144 lines
3.9 KiB
PHP
144 lines
3.9 KiB
PHP
<?php
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declare(strict_types=1);
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namespace Phpml\DimensionReduction;
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use Phpml\Math\Statistic\Covariance;
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use Phpml\Math\Statistic\Mean;
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class PCA extends EigenTransformerBase
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{
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/**
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* Temporary storage for mean values for each dimension in given data
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*
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* @var array
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*/
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protected $means = [];
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/**
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* @var bool
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*/
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protected $fit = false;
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/**
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* PCA (Principal Component Analysis) used to explain given
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* data with lower number of dimensions. This analysis transforms the
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* data to a lower dimensional version of it by conserving a proportion of total variance
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* within the data. It is a lossy data compression technique.<br>
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*
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* @param float $totalVariance Total explained variance to be preserved
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* @param int $numFeatures Number of features to be preserved
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*
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* @throws \Exception
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*/
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public function __construct($totalVariance = null, $numFeatures = null)
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{
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if ($totalVariance !== null && ($totalVariance < 0.1 || $totalVariance > 0.99)) {
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throw new \Exception('Total variance can be a value between 0.1 and 0.99');
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}
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if ($numFeatures !== null && $numFeatures <= 0) {
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throw new \Exception('Number of features to be preserved should be greater than 0');
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}
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if ($totalVariance !== null && $numFeatures !== null) {
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throw new \Exception('Either totalVariance or numFeatures should be specified in order to run the algorithm');
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}
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if ($numFeatures !== null) {
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$this->numFeatures = $numFeatures;
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}
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if ($totalVariance !== null) {
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$this->totalVariance = $totalVariance;
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}
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}
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/**
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* Takes a data and returns a lower dimensional version
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* of this data while preserving $totalVariance or $numFeatures. <br>
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* $data is an n-by-m matrix and returned array is
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* n-by-k matrix where k <= m
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*
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* @param array $data
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*
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* @return array
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*/
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public function fit(array $data)
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{
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$n = count($data[0]);
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$data = $this->normalize($data, $n);
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$covMatrix = Covariance::covarianceMatrix($data, array_fill(0, $n, 0));
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$this->eigenDecomposition($covMatrix);
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$this->fit = true;
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return $this->reduce($data);
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}
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/**
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* @param array $data
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* @param int $n
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*/
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protected function calculateMeans(array $data, int $n)
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{
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// Calculate means for each dimension
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$this->means = [];
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for ($i = 0; $i < $n; ++$i) {
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$column = array_column($data, $i);
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$this->means[] = Mean::arithmetic($column);
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}
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}
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/**
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* Normalization of the data includes subtracting mean from
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* each dimension therefore dimensions will be centered to zero
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*
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* @param array $data
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* @param int $n
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*
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* @return array
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*/
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protected function normalize(array $data, int $n)
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{
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if (empty($this->means)) {
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$this->calculateMeans($data, $n);
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}
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// Normalize data
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foreach ($data as $i => $row) {
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for ($k = 0; $k < $n; ++$k) {
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$data[$i][$k] -= $this->means[$k];
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}
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}
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return $data;
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}
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/**
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* Transforms the given sample to a lower dimensional vector by using
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* the eigenVectors obtained in the last run of <code>fit</code>.
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*
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* @param array $sample
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*
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* @return array
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*
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* @throws \Exception
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*/
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public function transform(array $sample)
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{
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if (!$this->fit) {
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throw new \Exception('PCA has not been fitted with respect to original dataset, please run PCA::fit() first');
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}
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if (!is_array($sample[0])) {
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$sample = [$sample];
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}
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$sample = $this->normalize($sample, count($sample[0]));
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return $this->reduce($sample);
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}
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}
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