Linear Discrimant Analysis (LDA) (#82)
* Linear Discrimant Analysis (LDA) * LDA test file * Matrix inverse via LUDecomposition * LUDecomposition inverse() and det() applied * Readme update for LDA
This commit is contained in:
Mustafa Karabulut
Arkadiusz Kondas
parent
12b8b118dd
commit
5b373fa7c2
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@ -88,8 +88,9 @@ Example scripts are available in a separate repository [php-ai/php-ml-examples](
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* [Token Count Vectorizer](http://php-ml.readthedocs.io/en/latest/machine-learning/feature-extraction/token-count-vectorizer/)
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* [Tf-idf Transformer](http://php-ml.readthedocs.io/en/latest/machine-learning/feature-extraction/tf-idf-transformer/)
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* Dimensionality Reduction
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* PCA
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* PCA (Principal Component Analysis)
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* Kernel PCA
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* LDA (Linear Discriminant Analysis)
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* Datasets
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* [Array](http://php-ml.readthedocs.io/en/latest/machine-learning/datasets/array-dataset/)
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* [CSV](http://php-ml.readthedocs.io/en/latest/machine-learning/datasets/csv-dataset/)
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@ -0,0 +1,98 @@
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<?php declare(strict_types=1);
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namespace Phpml\DimensionReduction;
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use Phpml\Math\LinearAlgebra\EigenvalueDecomposition;
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use Phpml\Math\Matrix;
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/**
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* Class to compute eigen pairs (values & vectors) of a given matrix
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* with the consideration of numFeatures or totalVariance to be preserved
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*
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* @author hp
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*/
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abstract class EigenTransformerBase
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{
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/**
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* Total variance to be conserved after the reduction
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*
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* @var float
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*/
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public $totalVariance = 0.9;
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/**
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* Number of features to be preserved after the reduction
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*
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* @var int
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*/
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public $numFeatures = null;
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/**
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* Top eigenvectors of the matrix
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*
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* @var array
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*/
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protected $eigVectors = [];
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/**
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* Top eigenValues of the matrix
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*
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* @var type
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*/
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protected $eigValues = [];
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/**
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* Calculates eigenValues and eigenVectors of the given matrix. Returns
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* top eigenVectors along with the largest eigenValues. The total explained variance
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* of these eigenVectors will be no less than desired $totalVariance value
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*
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* @param array $matrix
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*/
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protected function eigenDecomposition(array $matrix)
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{
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$eig = new EigenvalueDecomposition($matrix);
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$eigVals = $eig->getRealEigenvalues();
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$eigVects= $eig->getEigenvectors();
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$totalEigVal = array_sum($eigVals);
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// Sort eigenvalues in descending order
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arsort($eigVals);
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$explainedVar = 0.0;
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$vectors = [];
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$values = [];
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foreach ($eigVals as $i => $eigVal) {
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$explainedVar += $eigVal / $totalEigVal;
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$vectors[] = $eigVects[$i];
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$values[] = $eigVal;
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if ($this->numFeatures !== null) {
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if (count($vectors) == $this->numFeatures) {
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break;
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}
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} else {
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if ($explainedVar >= $this->totalVariance) {
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break;
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}
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}
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}
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$this->eigValues = $values;
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$this->eigVectors = $vectors;
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}
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/**
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* Returns the reduced data
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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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protected function reduce(array $data)
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{
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$m1 = new Matrix($data);
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$m2 = new Matrix($this->eigVectors);
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return $m1->multiply($m2->transpose())->toArray();
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}
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}
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@ -86,7 +86,7 @@ class KernelPCA extends PCA
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$matrix = $this->calculateKernelMatrix($this->data, $numRows);
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$matrix = $this->centerMatrix($matrix, $numRows);
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list($this->eigValues, $this->eigVectors) = $this->eigenDecomposition($matrix, $numRows);
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$this->eigenDecomposition($matrix, $numRows);
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$this->fit = true;
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@ -0,0 +1,247 @@
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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\Math\Statistic\Mean;
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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 $numFeatures Number of features to be preserved
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*
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* @throws \Exception
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*/
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public function __construct($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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* Trains the algorithm to transform the given data to a lower dimensional space.
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*
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* @param array $data
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* @param array $classes
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*
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* @return array
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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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* Returns unique labels in the dataset
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*
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* @param array $classes
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*
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* @return array
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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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* @param type $data
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* @param type $classes
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*
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* @return array
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*/
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protected function calculateMeans($data, $classes) : array
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{
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$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], $this->labels);
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foreach ($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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* @param array $data
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* @param array $classes
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*
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* @return Matrix
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*/
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protected function calculateClassVar($data, $classes)
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{
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// s is an n (number of classes) by m (number of column) matrix
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$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], $this->labels);
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$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 $sW;
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}
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/**
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* Returns between-class scatter matrix for each class, which
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* is an n by m matrix where n is number of classes and
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* m is number of columns
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*
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* @return Matrix
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*/
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protected function calculateClassCov()
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{
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// s is an n (number of classes) by m (number of column) matrix
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$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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* @param array $row
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* @param array $means
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*
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* @return Matrix
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*/
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protected function calculateVar(array $row, array $means)
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{
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$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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* 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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public function transform(array $sample)
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{
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if (!$this->fit) {
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throw new \Exception("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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@ -4,27 +4,12 @@ declare(strict_types=1);
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namespace Phpml\DimensionReduction;
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use Phpml\Math\LinearAlgebra\EigenvalueDecomposition;
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use Phpml\Math\Statistic\Covariance;
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use Phpml\Math\Statistic\Mean;
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use Phpml\Math\Matrix;
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class PCA
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class PCA extends EigenTransformerBase
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{
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/**
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* Total variance to be conserved after the reduction
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*
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* @var float
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*/
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public $totalVariance = 0.9;
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/**
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* Number of features to be preserved after the reduction
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*
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* @var int
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*/
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public $numFeatures = null;
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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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@ -32,20 +17,6 @@ class PCA
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*/
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protected $means = [];
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/**
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* Eigenvectors of the covariance matrix
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*
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* @var array
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*/
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protected $eigVectors = [];
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/**
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* Top eigenValues of the covariance matrix
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*
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* @var type
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*/
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protected $eigValues = [];
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/**
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* @var bool
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*/
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@ -100,7 +71,7 @@ class PCA
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$covMatrix = Covariance::covarianceMatrix($data, array_fill(0, $n, 0));
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list($this->eigValues, $this->eigVectors) = $this->eigenDecomposition($covMatrix, $n);
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$this->eigenDecomposition($covMatrix);
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$this->fit = true;
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@ -146,63 +117,6 @@ class PCA
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return $data;
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}
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/**
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* Calculates eigenValues and eigenVectors of the given matrix. Returns
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* top eigenVectors along with the largest eigenValues. The total explained variance
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* of these eigenVectors will be no less than desired $totalVariance value
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*
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* @param array $matrix
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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 eigenDecomposition(array $matrix, int $n)
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{
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$eig = new EigenvalueDecomposition($matrix);
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$eigVals = $eig->getRealEigenvalues();
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$eigVects= $eig->getEigenvectors();
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$totalEigVal = array_sum($eigVals);
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// Sort eigenvalues in descending order
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arsort($eigVals);
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$explainedVar = 0.0;
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$vectors = [];
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$values = [];
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foreach ($eigVals as $i => $eigVal) {
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$explainedVar += $eigVal / $totalEigVal;
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$vectors[] = $eigVects[$i];
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$values[] = $eigVal;
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if ($this->numFeatures !== null) {
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if (count($vectors) == $this->numFeatures) {
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break;
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}
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} else {
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if ($explainedVar >= $this->totalVariance) {
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break;
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}
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}
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}
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return [$values, $vectors];
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}
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/**
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* Returns the reduced data
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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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protected function reduce(array $data)
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{
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$m1 = new Matrix($data);
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$m2 = new Matrix($this->eigVectors);
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return $m1->multiply($m2->transpose())->toArray();
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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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@ -130,10 +130,10 @@ class EigenvalueDecomposition
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$this->e[$j] = $g;
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}
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$f = 0.0;
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if ($h === 0 || $h < 1e-32) {
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$h = 1e-32;
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}
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for ($j = 0; $j < $i; ++$j) {
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if ($h === 0) {
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$h = 1e-20;
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}
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$this->e[$j] /= $h;
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$f += $this->e[$j] * $this->d[$j];
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}
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@ -0,0 +1,297 @@
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<?php declare(strict_types=1);
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/**
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* @package JAMA
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*
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* For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n
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* unit lower triangular matrix L, an n-by-n upper triangular matrix U,
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* and a permutation vector piv of length m so that A(piv,:) = L*U.
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* If m < n, then L is m-by-m and U is m-by-n.
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*
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* The LU decompostion with pivoting always exists, even if the matrix is
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* singular, so the constructor will never fail. The primary use of the
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* LU decomposition is in the solution of square systems of simultaneous
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* linear equations. This will fail if isNonsingular() returns false.
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*
|
||||
* @author Paul Meagher
|
||||
* @author Bartosz Matosiuk
|
||||
* @author Michael Bommarito
|
||||
* @version 1.1
|
||||
* @license PHP v3.0
|
||||
*
|
||||
* Slightly changed to adapt the original code to PHP-ML library
|
||||
* @date 2017/04/24
|
||||
* @author Mustafa Karabulut
|
||||
*/
|
||||
|
||||
namespace Phpml\Math\LinearAlgebra;
|
||||
|
||||
use Phpml\Math\Matrix;
|
||||
use Phpml\Exception\MatrixException;
|
||||
|
||||
class LUDecomposition
|
||||
{
|
||||
/**
|
||||
* Decomposition storage
|
||||
* @var array
|
||||
*/
|
||||
private $LU = [];
|
||||
|
||||
/**
|
||||
* Row dimension.
|
||||
* @var int
|
||||
*/
|
||||
private $m;
|
||||
|
||||
/**
|
||||
* Column dimension.
|
||||
* @var int
|
||||
*/
|
||||
private $n;
|
||||
|
||||
/**
|
||||
* Pivot sign.
|
||||
* @var int
|
||||
*/
|
||||
private $pivsign;
|
||||
|
||||
/**
|
||||
* Internal storage of pivot vector.
|
||||
* @var array
|
||||
*/
|
||||
private $piv = [];
|
||||
|
||||
|
||||
/**
|
||||
* LU Decomposition constructor.
|
||||
*
|
||||
* @param $A Rectangular matrix
|
||||
* @return Structure to access L, U and piv.
|
||||
*/
|
||||
public function __construct(Matrix $A)
|
||||
{
|
||||
if ($A->getRows() != $A->getColumns()) {
|
||||
throw MatrixException::notSquareMatrix();
|
||||
}
|
||||
|
||||
// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
|
||||
$this->LU = $A->toArray();
|
||||
$this->m = $A->getRows();
|
||||
$this->n = $A->getColumns();
|
||||
for ($i = 0; $i < $this->m; ++$i) {
|
||||
$this->piv[$i] = $i;
|
||||
}
|
||||
$this->pivsign = 1;
|
||||
$LUrowi = $LUcolj = [];
|
||||
|
||||
// Outer loop.
|
||||
for ($j = 0; $j < $this->n; ++$j) {
|
||||
// Make a copy of the j-th column to localize references.
|
||||
for ($i = 0; $i < $this->m; ++$i) {
|
||||
$LUcolj[$i] = &$this->LU[$i][$j];
|
||||
}
|
||||
// Apply previous transformations.
|
||||
for ($i = 0; $i < $this->m; ++$i) {
|
||||
$LUrowi = $this->LU[$i];
|
||||
// Most of the time is spent in the following dot product.
|
||||
$kmax = min($i, $j);
|
||||
$s = 0.0;
|
||||
for ($k = 0; $k < $kmax; ++$k) {
|
||||
$s += $LUrowi[$k] * $LUcolj[$k];
|
||||
}
|
||||
$LUrowi[$j] = $LUcolj[$i] -= $s;
|
||||
}
|
||||
// Find pivot and exchange if necessary.
|
||||
$p = $j;
|
||||
for ($i = $j+1; $i < $this->m; ++$i) {
|
||||
if (abs($LUcolj[$i]) > abs($LUcolj[$p])) {
|
||||
$p = $i;
|
||||
}
|
||||
}
|
||||
if ($p != $j) {
|
||||
for ($k = 0; $k < $this->n; ++$k) {
|
||||
$t = $this->LU[$p][$k];
|
||||
$this->LU[$p][$k] = $this->LU[$j][$k];
|
||||
$this->LU[$j][$k] = $t;
|
||||
}
|
||||
$k = $this->piv[$p];
|
||||
$this->piv[$p] = $this->piv[$j];
|
||||
$this->piv[$j] = $k;
|
||||
$this->pivsign = $this->pivsign * -1;
|
||||
}
|
||||
// Compute multipliers.
|
||||
if (($j < $this->m) && ($this->LU[$j][$j] != 0.0)) {
|
||||
for ($i = $j+1; $i < $this->m; ++$i) {
|
||||
$this->LU[$i][$j] /= $this->LU[$j][$j];
|
||||
}
|
||||
}
|
||||
}
|
||||
} // function __construct()
|
||||
|
||||
|
||||
/**
|
||||
* Get lower triangular factor.
|
||||
*
|
||||
* @return array Lower triangular factor
|
||||
*/
|
||||
public function getL()
|
||||
{
|
||||
$L = [];
|
||||
for ($i = 0; $i < $this->m; ++$i) {
|
||||
for ($j = 0; $j < $this->n; ++$j) {
|
||||
if ($i > $j) {
|
||||
$L[$i][$j] = $this->LU[$i][$j];
|
||||
} elseif ($i == $j) {
|
||||
$L[$i][$j] = 1.0;
|
||||
} else {
|
||||
$L[$i][$j] = 0.0;
|
||||
}
|
||||
}
|
||||
}
|
||||
return new Matrix($L);
|
||||
} // function getL()
|
||||
|
||||
|
||||
/**
|
||||
* Get upper triangular factor.
|
||||
*
|
||||
* @return array Upper triangular factor
|
||||
*/
|
||||
public function getU()
|
||||
{
|
||||
$U = [];
|
||||
for ($i = 0; $i < $this->n; ++$i) {
|
||||
for ($j = 0; $j < $this->n; ++$j) {
|
||||
if ($i <= $j) {
|
||||
$U[$i][$j] = $this->LU[$i][$j];
|
||||
} else {
|
||||
$U[$i][$j] = 0.0;
|
||||
}
|
||||
}
|
||||
}
|
||||
return new Matrix($U);
|
||||
} // function getU()
|
||||
|
||||
|
||||
/**
|
||||
* Return pivot permutation vector.
|
||||
*
|
||||
* @return array Pivot vector
|
||||
*/
|
||||
public function getPivot()
|
||||
{
|
||||
return $this->piv;
|
||||
} // function getPivot()
|
||||
|
||||
|
||||
/**
|
||||
* Alias for getPivot
|
||||
*
|
||||
* @see getPivot
|
||||
*/
|
||||
public function getDoublePivot()
|
||||
{
|
||||
return $this->getPivot();
|
||||
} // function getDoublePivot()
|
||||
|
||||
|
||||
/**
|
||||
* Is the matrix nonsingular?
|
||||
*
|
||||
* @return true if U, and hence A, is nonsingular.
|
||||
*/
|
||||
public function isNonsingular()
|
||||
{
|
||||
for ($j = 0; $j < $this->n; ++$j) {
|
||||
if ($this->LU[$j][$j] == 0) {
|
||||
return false;
|
||||
}
|
||||
}
|
||||
return true;
|
||||
} // function isNonsingular()
|
||||
|
||||
|
||||
/**
|
||||
* Count determinants
|
||||
*
|
||||
* @return array d matrix deterninat
|
||||
*/
|
||||
public function det()
|
||||
{
|
||||
if ($this->m == $this->n) {
|
||||
$d = $this->pivsign;
|
||||
for ($j = 0; $j < $this->n; ++$j) {
|
||||
$d *= $this->LU[$j][$j];
|
||||
}
|
||||
return $d;
|
||||
} else {
|
||||
throw MatrixException::notSquareMatrix();
|
||||
}
|
||||
} // function det()
|
||||
|
||||
|
||||
/**
|
||||
* Solve A*X = B
|
||||
*
|
||||
* @param Matrix $B A Matrix with as many rows as A and any number of columns.
|
||||
*
|
||||
* @return array X so that L*U*X = B(piv,:)
|
||||
*
|
||||
* @throws MatrixException
|
||||
*/
|
||||
public function solve(Matrix $B)
|
||||
{
|
||||
if ($B->getRows() != $this->m) {
|
||||
throw MatrixException::notSquareMatrix();
|
||||
}
|
||||
|
||||
if (! $this->isNonsingular()) {
|
||||
throw MatrixException::singularMatrix();
|
||||
}
|
||||
|
||||
// Copy right hand side with pivoting
|
||||
$nx = $B->getColumns();
|
||||
$X = $this->getSubMatrix($B->toArray(), $this->piv, 0, $nx-1);
|
||||
// Solve L*Y = B(piv,:)
|
||||
for ($k = 0; $k < $this->n; ++$k) {
|
||||
for ($i = $k+1; $i < $this->n; ++$i) {
|
||||
for ($j = 0; $j < $nx; ++$j) {
|
||||
$X[$i][$j] -= $X[$k][$j] * $this->LU[$i][$k];
|
||||
}
|
||||
}
|
||||
}
|
||||
// Solve U*X = Y;
|
||||
for ($k = $this->n-1; $k >= 0; --$k) {
|
||||
for ($j = 0; $j < $nx; ++$j) {
|
||||
$X[$k][$j] /= $this->LU[$k][$k];
|
||||
}
|
||||
for ($i = 0; $i < $k; ++$i) {
|
||||
for ($j = 0; $j < $nx; ++$j) {
|
||||
$X[$i][$j] -= $X[$k][$j] * $this->LU[$i][$k];
|
||||
}
|
||||
}
|
||||
}
|
||||
return $X;
|
||||
} // function solve()
|
||||
|
||||
/**
|
||||
* @param Matrix $matrix
|
||||
* @param int $j0
|
||||
* @param int $jF
|
||||
*
|
||||
* @return array
|
||||
*/
|
||||
protected function getSubMatrix(array $matrix, array $RL, int $j0, int $jF)
|
||||
{
|
||||
$m = count($RL);
|
||||
$n = $jF - $j0;
|
||||
$R = array_fill(0, $m, array_fill(0, $n+1, 0.0));
|
||||
|
||||
for ($i = 0; $i < $m; ++$i) {
|
||||
for ($j = $j0; $j <= $jF; ++$j) {
|
||||
$R[$i][$j - $j0]= $matrix[ $RL[$i] ][$j];
|
||||
}
|
||||
}
|
||||
|
||||
return $R;
|
||||
}
|
||||
} // class LUDecomposition
|
||||
|
|
@ -4,6 +4,7 @@ declare(strict_types=1);
|
|||
|
||||
namespace Phpml\Math;
|
||||
|
||||
use Phpml\Math\LinearAlgebra\LUDecomposition;
|
||||
use Phpml\Exception\InvalidArgumentException;
|
||||
use Phpml\Exception\MatrixException;
|
||||
|
||||
|
|
@ -137,32 +138,8 @@ class Matrix
|
|||
throw MatrixException::notSquareMatrix();
|
||||
}
|
||||
|
||||
return $this->determinant = $this->calculateDeterminant();
|
||||
}
|
||||
|
||||
/**
|
||||
* @return float|int
|
||||
*
|
||||
* @throws MatrixException
|
||||
*/
|
||||
private function calculateDeterminant()
|
||||
{
|
||||
$determinant = 0;
|
||||
if ($this->rows == 1 && $this->columns == 1) {
|
||||
$determinant = $this->matrix[0][0];
|
||||
} elseif ($this->rows == 2 && $this->columns == 2) {
|
||||
$determinant =
|
||||
$this->matrix[0][0] * $this->matrix[1][1] -
|
||||
$this->matrix[0][1] * $this->matrix[1][0];
|
||||
} else {
|
||||
for ($j = 0; $j < $this->columns; ++$j) {
|
||||
$subMatrix = $this->crossOut(0, $j);
|
||||
$minor = $this->matrix[0][$j] * $subMatrix->getDeterminant();
|
||||
$determinant += fmod((float) $j, 2.0) == 0 ? $minor : -$minor;
|
||||
}
|
||||
}
|
||||
|
||||
return $determinant;
|
||||
$lu = new LUDecomposition($this);
|
||||
return $this->determinant = $lu->det();
|
||||
}
|
||||
|
||||
/**
|
||||
|
|
@ -303,21 +280,26 @@ class Matrix
|
|||
throw MatrixException::notSquareMatrix();
|
||||
}
|
||||
|
||||
if ($this->isSingular()) {
|
||||
throw MatrixException::singularMatrix();
|
||||
$LU = new LUDecomposition($this);
|
||||
$identity = $this->getIdentity();
|
||||
$inverse = $LU->solve($identity);
|
||||
|
||||
return new self($inverse, false);
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns diagonal identity matrix of the same size of this matrix
|
||||
*
|
||||
* @return Matrix
|
||||
*/
|
||||
protected function getIdentity()
|
||||
{
|
||||
$array = array_fill(0, $this->rows, array_fill(0, $this->columns, 0));
|
||||
for ($i=0; $i < $this->rows; $i++) {
|
||||
$array[$i][$i] = 1;
|
||||
}
|
||||
|
||||
$newMatrix = [];
|
||||
for ($i = 0; $i < $this->rows; ++$i) {
|
||||
for ($j = 0; $j < $this->columns; ++$j) {
|
||||
$minor = $this->crossOut($i, $j)->getDeterminant();
|
||||
$newMatrix[$i][$j] = fmod((float) ($i + $j), 2.0) == 0 ? $minor : -$minor;
|
||||
}
|
||||
}
|
||||
|
||||
$cofactorMatrix = new self($newMatrix, false);
|
||||
|
||||
return $cofactorMatrix->transpose()->divideByScalar($this->getDeterminant());
|
||||
return new self($array, false);
|
||||
}
|
||||
|
||||
/**
|
||||
|
|
|
|||
|
|
@ -0,0 +1,65 @@
|
|||
<?php
|
||||
|
||||
declare(strict_types=1);
|
||||
|
||||
namespace tests\DimensionReduction;
|
||||
|
||||
use Phpml\DimensionReduction\LDA;
|
||||
use Phpml\Dataset\Demo\IrisDataset;
|
||||
use PHPUnit\Framework\TestCase;
|
||||
|
||||
class LDATest extends TestCase
|
||||
{
|
||||
public function testLDA()
|
||||
{
|
||||
// Acceptable error
|
||||
$epsilon = 0.001;
|
||||
|
||||
// IRIS dataset will be used to train LDA
|
||||
$dataset = new IrisDataset();
|
||||
$lda = new LDA(null, 2);
|
||||
$transformed = $lda->fit($dataset->getSamples(), $dataset->getTargets());
|
||||
|
||||
// Some samples of the Iris data will be checked manually
|
||||
// First 3 and last 3 rows from the original dataset
|
||||
$data = [
|
||||
[5.1, 3.5, 1.4, 0.2],
|
||||
[4.9, 3.0, 1.4, 0.2],
|
||||
[4.7, 3.2, 1.3, 0.2],
|
||||
[6.5, 3.0, 5.2, 2.0],
|
||||
[6.2, 3.4, 5.4, 2.3],
|
||||
[5.9, 3.0, 5.1, 1.8]
|
||||
];
|
||||
$transformed2 = [
|
||||
[-1.4922092756753, 1.9047102045574],
|
||||
[-1.2576556684358, 1.608414450935],
|
||||
[-1.3487505965419, 1.749846351699],
|
||||
[1.7759343101456, 2.0371552314006],
|
||||
[2.0059819019159, 2.4493123003226],
|
||||
[1.701474913008, 1.9037880473772]
|
||||
];
|
||||
|
||||
$control = [];
|
||||
$control = array_merge($control, array_slice($transformed, 0, 3));
|
||||
$control = array_merge($control, array_slice($transformed, -3));
|
||||
|
||||
$check = function ($row1, $row2) use ($epsilon) {
|
||||
// Due to the fact that the sign of values can be flipped
|
||||
// during the calculation of eigenValues, we have to compare
|
||||
// absolute value of the values
|
||||
$row1 = array_map('abs', $row1);
|
||||
$row2 = array_map('abs', $row2);
|
||||
$this->assertEquals($row1, $row2, '', $epsilon);
|
||||
};
|
||||
array_map($check, $control, $transformed2);
|
||||
|
||||
// Fitted LDA object should be able to return same values again
|
||||
// for each projected row
|
||||
foreach ($data as $i => $row) {
|
||||
$newRow = [$transformed2[$i]];
|
||||
$newRow2= $lda->transform($row);
|
||||
|
||||
array_map($check, $newRow, $newRow2);
|
||||
}
|
||||
}
|
||||
}
|
||||
Loading…
Reference in New Issue