Update NaiveBayes.php (#30)

* Update NaiveBayes.php

* Update NaiveBayes.php

* Update NaiveBayes.php

Update to fix "predictSample" function to enable it handle samples given as multi-dimensional arrays.

* Update NaiveBayes.php

* Update NaiveBayes.php

src/Phpml/Classification/NaiveBayes.php

@@ -6,31 +6,152 @@
 
 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;
+    private $std = array();
+    private $mean= array();
+    private $discreteProb = array();
+    private $dataType = array();
+    private $p = array();
+    private $sampleCount = 0;
+    private $featureCount = 0;
+    private $labels = array();
+    public function train(array $samples, array $targets)
+    {
+        $this->samples = $samples;
+        $this->targets = $targets;
+        $this->sampleCount = count($samples);
+        $this->featureCount = count($samples[0]);
+        // Get distinct targets
+        $this->labels = $targets;
+        array_unique($this->labels);
+        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 $label
+     */
+    private function sampleProbability($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)
+    {
+        $samples = array();
+        for ($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)
     {
-        $predictions = [];
-        foreach ($this->targets as $index => $label) {
-            $predictions[$label] = 0;
-            foreach ($sample as $token => $count) {
-                if (array_key_exists($token, $this->samples[$index])) {
-                    $predictions[$label] += $count * $this->samples[$index][$token];
+        $isArray = is_array($sample[0]);
+        $samples = $sample;
+        if (!$isArray) {
+            $samples = array($sample);
+        }
+        $samplePredictions = array();
+        foreach ($samples as $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
+            $predictions = array();
+            foreach ($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);
+            $samplePredictions[] = key($predictions);
         }
-
-        arsort($predictions, SORT_NUMERIC);
-        reset($predictions);
-
-        return key($predictions);
+        if (! $isArray) {
+            return $samplePredictions[0];
+        }
+        return $samplePredictions;
     }
 }