*
* @param float $totalVariance Total explained variance to be preserved
* @param int $numFeatures Number of features to be preserved
*
* @throws \Exception
*/
public function __construct($totalVariance = null, $numFeatures = null)
{
if ($totalVariance !== null && ($totalVariance < 0.1 || $totalVariance > 0.99)) {
throw new \Exception("Total variance can be a value between 0.1 and 0.99");
}
if ($numFeatures !== null && $numFeatures <= 0) {
throw new \Exception("Number of features to be preserved should be greater than 0");
}
if ($totalVariance !== null && $numFeatures !== null) {
throw new \Exception("Either totalVariance or numFeatures should be specified in order to run the algorithm");
}
if ($numFeatures !== null) {
$this->numFeatures = $numFeatures;
}
if ($totalVariance !== null) {
$this->totalVariance = $totalVariance;
}
}
/**
* Takes a data and returns a lower dimensional version
* of this data while preserving $totalVariance or $numFeatures.
* $data is an n-by-m matrix and returned array is
* n-by-k matrix where k <= m
*
* @param array $data
*
* @return array
*/
public function fit(array $data)
{
$n = count($data[0]);
$data = $this->normalize($data, $n);
$covMatrix = Covariance::covarianceMatrix($data, array_fill(0, $n, 0));
list($this->eigValues, $this->eigVectors) = $this->eigenDecomposition($covMatrix, $n);
$this->fit = true;
return $this->reduce($data);
}
/**
* @param array $data
* @param int $n
*/
protected function calculateMeans(array $data, int $n)
{
// Calculate means for each dimension
$this->means = [];
for ($i=0; $i < $n; $i++) {
$column = array_column($data, $i);
$this->means[] = Mean::arithmetic($column);
}
}
/**
* Normalization of the data includes subtracting mean from
* each dimension therefore dimensions will be centered to zero
*
* @param array $data
* @param int $n
*
* @return array
*/
protected function normalize(array $data, int $n)
{
if (empty($this->means)) {
$this->calculateMeans($data, $n);
}
// Normalize data
foreach ($data as $i => $row) {
for ($k=0; $k < $n; $k++) {
$data[$i][$k] -= $this->means[$k];
}
}
return $data;
}
/**
* Calculates eigenValues and eigenVectors of the given matrix. Returns
* top eigenVectors along with the largest eigenValues. The total explained variance
* of these eigenVectors will be no less than desired $totalVariance value
*
* @param array $matrix
* @param int $n
*
* @return array
*/
protected function eigenDecomposition(array $matrix, int $n)
{
$eig = new EigenvalueDecomposition($matrix);
$eigVals = $eig->getRealEigenvalues();
$eigVects= $eig->getEigenvectors();
$totalEigVal = array_sum($eigVals);
// Sort eigenvalues in descending order
arsort($eigVals);
$explainedVar = 0.0;
$vectors = [];
$values = [];
foreach ($eigVals as $i => $eigVal) {
$explainedVar += $eigVal / $totalEigVal;
$vectors[] = $eigVects[$i];
$values[] = $eigVal;
if ($this->numFeatures !== null) {
if (count($vectors) == $this->numFeatures) {
break;
}
} else {
if ($explainedVar >= $this->totalVariance) {
break;
}
}
}
return [$values, $vectors];
}
/**
* Returns the reduced data
*
* @param array $data
*
* @return array
*/
protected function reduce(array $data)
{
$m1 = new Matrix($data);
$m2 = new Matrix($this->eigVectors);
return $m1->multiply($m2->transpose())->toArray();
}
/**
* Transforms the given sample to a lower dimensional vector by using
* the eigenVectors obtained in the last run of fit.
*
* @param array $sample
*
* @return array
*/
public function transform(array $sample)
{
if (!$this->fit) {
throw new \Exception("PCA has not been fitted with respect to original dataset, please run PCA::fit() first");
}
if (! is_array($sample[0])) {
$sample = [$sample];
}
$sample = $this->normalize($sample, count($sample[0]));
return $this->reduce($sample);
}
}