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# Association rule learning - Apriori algorithm
* Generating frequent k-length item sets * Generating rules based on frequent item sets * Algorithm has exponential complexity, be aware of it * Apriori algorithm is split into apriori and candidates method * Second step rule generation is implemented by rules method * Internal methods are invoked for fine grain unit tests * Wikipedia's train samples and an alternative are provided for test cases * Small documentation for public interface is also shipped
This commit is contained in:
Patrick Florek
parent
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commit
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1
.gitignore
vendored
1
.gitignore
vendored
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/.idea/
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/vendor/
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humbuglog.*
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/bin/phpunit
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54
docs/machine-learning/association/apriori.md
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54
docs/machine-learning/association/apriori.md
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# Apriori Associator
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Association rule learning based on [Apriori algorithm](https://en.wikipedia.org/wiki/Apriori_algorithm) for frequent item set mining.
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### Constructor Parameters
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* $support - [confidence](https://en.wikipedia.org/wiki/Association_rule_learning#Support), minimum relative amount of frequent item set in train sample
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* $confidence - [confidence](https://en.wikipedia.org/wiki/Association_rule_learning#Confidence), minimum relative amount of item set in frequent item sets
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```
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$associator = new \Phpml\Association\Apriori($support = 0.5, $confidence = 0.5);
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```
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### Train
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To train a associator simply provide train samples and labels (as `array`). Example:
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```
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$samples = [['alpha', 'beta', 'epsilon'], ['alpha', 'beta', 'theta'], ['alpha', 'beta', 'epsilon'], ['alpha', 'beta', 'theta']];
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$labels = [];
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$associator = new \Phpml\Association\Apriori(0.5, 0.5);
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$associator->train($samples, $labels);
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```
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### Predict
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To predict sample label use `predict` method. You can provide one sample or array of samples:
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```
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$associator->predict(['alpha','theta']);
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// return [[['beta']]]
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$associator->predict([['alpha','epsilon'],['beta','theta']]);
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// return [[['beta']], [['alpha']]]
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```
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### Associating
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Generating association rules simply use `rules` method.
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```
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$associator->rules();
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// return [['antecedent' => ['alpha', 'theta'], 'consequent' => ['beta], 'support' => 1.0, 'confidence' => 1.0], ... ]
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```
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### Frequent item sets
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Generating k-length frequent item sets simply use `apriori` method.
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```
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$associator->apriori();
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// return [ 1 => [['alpha'], ['beta'], ['theta'], ['epsilon']], 2 => [...], ...]
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```
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325
src/Phpml/Association/Apriori.php
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325
src/Phpml/Association/Apriori.php
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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, Predictable;
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const ARRAY_KEY_ANTECEDENT = 'antecedent';
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const ARRAY_KEY_CONFIDENCE = 'confidence';
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const ARRAY_KEY_CONSEQUENT = 'consequent';
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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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* @param float $support
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* @param float $confidence
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*/
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public function __construct($support = 0.0, $confidence = 0.0)
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{
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$this->support = $support;
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$this->confidence = $confidence;
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}
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/**
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* Generates apriori association rules.
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*
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* @return mixed[][]
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*/
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public function rules()
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{
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if (!$this->large) {
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$this->large = $this->apriori();
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}
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if ($this->rules) {
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return $this->rules;
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}
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$this->rules = [];
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for ($k = 2; !empty($this->large[$k]); ++$k) {
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foreach ($this->large[$k] as $frequent) {
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foreach ($this->antecedents($frequent) as $antecedent) {
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if ($this->confidence <= ($confidence = $this->confidence($frequent, $antecedent))) {
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$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 => $this->support($consequent),
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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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return $this->rules;
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}
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/**
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* Generates frequent item sets
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*
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* @return mixed[][][]
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*/
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public function apriori()
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{
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$L = [];
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$L[1] = $this->items();
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$L[1] = $this->frequent($L[1]);
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for ($k = 2; !empty($L[$k - 1]); ++$k) {
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$L[$k] = $this->candidates($L[$k - 1]);
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$L[$k] = $this->frequent($L[$k]);
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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 $sample)
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{
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$predicts = array_values(array_filter($this->rules(), function($rule) use ($sample) {
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return $this->equals($rule[self::ARRAY_KEY_ANTECEDENT], $sample);
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}));
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return array_map(function($rule) { return $rule[self::ARRAY_KEY_CONSEQUENT]; }, $predicts);
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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 $sample)
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{
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$results = [[]];
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foreach ($sample as $item) {
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foreach ($results as $combination) {
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$results[] = array_merge(array($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 $sample)
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{
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$cardinality = count($sample);
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$antecedents = $this->powerSet($sample);
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return array_filter($antecedents, function($antecedent) use ($cardinality) {
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return (count($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()
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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[] = $item;
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}
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}
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}
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return array_map(function($entry) {
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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 $samples)
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{
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return array_filter($samples, function($entry) {
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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 $samples)
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{
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$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_unique(array_merge($p, $q));
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if ($this->contains($candidates, $candidate)) {
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continue;
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}
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foreach ((array)$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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* @return float
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*/
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private function confidence(array $set, array $subset)
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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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* @return float
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*/
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private function support(array $sample)
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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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* @return int
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*/
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private function frequency(array $sample)
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{
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return count(array_filter($this->samples, function($entry) use ($sample) {
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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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* @return bool
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*/
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private function contains(array $system, array $set)
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{
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return (bool)array_filter($system, function($entry) use ($set) {
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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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* @return bool
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*/
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private function subset(array $set, array $subset)
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{
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return !array_diff($subset, array_intersect($subset, $set));
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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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* @return bool
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*/
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private function equals(array $set1, array $set2)
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{
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return array_diff($set1, $set2) == array_diff($set2, $set1);
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}
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}
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11
src/Phpml/Association/Associator.php
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11
src/Phpml/Association/Associator.php
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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\Estimator;
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interface Associator extends Estimator
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{
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}
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187
tests/Phpml/Association/AprioriTest.php
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187
tests/Phpml/Association/AprioriTest.php
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<?php
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declare(strict_types = 1);
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namespace tests\Classification;
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use Phpml\Association\Apriori;
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class AprioriTest extends \PHPUnit_Framework_TestCase
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{
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private $sampleGreek = [
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['alpha', 'beta', 'epsilon'],
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['alpha', 'beta', 'theta'],
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['alpha', 'beta', 'epsilon'],
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['alpha', 'beta', 'theta'],
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];
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private $sampleChars = [
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['E', 'D', 'N', 'E+N', 'EN'],
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['E', 'R', 'N', 'E+R', 'E+N', 'ER', 'EN'],
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['D', 'R'],
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['E', 'D', 'N', 'E+N'],
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['E', 'R', 'N', 'E+R', 'E+N', 'ER'],
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['E', 'D', 'R', 'E+R', 'ER'],
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['E', 'D', 'N', 'E+N', 'EN'],
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['E', 'R', 'E+R'],
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['E'],
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['N',],
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];
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private $sampleBasket = [
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[1, 2, 3, 4],
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[1, 2, 4],
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[1, 2],
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[2, 3, 4],
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[2, 3],
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[3, 4],
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[2, 4],
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];
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public function testGreek()
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{
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$apriori = new Apriori(0.5, 0.5);
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$apriori->train($this->sampleGreek, []);
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$this->assertEquals('beta', $apriori->predict([['alpha', 'epsilon'], ['beta', 'theta']])[0][0][0]);
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$this->assertEquals('alpha', $apriori->predict([['alpha', 'epsilon'], ['beta', 'theta']])[1][0][0]);
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}
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public function testPowerSet()
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{
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$apriori = new Apriori();
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$this->assertCount(8, $this->invoke($apriori, 'powerSet', [['a', 'b', 'c']]));
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}
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public function testApriori()
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{
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$apriori = new Apriori(3 / 7);
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$apriori->train($this->sampleBasket, []);
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$L = $apriori->apriori();
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$this->assertCount(0, $L[3]);
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$this->assertCount(4, $L[2]);
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$this->assertTrue($this->invoke($apriori, 'contains', [$L[2], [1, 2]]));
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$this->assertFalse($this->invoke($apriori, 'contains', [$L[2], [1, 3]]));
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$this->assertFalse($this->invoke($apriori, 'contains', [$L[2], [1, 4]]));
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$this->assertTrue($this->invoke($apriori, 'contains', [$L[2], [2, 3]]));
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$this->assertTrue($this->invoke($apriori, 'contains', [$L[2], [2, 4]]));
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$this->assertTrue($this->invoke($apriori, 'contains', [$L[2], [3, 4]]));
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}
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public function testRules()
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{
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$apriori = new Apriori(0.4, 0.8);
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$apriori->train($this->sampleChars, []);
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$this->assertCount(19, $apriori->rules());
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}
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public function testAntecedents()
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{
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$apriori = new Apriori();
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$this->assertCount(6, $this->invoke($apriori, 'antecedents', [['a', 'b', 'c']]));
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}
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public function testItems()
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{
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$apriori = new Apriori();
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$apriori->train($this->sampleGreek, []);
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$this->assertCount(4, $this->invoke($apriori, 'items', []));
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}
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public function testFrequent()
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{
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$apriori = new Apriori(0.51);
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$apriori->train($this->sampleGreek, []);
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$this->assertCount(0, $this->invoke($apriori, 'frequent', [[['epsilon'], ['theta']]]));
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$this->assertCount(2, $this->invoke($apriori, 'frequent', [[['alpha'], ['beta']]]));
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}
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public function testCandidates()
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{
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$apriori = new Apriori();
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$apriori->train($this->sampleGreek, []);
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$this->assertArraySubset([0 => ['alpha', 'beta']], $this->invoke($apriori, 'candidates', [[['alpha'], ['beta'], ['theta']]]));
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$this->assertArraySubset([1 => ['alpha', 'theta']], $this->invoke($apriori, 'candidates', [[['alpha'], ['beta'], ['theta']]]));
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$this->assertArraySubset([2 => ['beta', 'theta']], $this->invoke($apriori, 'candidates', [[['alpha'], ['beta'], ['theta']]]));
|
||||
$this->assertCount(3, $this->invoke($apriori, 'candidates', [[['alpha'], ['beta'], ['theta']]]));
|
||||
}
|
||||
|
||||
public function testConfidence()
|
||||
{
|
||||
$apriori = new Apriori();
|
||||
$apriori->train($this->sampleGreek, []);
|
||||
|
||||
$this->assertEquals(0.5, $this->invoke($apriori, 'confidence', [['alpha', 'beta', 'theta'], ['alpha', 'beta']]));
|
||||
$this->assertEquals(1, $this->invoke($apriori, 'confidence', [['alpha', 'beta'], ['alpha']]));
|
||||
}
|
||||
|
||||
public function testSupport()
|
||||
{
|
||||
$apriori = new Apriori();
|
||||
$apriori->train($this->sampleGreek, []);
|
||||
|
||||
$this->assertEquals(1.0, $this->invoke($apriori, 'support', [['alpha', 'beta']]));
|
||||
$this->assertEquals(0.5, $this->invoke($apriori, 'support', [['epsilon']]));
|
||||
}
|
||||
|
||||
public function testFrequency()
|
||||
{
|
||||
$apriori = new Apriori();
|
||||
$apriori->train($this->sampleGreek, []);
|
||||
|
||||
$this->assertEquals(4, $this->invoke($apriori, 'frequency', [['alpha', 'beta']]));
|
||||
$this->assertEquals(2, $this->invoke($apriori, 'frequency', [['epsilon']]));
|
||||
}
|
||||
|
||||
public function testContains()
|
||||
{
|
||||
$apriori = new Apriori();
|
||||
|
||||
$this->assertTrue($this->invoke($apriori, 'contains', [[['a'], ['b']], ['a']]));
|
||||
$this->assertTrue($this->invoke($apriori, 'contains', [[[1, 2]], [1, 2]]));
|
||||
$this->assertFalse($this->invoke($apriori, 'contains', [[['a'], ['b']], ['c']]));
|
||||
}
|
||||
|
||||
public function testSubset()
|
||||
{
|
||||
$apriori = new Apriori();
|
||||
|
||||
$this->assertTrue($this->invoke($apriori, 'subset', [['a', 'b'], ['a']]));
|
||||
$this->assertTrue($this->invoke($apriori, 'subset', [['a'], ['a']]));
|
||||
$this->assertFalse($this->invoke($apriori, 'subset', [['a'], ['a', 'b']]));
|
||||
}
|
||||
|
||||
public function testEquals()
|
||||
{
|
||||
$apriori = new Apriori();
|
||||
|
||||
$this->assertTrue($this->invoke($apriori, 'equals', [['a'], ['a']]));
|
||||
$this->assertFalse($this->invoke($apriori, 'equals', [['a'], []]));
|
||||
$this->assertFalse($this->invoke($apriori, 'equals', [['a'], ['b', 'a']]));
|
||||
}
|
||||
|
||||
/**
|
||||
* Invokes objects method. Private/protected will be set accessible.
|
||||
*
|
||||
* @param object &$object Instantiated object to be called on
|
||||
* @param string $method Method name to be called
|
||||
* @param array $params Array of params to be passed
|
||||
*
|
||||
* @return mixed
|
||||
*/
|
||||
public function invoke(&$object, $method, array $params = array())
|
||||
{
|
||||
$reflection = new \ReflectionClass(get_class($object));
|
||||
$method = $reflection->getMethod($method);
|
||||
$method->setAccessible(true);
|
||||
|
||||
return $method->invokeArgs($object, $params);
|
||||
}
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user