate = 0.05;
$steps = 20000; // number of steps to take for gradient descent
$temp = array(); // temp array to hold updates for weights during the loop
for ($n = 0; $n < $steps; $n++) {
// For each weight, perform the gradient descent step and save the result to temp
for ($j = 0; $j < NUM_FEATURES+1; $j++) {
$sum_m = 0.0;
for ($i = 0; $i < $NUM_SAMPLES; $i++) {
$scaled_data = scale($training[$i], $scaling);
$h = hypothesis($scaled_data, $weights);
// The first weight has a dummy 1 "feature" value
$part = ($h - $labels[$i]) * ($j==0 ? 1.0 : $scaled_data[$j-1]);
$sum_m = $sum_m + $part;
}
$temp[$j] = $weights[$j] - $learning_rate * $sum_m/$NUM_SAMPLES;
}
$weights = $temp;
}
echo "Executed $n steps\n";
echo "Weights: ", vector_to_str($weights), "\n";
// Validate the results
print "\nValidating training\n";
$correct = 0;
for ($i = 0; $i < $NUM_SAMPLES; $i++) {
$predict = predict(scale($training[$i], $scaling), $weights);
printf("Input: %-16s actual: %d, predict: %d", vector_to_str($training[$i]), $labels[$i], $predict);
if ($labels[$i] != $predict)
print " - miss";
print "\n";
if ($predict == $labels[$i])
$correct++;
}
printf("Correctness = %.0f%%\n", $correct/$NUM_SAMPLES*100.0);
// Try some predictions
print "\nTesting the model\n";
$test = array(
array(-1., 1.1, 1.),
array(23., 0.9, 0.),
array( 4., 1.9, 0.),
array(-14., 1.1, 1.),
);
for ($i = 0; $i < sizeof($test); $i++) {
$predict = predict(scale($test[$i], $scaling), $weights);
printf("Input: %-16s predict: %d\n", vector_to_str($test[$i]), $predict);
}
function hypothesis($x, $weights)
{
$score = $weights[0]; // free weight
$k = sizeof($x);
// Calculate dot product
for ($i = 0; $i < $k; $i++)
$score += $weights[$i+1] * $x[$i];
// Run through the sigmoid (logistic) function
return 1.0/(1.0 + exp(-$score));
}
function predict($input, $weights)
{
$output = hypothesis($input, $weights);
// Threshold on 0.5
if ($output >= 0.50)
$predict = 1;
else
$predict = 0;
return $predict;
}
function scale($input, $scaling)
{
foreach ($input as $f => &$value) {
$value = ($value - $scaling['mean'][$f]) /
$scaling['variance'][$f];
}
return $input;
}
function calc_feature_scaling($data)
{
$mins = array_fill(0, NUM_FEATURES, INF);
$maxs = array_fill(0, NUM_FEATURES, -INF);
$sums = array_fill(0, NUM_FEATURES, 0);
$scaling = array('mean' => array(),
'variance' => array());
$N = sizeof($data);
foreach ($data as $i => $row) {
foreach ($row as $f => $value) {
if ($value > $maxs[$f])
$maxs[$f] = $value;
if ($value < $mins[$f])
$mins[$f] = $value;
$sums[$f] += $value;
}
}
for ($f = 0; $f < NUM_FEATURES; $f++) {
$scaling['mean'][$f] = $sums[$f] / $N;
$scaling['variance'][$f] = $maxs[$f] - $mins[$f];
if ($scaling['variance'][$f] == 0)
throw new Exception("Feature #$f has the same value in all the samples, invalid data");
}
return $scaling;
}
function vector_to_str($x)
{
return '['.implode(", ", $x).']';
}
?>
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