* The algorithm can be initialized by speciyfing
* either with the totalVariance(a value between 0.1 and 0.99)
* or numFeatures (number of features in the dataset) to be preserved.
*
* @param float|null $totalVariance Total explained variance to be preserved
* @param int|null $numFeatures Number of features to be preserved
*
* @throws \Exception
*/
public function __construct(?float $totalVariance = null, ?int $numFeatures = null)
{
if ($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;
}
}
/**
* Trains the algorithm to transform the given data to a lower dimensional space.
*/
public function fit(array $data, array $classes) : array
{
$this->labels = $this->getLabels($classes);
$this->means = $this->calculateMeans($data, $classes);
$sW = $this->calculateClassVar($data, $classes);
$sB = $this->calculateClassCov();
$S = $sW->inverse()->multiply($sB);
$this->eigenDecomposition($S->toArray());
$this->fit = true;
return $this->reduce($data);
}
/**
* Returns unique labels in the dataset
*/
protected function getLabels(array $classes) : array
{
$counts = array_count_values($classes);
return array_keys($counts);
}
/**
* Calculates mean of each column for each class and returns
* n by m matrix where n is number of labels and m is number of columns
*/
protected function calculateMeans(array $data, array $classes) : array
{
$means = [];
$counts = [];
$overallMean = array_fill(0, count($data[0]), 0.0);
foreach ($data as $index => $row) {
$label = array_search($classes[$index], $this->labels);
foreach ($row as $col => $val) {
if (!isset($means[$label][$col])) {
$means[$label][$col] = 0.0;
}
$means[$label][$col] += $val;
$overallMean[$col] += $val;
}
if (!isset($counts[$label])) {
$counts[$label] = 0;
}
++$counts[$label];
}
foreach ($means as $index => $row) {
foreach ($row as $col => $sum) {
$means[$index][$col] = $sum / $counts[$index];
}
}
// Calculate overall mean of the dataset for each column
$numElements = array_sum($counts);
$map = function ($el) use ($numElements) {
return $el / $numElements;
};
$this->overallMean = array_map($map, $overallMean);
$this->counts = $counts;
return $means;
}
/**
* Returns in-class scatter matrix for each class, which
* is a n by m matrix where n is number of classes and
* m is number of columns
*/
protected function calculateClassVar(array $data, array $classes) : Matrix
{
// s is an n (number of classes) by m (number of column) matrix
$s = array_fill(0, count($data[0]), array_fill(0, count($data[0]), 0));
$sW = new Matrix($s, false);
foreach ($data as $index => $row) {
$label = array_search($classes[$index], $this->labels);
$means = $this->means[$label];
$row = $this->calculateVar($row, $means);
$sW = $sW->add($row);
}
return $sW;
}
/**
* Returns between-class scatter matrix for each class, which
* is an n by m matrix where n is number of classes and
* m is number of columns
*/
protected function calculateClassCov() : Matrix
{
// s is an n (number of classes) by m (number of column) matrix
$s = array_fill(0, count($this->overallMean), array_fill(0, count($this->overallMean), 0));
$sB = new Matrix($s, false);
foreach ($this->means as $index => $classMeans) {
$row = $this->calculateVar($classMeans, $this->overallMean);
$N = $this->counts[$index];
$sB = $sB->add($row->multiplyByScalar($N));
}
return $sB;
}
/**
* Returns the result of the calculation (x - m)T.(x - m)
*/
protected function calculateVar(array $row, array $means) : Matrix
{
$x = new Matrix($row, false);
$m = new Matrix($means, false);
$diff = $x->subtract($m);
return $diff->transpose()->multiply($diff);
}
/**
* Transforms the given sample to a lower dimensional vector by using
* the eigenVectors obtained in the last run of fit.
*
* @throws \Exception
*/
public function transform(array $sample) : array
{
if (!$this->fit) {
throw new \Exception('LDA has not been fitted with respect to original dataset, please run LDA::fit() first');
}
if (!is_array($sample[0])) {
$sample = [$sample];
}
return $this->reduce($sample);
}
}