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<?php |
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declare(strict_types=1); |
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namespace Phpml\DimensionReduction; |
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use Exception; |
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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(?float $totalVariance = null, ?int $numFeatures = null) |
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{ |
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if ($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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public function fit(array $data): array |
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{ |
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$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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* 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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* @throws \Exception |
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*/ |
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public function transform(array $sample): array |
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{ |
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if (!$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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protected function calculateMeans(array $data, int $n): void |
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{ |
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// Calculate means for each dimension |
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$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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protected function normalize(array $data, int $n): array |
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{ |
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if (empty($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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php-ai /
php-ml
