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<?php |
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declare(strict_types=1); |
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namespace Phpml\Association; |
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use Phpml\Helper\Predictable; |
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use Phpml\Helper\Trainable; |
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class Apriori implements Associator |
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{ |
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use Trainable; |
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use Predictable; |
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public const ARRAY_KEY_ANTECEDENT = 'antecedent'; |
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public const ARRAY_KEY_CONFIDENCE = 'confidence'; |
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public const ARRAY_KEY_CONSEQUENT = 'consequent'; |
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public const ARRAY_KEY_SUPPORT = 'support'; |
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/** |
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* Minimum relative probability of frequent transactions. |
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* |
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* @var float |
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*/ |
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private $confidence; |
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/** |
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* The large set contains frequent k-length item sets. |
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* |
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* @var mixed[][][] |
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*/ |
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private $large = []; |
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/** |
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* Minimum relative frequency of transactions. |
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* |
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* @var float |
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*/ |
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private $support; |
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/** |
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* The generated Apriori association rules. |
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* |
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* @var mixed[][] |
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*/ |
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private $rules = []; |
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/** |
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* Apriori constructor. |
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*/ |
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public function __construct(float $support = 0.0, float $confidence = 0.0) |
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{ |
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$this->support = $support; |
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$this->confidence = $confidence; |
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} |
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/** |
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* Get all association rules which are generated for every k-length frequent item set. |
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* |
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* @return mixed[][] |
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*/ |
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public function getRules(): array |
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{ |
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if (count($this->large) === 0) { |
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$this->large = $this->apriori(); |
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} |
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if (count($this->rules) > 0) { |
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return $this->rules; |
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} |
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$this->rules = []; |
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$this->generateAllRules(); |
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return $this->rules; |
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} |
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/** |
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* Generates frequent item sets. |
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* |
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* @return mixed[][][] |
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*/ |
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public function apriori(): array |
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{ |
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$L = []; |
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$items = $this->frequent($this->items()); |
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for ($k = 1; isset($items[0]); ++$k) { |
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$L[$k] = $items; |
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$items = $this->frequent($this->candidates($items)); |
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} |
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return $L; |
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} |
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/** |
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* @param mixed[] $sample |
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* |
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* @return mixed[][] |
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*/ |
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protected function predictSample(array $sample): array |
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{ |
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$predicts = array_values(array_filter($this->getRules(), function ($rule) use ($sample): bool { |
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return $this->equals($rule[self::ARRAY_KEY_ANTECEDENT], $sample); |
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})); |
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return array_map(static function ($rule) { |
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return $rule[self::ARRAY_KEY_CONSEQUENT]; |
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}, $predicts); |
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} |
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/** |
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* Generate rules for each k-length frequent item set. |
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*/ |
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private function generateAllRules(): void |
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{ |
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for ($k = 2; isset($this->large[$k]); ++$k) { |
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foreach ($this->large[$k] as $frequent) { |
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$this->generateRules($frequent); |
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} |
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} |
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} |
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/** |
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* Generate confident rules for frequent item set. |
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* |
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* @param mixed[] $frequent |
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*/ |
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private function generateRules(array $frequent): void |
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{ |
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foreach ($this->antecedents($frequent) as $antecedent) { |
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$confidence = $this->confidence($frequent, $antecedent); |
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if ($this->confidence <= $confidence) { |
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$consequent = array_values(array_diff($frequent, $antecedent)); |
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$this->rules[] = [ |
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self::ARRAY_KEY_ANTECEDENT => $antecedent, |
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self::ARRAY_KEY_CONSEQUENT => $consequent, |
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self::ARRAY_KEY_SUPPORT => $this->support($frequent), |
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self::ARRAY_KEY_CONFIDENCE => $confidence, |
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]; |
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} |
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} |
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} |
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/** |
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* Generates the power set for given item set $sample. |
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* |
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* @param mixed[] $sample |
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* |
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* @return mixed[][] |
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*/ |
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private function powerSet(array $sample): array |
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{ |
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$results = [[]]; |
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foreach ($sample as $item) { |
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foreach ($results as $combination) { |
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$results[] = array_merge([$item], $combination); |
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} |
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} |
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return $results; |
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} |
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/** |
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* Generates all proper subsets for given set $sample without the empty set. |
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* |
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* @param mixed[] $sample |
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* |
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* @return mixed[][] |
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*/ |
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private function antecedents(array $sample): array |
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{ |
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$cardinality = count($sample); |
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$antecedents = $this->powerSet($sample); |
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return array_filter($antecedents, static function ($antecedent) use ($cardinality): bool { |
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return (count($antecedent) != $cardinality) && ($antecedent != []); |
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}); |
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} |
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/** |
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* Calculates frequent k = 1 item sets. |
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* |
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* @return mixed[][] |
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*/ |
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private function items(): array |
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{ |
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$items = []; |
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foreach ($this->samples as $sample) { |
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foreach ($sample as $item) { |
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if (!in_array($item, $items, true)) { |
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$items[] = $item; |
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} |
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} |
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} |
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return array_map(static function ($entry): array { |
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return [$entry]; |
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}, $items); |
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} |
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/** |
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* Returns frequent item sets only. |
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* |
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* @param mixed[][] $samples |
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* |
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* @return mixed[][] |
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*/ |
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private function frequent(array $samples): array |
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{ |
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return array_values(array_filter($samples, function ($entry): bool { |
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return $this->support($entry) >= $this->support; |
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})); |
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} |
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/** |
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* Calculates frequent k item sets, where count($samples) == $k - 1. |
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* |
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* @param mixed[][] $samples |
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* |
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* @return mixed[][] |
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*/ |
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private function candidates(array $samples): array |
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{ |
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$candidates = []; |
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foreach ($samples as $p) { |
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foreach ($samples as $q) { |
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if (count(array_merge(array_diff($p, $q), array_diff($q, $p))) != 2) { |
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continue; |
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} |
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$candidate = array_values(array_unique(array_merge($p, $q))); |
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if ($this->contains($candidates, $candidate)) { |
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continue; |
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} |
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foreach ($this->samples as $sample) { |
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if ($this->subset($sample, $candidate)) { |
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$candidates[] = $candidate; |
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continue 2; |
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} |
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} |
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} |
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} |
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return $candidates; |
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} |
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/** |
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* Calculates confidence for $set. Confidence is the relative amount of sets containing $subset which also contain |
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* $set. |
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* |
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* @param mixed[] $set |
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* @param mixed[] $subset |
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*/ |
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private function confidence(array $set, array $subset): float |
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{ |
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return $this->support($set) / $this->support($subset); |
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} |
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/** |
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* Calculates support for item set $sample. Support is the relative amount of sets containing $sample in the data |
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* pool. |
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* |
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* @see \Phpml\Association\Apriori::samples |
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* |
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* @param mixed[] $sample |
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*/ |
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private function support(array $sample): float |
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{ |
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return $this->frequency($sample) / count($this->samples); |
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} |
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/** |
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* Counts occurrences of $sample as subset in data pool. |
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* |
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* @see \Phpml\Association\Apriori::samples |
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* |
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* @param mixed[] $sample |
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*/ |
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private function frequency(array $sample): int |
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{ |
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return count(array_filter($this->samples, function ($entry) use ($sample): bool { |
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return $this->subset($entry, $sample); |
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})); |
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} |
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/** |
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* Returns true if set is an element of system. |
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* |
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* @see \Phpml\Association\Apriori::equals() |
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* |
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* @param mixed[][] $system |
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* @param mixed[] $set |
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*/ |
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private function contains(array $system, array $set): bool |
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{ |
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return (bool) array_filter($system, function ($entry) use ($set): bool { |
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return $this->equals($entry, $set); |
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}); |
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} |
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/** |
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* Returns true if subset is a (proper) subset of set by its items string representation. |
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* |
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* @param mixed[] $set |
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* @param mixed[] $subset |
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*/ |
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private function subset(array $set, array $subset): bool |
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{ |
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return count(array_diff($subset, array_intersect($subset, $set))) === 0; |
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} |
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/** |
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* Returns true if string representation of items does not differ. |
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* |
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* @param mixed[] $set1 |
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* @param mixed[] $set2 |
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*/ |
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private function equals(array $set1, array $set2): bool |
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{ |
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return array_diff($set1, $set2) == array_diff($set2, $set1); |
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} |
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} |
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