Skip to content
This repository

HTTPS clone URL

Subversion checkout URL

You can clone with HTTPS or Subversion.

Download ZIP
branch: master
Fetching contributors…

Octocat-spinner-32-eaf2f5

Cannot retrieve contributors at this time

file 271 lines (231 sloc) 6.022 kb
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271
<?php

class MVGradient {

protected $data;
protected $learning_rate = 0.1;

/**
* Set the data for the function.
* @param array - 0 => (x1, x2, x3, x4), 1 => y
*/
public function set_data($data) {
$this->data = $this->scale_data($data);
}

/**
* Set the rate at which the algorithm updates.
* Normal values are 0.1 - 0.001
*
* @param float $rate
* @return void
*/
public function set_learning_rate($rate) {
$this->learning_rate = $rate;
}

/**
* Normalise variance and scale data to:
* xi - avg(xi) / range(max-min)
* so we get in a -0.5 - 0.5 range with an
* avg of 0
* - this is a bit of clunky method!
*/
protected function scale_data($data) {
$minmax = array();
$rows = count($data);

foreach($data as $key => $row) {
foreach($row[0] as $id => $val) {
/* Initialise Arrays */
if(!isset($minmax[$id])) {
$minmax[$id] = array();
$minmax[$id]['min'] = false;
$minmax[$id]['max'] = false;
$minmax[$id]['total'] = 0;
}

/* Get stats */
if( $minmax[$id]['min'] == false ||
$minmax[$id]['min'] > $val) {
$minmax[$id]['min'] = $val;
}
if( $minmax[$id]['max'] == false ||
$minmax[$id]['max'] < $val) {
$minmax[$id]['max'] = $val;
}

$minmax[$id]['total'] += $val;
}
}

/* Compute average and variance */
foreach($minmax as $id => $row) {
$minmax[$id]['var'] = $row['max'] - $row['min'];
$minmax[$id]['avg'] = $row['total'] / $rows;

}

foreach($data as $key => $row) {
foreach($row[0] as $id => $val) {
$data[$key][0][$id] = ( $val - $minmax[$id]['avg'] )
/ $minmax[$id]['var'];
}
}

return $data;
}

/**
* Update the parameters, including using a dummy row value
* of 1 for the first parameter.
*
* @param array $params
* @return array
*/
protected function learn($params) {
$data_rate = 1/count($this->data);

foreach($params as $id => $p) {
foreach($this->data as $row) {
$score = $this->mv_hypothesis($row[0], $params) - $row[1];

// Update parameters
$params[$id] -= $this->learning_rate *
($data_rate *
( $score * ($id == 0 ? 1 : $row[0][$id-1]) )
);
}
}

return $params;
}

/**
* Generate a score based on the data and passed parameters
*
* @param array $params
* @return int
*/
protected function mv_hypothesis($rowdata, $params) {
$score = $params[0];
foreach($rowdata as $id => $value) {
$score += $value * $params[$id+1];
}
return $score;
}

/**
* Return the sum of squared error score
*
* @param array $params
* @return int
*/
public function score($params) {
$score = 0;
foreach($this->data as $row) {
$score += pow($this->mv_hypothesis($row[0], $params) - $row[1], 2);
}
return $score;
}

/**
* Update parameters
*
* @param string $data
* @param string $parameters
* @return array parameters
*/
function mv_gradient($parameters) {
$score = $this->score($parameters);

// Create a new hypothesis to test our score
$parameters = $this->learn($parameters);

if($score < $this->score($parameters)) {
return false;
}

return $parameters;
}

/**
* Find the parameters that best fit the data
*
* @param int $iterations - max iterations to run
* @param array $defaults - optional starting params
* @return array - best fit parameters
*/
public function find_params($iterations = 5000, $defaults = null) {
if(!$defaults) {
$defaults = array_fill(0, count($this->data[0][0]) + 1, 0);
}

$parameters = $defaults;
$iters = 0;
do {
$last_parameters = $parameters;
$parameters = $this->mv_gradient($parameters);
} while($parameters != false && $iters++ < $iterations);

return $parameters ? $parameters : $last_parameters;
}

}

/* Nice regular data for testing */
$data = array(
array(array(2, 4000, 0.5), 2+2+(2*4)+(3*5)),
array(array(2, 4000, 0.4), 2+2+(2*4)+(3*4)),
array(array(2, 4000, 0.6), 2+2+(2*4)+(3*6)),
array(array(1, 5000, 0.5), 2+1+(2*5)+(3*5)),
array(array(2, 5000, 0.1), 2+2+(2*5)+(3*1)),
);

class PolyMV extends MVGradient {

/**
* Skip scaling just for the example
*/
protected function scale_data($data) {
return $data;
}

/**
* Generate a score based on the data and passed parameters
*
* @param array $params
* @return int
*/
protected function mv_hypothesis($rowdata, $params) {
$score = $params[0];
foreach($rowdata as $id => $value) {
$score += pow($value, $id+2) * $params[$id+1];
}
return $score;
}

/**
* Update the parameters, including using a dummy row value
* of 1 for the first parameter.
*
* @param array $params
* @return array
*/
protected function learn($params) {
$data_rate = 1/count($this->data);

foreach($params as $id => $p) {
foreach($this->data as $row) {
$score = $this->mv_hypothesis($row[0], $params) - $row[1];

// Update parameters
// We have to multiply by an appropriate power as part of the
// partial derivative
$params[$id] -= $this->learning_rate *
($data_rate *
( $score * ($id == 0 ? 1 : pow($row[0][$id-1], $id+1)) )
);
}
}

return $params;
}
}
/*


$iterations = array(10, 100, 500, 1000, 2000, 5000, 10000);
$mvg = new MVGradient();
$mvg->set_data($data);
foreach(array(0.1, 0.01, 0.001, 0.001) as $rate) {
$mvg->set_learning_rate($rate);
foreach($iterations as $i) {
$params = $mvg->find_params($i);
echo $mvg->score($params), "\n";
}
echo "\n";
}
die();


// We have a polynomial example here

$data = array(
array(array(2, 2), 1+(3*pow(2, 2))+(2*pow(2, 3))),
array(array(3, 3), 1+(3*pow(3, 2))+(2*pow(3, 3))),
array(array(4, 4), 1+(3*pow(4, 2))+(2*pow(4, 3))),
array(array(5, 5), 1+(3*pow(5, 2))+(2*pow(5, 3))),
);

$iterations = array(10000);
$mvg = new PolyMV();
$mvg->set_data($data);
$mvg->set_learning_rate(0.001);
foreach($iterations as $i) {
$params = $mvg->find_params($i);
echo $mvg->score($params), "\n";
var_dump($params);
}
echo "\n";
*/
Something went wrong with that request. Please try again.