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<?php |
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declare(strict_types=1); |
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namespace Phpml\Math\Statistic; |
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use Phpml\Exception\InvalidArgumentException; |
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/** |
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* Analysis of variance |
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* https://en.wikipedia.org/wiki/Analysis_of_variance |
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*/ |
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final class ANOVA |
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{ |
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/** |
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* The one-way ANOVA tests the null hypothesis that 2 or more groups have |
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* the same population mean. The test is applied to samples from two or |
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* more groups, possibly with differing sizes. |
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* |
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* @param array[] $samples - each row is class samples |
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* |
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* @return float[] |
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*/ |
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public static function oneWayF(array $samples): array |
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{ |
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$classes = count($samples); |
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if ($classes < 2) { |
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throw new InvalidArgumentException('The array must have at least 2 elements'); |
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} |
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$samplesPerClass = array_map(static function (array $class): int { |
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return count($class); |
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}, $samples); |
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$allSamples = (int) array_sum($samplesPerClass); |
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$ssAllSamples = self::sumOfSquaresPerFeature($samples); |
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$sumSamples = self::sumOfFeaturesPerClass($samples); |
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$squareSumSamples = self::sumOfSquares($sumSamples); |
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$sumSamplesSquare = self::squaresSum($sumSamples); |
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$ssbn = self::calculateSsbn($samples, $sumSamplesSquare, $samplesPerClass, $squareSumSamples, $allSamples); |
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$sswn = self::calculateSswn($ssbn, $ssAllSamples, $squareSumSamples, $allSamples); |
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$dfbn = $classes - 1; |
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$dfwn = $allSamples - $classes; |
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$msb = array_map(static function ($s) use ($dfbn) { |
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return $s / $dfbn; |
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}, $ssbn); |
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$msw = array_map(static function ($s) use ($dfwn) { |
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if ($dfwn === 0) { |
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return 1; |
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} |
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return $s / $dfwn; |
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}, $sswn); |
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$f = []; |
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foreach ($msb as $index => $msbValue) { |
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$f[$index] = $msbValue / $msw[$index]; |
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} |
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return $f; |
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} |
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private static function sumOfSquaresPerFeature(array $samples): array |
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{ |
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$sum = array_fill(0, count($samples[0][0]), 0); |
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foreach ($samples as $class) { |
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foreach ($class as $sample) { |
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foreach ($sample as $index => $feature) { |
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$sum[$index] += $feature ** 2; |
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} |
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} |
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} |
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return $sum; |
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} |
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private static function sumOfFeaturesPerClass(array $samples): array |
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{ |
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return array_map(static function (array $class): array { |
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$sum = array_fill(0, count($class[0]), 0); |
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foreach ($class as $sample) { |
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foreach ($sample as $index => $feature) { |
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$sum[$index] += $feature; |
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} |
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} |
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return $sum; |
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}, $samples); |
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} |
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private static function sumOfSquares(array $sums): array |
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{ |
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$squares = array_fill(0, count($sums[0]), 0); |
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foreach ($sums as $row) { |
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foreach ($row as $index => $sum) { |
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$squares[$index] += $sum; |
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} |
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} |
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return array_map(static function ($sum) { |
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return $sum ** 2; |
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}, $squares); |
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} |
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private static function squaresSum(array $sums): array |
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{ |
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foreach ($sums as &$row) { |
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foreach ($row as &$sum) { |
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$sum **= 2; |
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} |
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} |
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return $sums; |
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} |
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private static function calculateSsbn(array $samples, array $sumSamplesSquare, array $samplesPerClass, array $squareSumSamples, int $allSamples): array |
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{ |
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$ssbn = array_fill(0, count($samples[0][0]), 0); |
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foreach ($sumSamplesSquare as $classIndex => $class) { |
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foreach ($class as $index => $feature) { |
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$ssbn[$index] += $feature / $samplesPerClass[$classIndex]; |
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} |
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} |
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foreach ($squareSumSamples as $index => $sum) { |
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$ssbn[$index] -= $sum / $allSamples; |
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} |
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return $ssbn; |
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} |
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private static function calculateSswn(array $ssbn, array $ssAllSamples, array $squareSumSamples, int $allSamples): array |
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{ |
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$sswn = []; |
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foreach ($ssAllSamples as $index => $ss) { |
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$sswn[$index] = ($ss - $squareSumSamples[$index] / $allSamples) - $ssbn[$index]; |
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} |
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return $sswn; |
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} |
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} |
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php-ai /
php-ml
