php-ml/src/Phpml/Classification/NaiveBayes.php

<?php

declare(strict_types=1);

namespace Phpml\Classification;

use Phpml\Helper\Predictable;
use Phpml\Helper\Trainable;
use Phpml\Math\Statistic\Mean;
use Phpml\Math\Statistic\StandardDeviation;

class NaiveBayes implements Classifier
{
    use Trainable, Predictable;

    const CONTINUOS    = 1;
    const NOMINAL    = 2;
    const EPSILON = 1e-10;

    /**
     * @var array
     */
    private $std = [];

    /**
     * @var array
     */
    private $mean= [];

    /**
     * @var array
     */
    private $discreteProb = [];

    /**
     * @var array
     */
    private $dataType = [];

    /**
     * @var array
     */
    private $p = [];

    /**
     * @var int
     */
    private $sampleCount = 0;

    /**
     * @var int
     */
    private $featureCount = 0;

    /**
     * @var array
     */
    private $labels = [];

    /**
     * @param array $samples
     * @param array $targets
     */
    public function train(array $samples, array $targets)
    {
        $this->samples = array_merge($this->samples, $samples);
        $this->targets = array_merge($this->targets, $targets);
        $this->sampleCount = count($this->samples);
        $this->featureCount = count($this->samples[0]);

        $labelCounts = array_count_values($this->targets);
        $this->labels = array_keys($labelCounts);
        foreach ($this->labels as $label) {
            $samples = $this->getSamplesByLabel($label);
            $this->p[$label] = count($samples) / $this->sampleCount;
            $this->calculateStatistics($label, $samples);
        }
    }

    /**
     * Calculates vital statistics for each label & feature. Stores these
     * values in private array in order to avoid repeated calculation
     * @param string $label
     * @param array $samples
     */
    private function calculateStatistics($label, $samples)
    {
        $this->std[$label] = array_fill(0, $this->featureCount, 0);
        $this->mean[$label]= array_fill(0, $this->featureCount, 0);
        $this->dataType[$label] = array_fill(0, $this->featureCount, self::CONTINUOS);
        $this->discreteProb[$label] = array_fill(0, $this->featureCount, self::CONTINUOS);
        for ($i = 0; $i < $this->featureCount; ++$i) {
            // Get the values of nth column in the samples array
            // Mean::arithmetic is called twice, can be optimized
            $values = array_column($samples, $i);
            $numValues = count($values);
            // if the values contain non-numeric data,
            // then it should be treated as nominal/categorical/discrete column
            if ($values !== array_filter($values, 'is_numeric')) {
                $this->dataType[$label][$i] = self::NOMINAL;
                $this->discreteProb[$label][$i] = array_count_values($values);
                $db = &$this->discreteProb[$label][$i];
                $db = array_map(function ($el) use ($numValues) {
                    return $el / $numValues;
                }, $db);
            } else {
                $this->mean[$label][$i] = Mean::arithmetic($values);
                // Add epsilon in order to avoid zero stdev
                $this->std[$label][$i] = 1e-10 + StandardDeviation::population($values, false);
            }
        }
    }

    /**
     * Calculates the probability P(label|sample_n)
     *
     * @param array  $sample
     * @param int    $feature
     * @param string $label
     *
     * @return float
     */
    private function sampleProbability($sample, $feature, $label)
    {
        $value = $sample[$feature];
        if ($this->dataType[$label][$feature] == self::NOMINAL) {
            if (!isset($this->discreteProb[$label][$feature][$value]) ||
                $this->discreteProb[$label][$feature][$value] == 0) {
                return self::EPSILON;
            }
            return $this->discreteProb[$label][$feature][$value];
        }
        $std = $this->std[$label][$feature] ;
        $mean= $this->mean[$label][$feature];
        // Calculate the probability density by use of normal/Gaussian distribution
        // Ref: https://en.wikipedia.org/wiki/Normal_distribution
        //
        // In order to avoid numerical errors because of small or zero values,
        // some libraries adopt taking log of calculations such as
        // scikit-learn did.
        // (See : https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/naive_bayes.py)
        $pdf  =  -0.5 * log(2.0 * pi() * $std * $std);
        $pdf -= 0.5 * pow($value - $mean, 2) / ($std * $std);
        return $pdf;
    }

    /**
     * Return samples belonging to specific label
     *
     * @param string $label
     *
     * @return array
     */
    private function getSamplesByLabel($label)
    {
        $samples = [];
        for ($i = 0; $i < $this->sampleCount; ++$i) {
            if ($this->targets[$i] == $label) {
                $samples[] = $this->samples[$i];
            }
        }
        return $samples;
    }

    /**
     * @param array $sample
     * @return mixed
     */
    protected function predictSample(array $sample)
    {
        // Use NaiveBayes assumption for each label using:
        //	P(label|features) = P(label) * P(feature0|label) * P(feature1|label) .... P(featureN|label)
        // Then compare probability for each class to determine which label is most likely
        $predictions = [];
        foreach ($this->labels as $label) {
            $p = $this->p[$label];
            for ($i = 0; $i<$this->featureCount; ++$i) {
                $Plf = $this->sampleProbability($sample, $i, $label);
                $p += $Plf;
            }
            $predictions[$label] = $p;
        }

        arsort($predictions, SORT_NUMERIC);
        reset($predictions);
        return key($predictions);
    }
}