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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 Phpml\Exception\InvalidArgumentException; |
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use Phpml\Exception\InvalidOperationException; |
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use Phpml\Math\Matrix; |
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class LDA extends EigenTransformerBase |
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{ |
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/** |
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* @var bool |
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*/ |
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public $fit = false; |
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/** |
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* @var array |
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*/ |
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public $labels = []; |
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/** |
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* @var array |
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*/ |
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public $means = []; |
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/** |
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* @var array |
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*/ |
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public $counts = []; |
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/** |
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* @var float[] |
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*/ |
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public $overallMean = []; |
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/** |
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* Linear Discriminant Analysis (LDA) is used to reduce the dimensionality |
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* of the data. Unlike Principal Component Analysis (PCA), it is a supervised |
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* technique that requires the class labels in order to fit the data to a |
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* lower dimensional space. <br><br> |
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* The algorithm can be initialized by speciyfing |
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* either with the totalVariance(a value between 0.1 and 0.99) |
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* or numFeatures (number of features in the dataset) to be preserved. |
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* |
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* @param float|null $totalVariance Total explained variance to be preserved |
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* @param int|null $numFeatures Number of features to be preserved |
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* |
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* @throws InvalidArgumentException |
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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 || $totalVariance > 0.99)) { |
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throw new InvalidArgumentException('Total variance can be a value between 0.1 and 0.99'); |
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} |
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if ($numFeatures !== null && $numFeatures <= 0) { |
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throw new InvalidArgumentException('Number of features to be preserved should be greater than 0'); |
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} |
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if (($totalVariance !== null) === ($numFeatures !== null)) { |
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throw new InvalidArgumentException('Either totalVariance or numFeatures should be specified in order to run the algorithm'); |
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} |
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if ($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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* Trains the algorithm to transform the given data to a lower dimensional space. |
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*/ |
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public function fit(array $data, array $classes): array |
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{ |
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$this->labels = $this->getLabels($classes); |
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$this->means = $this->calculateMeans($data, $classes); |
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$sW = $this->calculateClassVar($data, $classes); |
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$sB = $this->calculateClassCov(); |
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$S = $sW->inverse()->multiply($sB); |
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$this->eigenDecomposition($S->toArray()); |
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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 InvalidOperationException |
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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 InvalidOperationException('LDA has not been fitted with respect to original dataset, please run LDA::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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return $this->reduce($sample); |
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} |
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/** |
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* Returns unique labels in the dataset |
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*/ |
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protected function getLabels(array $classes): array |
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{ |
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$counts = array_count_values($classes); |
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return array_keys($counts); |
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} |
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/** |
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* Calculates mean of each column for each class and returns |
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* n by m matrix where n is number of labels and m is number of columns |
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*/ |
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protected function calculateMeans(array $data, array $classes): array |
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{ |
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$means = []; |
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$counts = []; |
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$overallMean = array_fill(0, count($data[0]), 0.0); |
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foreach ($data as $index => $row) { |
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$label = array_search($classes[$index], $this->labels, true); |
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foreach ($row as $col => $val) { |
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if (!isset($means[$label][$col])) { |
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$means[$label][$col] = 0.0; |
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} |
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$means[$label][$col] += $val; |
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$overallMean[$col] += $val; |
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} |
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if (!isset($counts[$label])) { |
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$counts[$label] = 0; |
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} |
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++$counts[$label]; |
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} |
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foreach ($means as $index => $row) { |
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foreach ($row as $col => $sum) { |
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$means[$index][$col] = $sum / $counts[$index]; |
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} |
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} |
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// Calculate overall mean of the dataset for each column |
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$numElements = array_sum($counts); |
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$map = function ($el) use ($numElements) { |
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return $el / $numElements; |
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}; |
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$this->overallMean = array_map($map, $overallMean); |
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$this->counts = $counts; |
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return $means; |
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} |
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/** |
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* Returns in-class scatter matrix for each class, which |
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* is a n by m matrix where n is number of classes and |
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* m is number of columns |
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*/ |
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protected function calculateClassVar(array $data, array $classes): Matrix |
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{ |
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// s is an n (number of classes) by m (number of column) matrix |
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$s = array_fill(0, count($data[0]), array_fill(0, count($data[0]), 0)); |
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$sW = new Matrix($s, false); |
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foreach ($data as $index => $row) { |
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$label = array_search($classes[$index], $this->labels, true); |
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$means = $this->means[$label]; |
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$row = $this->calculateVar($row, $means); |
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$sW = $sW->add($row); |
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} |
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return $sW; |
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} |
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/** |
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* Returns between-class scatter matrix for each class, which |
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* is an n by m matrix where n is number of classes and |
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* m is number of columns |
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*/ |
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protected function calculateClassCov(): Matrix |
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{ |
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// s is an n (number of classes) by m (number of column) matrix |
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$s = array_fill(0, count($this->overallMean), array_fill(0, count($this->overallMean), 0)); |
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$sB = new Matrix($s, false); |
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foreach ($this->means as $index => $classMeans) { |
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$row = $this->calculateVar($classMeans, $this->overallMean); |
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$N = $this->counts[$index]; |
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$sB = $sB->add($row->multiplyByScalar($N)); |
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} |
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return $sB; |
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} |
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/** |
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* Returns the result of the calculation (x - m)T.(x - m) |
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*/ |
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protected function calculateVar(array $row, array $means): Matrix |
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{ |
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$x = new Matrix($row, false); |
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$m = new Matrix($means, false); |
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$diff = $x->subtract($m); |
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return $diff->transpose()->multiply($diff); |
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} |
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} |
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