*
* @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));
$this->eigenDecomposition($covMatrix);
$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;
}
/**
* 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
*
* @throws \Exception
*/
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);
}
}