DecisionTree and Fuzzy C Means classifiers (#35)
* Fuzzy C-Means implementation * Update FuzzyCMeans * Rename FuzzyCMeans to FuzzyCMeans.php * Update NaiveBayes.php * Small fix applied to improve training performance array_unique is replaced with array_count_values+array_keys which is way faster * Revert "Small fix applied to improve training performance" This reverts commit c20253f16ac3e8c37d33ecaee28a87cc767e3b7f. * Revert "Revert "Small fix applied to improve training performance"" This reverts commit ea10e136c4c11b71609ccdcaf9999067e4be473e. * Revert "Small fix applied to improve training performance" This reverts commit c20253f16ac3e8c37d33ecaee28a87cc767e3b7f. * DecisionTree * FCM Test * FCM Test * DecisionTree Test
This commit is contained in:
Mustafa Karabulut
Arkadiusz Kondas
parent
95fc139170
commit
87396ebe58
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@ -0,0 +1,274 @@
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<?php
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declare(strict_types=1);
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namespace Phpml\Classification;
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use Phpml\Helper\Predictable;
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use Phpml\Helper\Trainable;
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use Phpml\Math\Statistic\Mean;
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use Phpml\Classification\DecisionTree\DecisionTreeLeaf;
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class DecisionTree implements Classifier
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{
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use Trainable, Predictable;
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const CONTINUOS = 1;
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const NOMINAL = 2;
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/**
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* @var array
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*/
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private $samples = array();
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/**
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* @var array
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*/
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private $columnTypes;
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/**
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* @var array
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*/
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private $labels = array();
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/**
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* @var int
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*/
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private $featureCount = 0;
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/**
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* @var DecisionTreeLeaf
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*/
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private $tree = null;
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/**
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* @var int
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*/
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private $maxDepth;
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/**
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* @var int
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*/
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public $actualDepth = 0;
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/**
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* @param int $maxDepth
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*/
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public function __construct($maxDepth = 10)
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{
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$this->maxDepth = $maxDepth;
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}
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/**
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* @param array $samples
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* @param array $targets
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*/
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public function train(array $samples, array $targets)
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{
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$this->featureCount = count($samples[0]);
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$this->columnTypes = $this->getColumnTypes($samples);
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$this->samples = $samples;
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$this->targets = $targets;
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$this->labels = array_keys(array_count_values($targets));
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$this->tree = $this->getSplitLeaf(range(0, count($samples) - 1));
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}
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protected function getColumnTypes(array $samples)
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{
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$types = [];
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for ($i=0; $i<$this->featureCount; $i++) {
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$values = array_column($samples, $i);
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$isCategorical = $this->isCategoricalColumn($values);
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$types[] = $isCategorical ? self::NOMINAL : self::CONTINUOS;
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}
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return $types;
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}
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/**
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* @param null|array $records
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* @return DecisionTreeLeaf
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*/
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protected function getSplitLeaf($records, $depth = 0)
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{
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$split = $this->getBestSplit($records);
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$split->level = $depth;
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if ($this->actualDepth < $depth) {
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$this->actualDepth = $depth;
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}
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$leftRecords = [];
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$rightRecords= [];
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$remainingTargets = [];
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$prevRecord = null;
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$allSame = true;
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foreach ($records as $recordNo) {
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$record = $this->samples[$recordNo];
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if ($prevRecord && $prevRecord != $record) {
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$allSame = false;
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}
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$prevRecord = $record;
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if ($split->evaluate($record)) {
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$leftRecords[] = $recordNo;
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} else {
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$rightRecords[]= $recordNo;
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}
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$target = $this->targets[$recordNo];
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if (! in_array($target, $remainingTargets)) {
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$remainingTargets[] = $target;
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}
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}
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if (count($remainingTargets) == 1 || $allSame || $depth >= $this->maxDepth) {
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$split->isTerminal = 1;
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$classes = array_count_values($remainingTargets);
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arsort($classes);
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$split->classValue = key($classes);
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} else {
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if ($leftRecords) {
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$split->leftLeaf = $this->getSplitLeaf($leftRecords, $depth + 1);
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}
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if ($rightRecords) {
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$split->rightLeaf= $this->getSplitLeaf($rightRecords, $depth + 1);
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}
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}
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return $split;
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}
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/**
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* @param array $records
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* @return DecisionTreeLeaf[]
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*/
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protected function getBestSplit($records)
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{
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$targets = array_intersect_key($this->targets, array_flip($records));
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$samples = array_intersect_key($this->samples, array_flip($records));
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$samples = array_combine($records, $this->preprocess($samples));
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$bestGiniVal = 1;
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$bestSplit = null;
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for ($i=0; $i<$this->featureCount; $i++) {
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$colValues = [];
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$baseValue = null;
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foreach ($samples as $index => $row) {
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$colValues[$index] = $row[$i];
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if ($baseValue === null) {
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$baseValue = $row[$i];
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}
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}
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$gini = $this->getGiniIndex($baseValue, $colValues, $targets);
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if ($bestSplit == null || $bestGiniVal > $gini) {
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$split = new DecisionTreeLeaf();
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$split->value = $baseValue;
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$split->giniIndex = $gini;
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$split->columnIndex = $i;
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$split->records = $records;
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$bestSplit = $split;
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$bestGiniVal = $gini;
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}
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}
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return $bestSplit;
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}
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/**
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* @param string $baseValue
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* @param array $colValues
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* @param array $targets
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*/
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public function getGiniIndex($baseValue, $colValues, $targets)
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{
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$countMatrix = [];
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foreach ($this->labels as $label) {
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$countMatrix[$label] = [0, 0];
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}
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foreach ($colValues as $index => $value) {
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$label = $targets[$index];
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$rowIndex = $value == $baseValue ? 0 : 1;
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$countMatrix[$label][$rowIndex]++;
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}
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$giniParts = [0, 0];
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for ($i=0; $i<=1; $i++) {
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$part = 0;
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$sum = array_sum(array_column($countMatrix, $i));
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if ($sum > 0) {
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foreach ($this->labels as $label) {
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$part += pow($countMatrix[$label][$i] / floatval($sum), 2);
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}
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}
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$giniParts[$i] = (1 - $part) * $sum;
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}
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return array_sum($giniParts) / count($colValues);
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}
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/**
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* @param array $samples
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* @return array
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*/
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protected function preprocess(array $samples)
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{
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// Detect and convert continuous data column values into
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// discrete values by using the median as a threshold value
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$columns = array();
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for ($i=0; $i<$this->featureCount; $i++) {
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$values = array_column($samples, $i);
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if ($this->columnTypes[$i] == self::CONTINUOS) {
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$median = Mean::median($values);
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foreach ($values as &$value) {
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if ($value <= $median) {
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$value = "<= $median";
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} else {
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$value = "> $median";
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}
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}
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}
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$columns[] = $values;
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}
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// Below method is a strange yet very simple & efficient method
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// to get the transpose of a 2D array
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return array_map(null, ...$columns);
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}
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/**
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* @param array $columnValues
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* @return bool
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*/
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protected function isCategoricalColumn(array $columnValues)
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{
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$count = count($columnValues);
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// There are two main indicators that *may* show whether a
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// column is composed of discrete set of values:
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// 1- Column may contain string values
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// 2- Number of unique values in the column is only a small fraction of
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// all values in that column (Lower than or equal to %20 of all values)
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$numericValues = array_filter($columnValues, 'is_numeric');
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if (count($numericValues) != $count) {
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return true;
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}
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$distinctValues = array_count_values($columnValues);
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if (count($distinctValues) <= $count / 5) {
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return true;
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}
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return false;
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}
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/**
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* @return string
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*/
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public function getHtml()
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{
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return $this->tree->__toString();
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}
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/**
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* @param array $sample
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* @return mixed
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*/
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protected function predictSample(array $sample)
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{
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$node = $this->tree;
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do {
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if ($node->isTerminal) {
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break;
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}
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if ($node->evaluate($sample)) {
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$node = $node->leftLeaf;
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} else {
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$node = $node->rightLeaf;
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}
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} while ($node);
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return $node->classValue;
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}
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}
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@ -0,0 +1,106 @@
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<?php
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declare(strict_types=1);
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namespace Phpml\Classification\DecisionTree;
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class DecisionTreeLeaf
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{
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const OPERATOR_EQ = '=';
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/**
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* @var string
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*/
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public $value;
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/**
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* @var int
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*/
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public $columnIndex;
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/**
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* @var DecisionTreeLeaf
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*/
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public $leftLeaf = null;
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/**
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* @var DecisionTreeLeaf
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*/
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public $rightLeaf= null;
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/**
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* @var array
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*/
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public $records = [];
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/**
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* Class value represented by the leaf, this value is non-empty
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* only for terminal leaves
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*
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* @var string
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*/
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public $classValue = '';
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/**
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* @var bool
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*/
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public $isTerminal = false;
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/**
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* @var float
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*/
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public $giniIndex = 0;
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/**
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* @var int
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*/
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public $level = 0;
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/**
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* @param array $record
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* @return bool
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*/
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public function evaluate($record)
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{
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$recordField = $record[$this->columnIndex];
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if (preg_match("/^([<>=]{1,2})\s*(.*)/", $this->value, $matches)) {
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$op = $matches[1];
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$value= floatval($matches[2]);
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$recordField = strval($recordField);
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eval("\$result = $recordField $op $value;");
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return $result;
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}
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return $recordField == $this->value;
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}
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public function __toString()
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{
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if ($this->isTerminal) {
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$value = "<b>$this->classValue</b>";
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} else {
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$value = $this->value;
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$col = "col_$this->columnIndex";
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if (! preg_match("/^[<>=]{1,2}/", $value)) {
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$value = "=$value";
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}
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$value = "<b>$col $value</b><br>Gini: ". number_format($this->giniIndex, 2);
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}
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$str = "<table ><tr><td colspan=3 align=center style='border:1px solid;'>
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$value</td></tr>";
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if ($this->leftLeaf || $this->rightLeaf) {
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$str .='<tr>';
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if ($this->leftLeaf) {
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$str .="<td valign=top><b>| Yes</b><br>$this->leftLeaf</td>";
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} else {
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$str .='<td></td>';
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}
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$str .='<td> </td>';
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if ($this->rightLeaf) {
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$str .="<td valign=top align=right><b>No |</b><br>$this->rightLeaf</td>";
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} else {
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$str .='<td></td>';
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}
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$str .= '</tr>';
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}
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$str .= '</table>';
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return $str;
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}
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}
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@ -68,8 +68,8 @@ class NaiveBayes implements Classifier
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$this->sampleCount = count($samples);
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$this->featureCount = count($samples[0]);
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$this->labels = $targets;
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array_unique($this->labels);
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$labelCounts = array_count_values($targets);
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$this->labels = array_keys($labelCounts);
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foreach ($this->labels as $label) {
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$samples = $this->getSamplesByLabel($label);
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$this->p[$label] = count($samples) / $this->sampleCount;
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@ -165,32 +165,20 @@ class NaiveBayes implements Classifier
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*/
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protected function predictSample(array $sample)
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{
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$isArray = is_array($sample[0]);
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$samples = $sample;
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if (!$isArray) {
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$samples = array($sample);
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}
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$samplePredictions = array();
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foreach ($samples as $sample) {
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// Use NaiveBayes assumption for each label using:
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// P(label|features) = P(label) * P(feature0|label) * P(feature1|label) .... P(featureN|label)
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// Then compare probability for each class to determine which label is most likely
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$predictions = array();
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foreach ($this->labels as $label) {
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$p = $this->p[$label];
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for ($i=0; $i<$this->featureCount; $i++) {
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$Plf = $this->sampleProbability($sample, $i, $label);
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$p += $Plf;
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}
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$predictions[$label] = $p;
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// Use NaiveBayes assumption for each label using:
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// P(label|features) = P(label) * P(feature0|label) * P(feature1|label) .... P(featureN|label)
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// Then compare probability for each class to determine which label is most likely
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$predictions = array();
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foreach ($this->labels as $label) {
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$p = $this->p[$label];
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for ($i=0; $i<$this->featureCount; $i++) {
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$Plf = $this->sampleProbability($sample, $i, $label);
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$p += $Plf;
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}
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arsort($predictions, SORT_NUMERIC);
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reset($predictions);
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$samplePredictions[] = key($predictions);
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$predictions[$label] = $p;
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}
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if (! $isArray) {
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return $samplePredictions[0];
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}
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return $samplePredictions;
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arsort($predictions, SORT_NUMERIC);
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reset($predictions);
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return key($predictions);
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}
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}
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@ -0,0 +1,242 @@
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<?php
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declare(strict_types=1);
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namespace Phpml\Clustering;
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use Phpml\Clustering\KMeans\Point;
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use Phpml\Clustering\KMeans\Cluster;
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use Phpml\Clustering\KMeans\Space;
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use Phpml\Math\Distance\Euclidean;
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class FuzzyCMeans implements Clusterer
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{
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/**
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* @var int
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*/
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private $clustersNumber;
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/**
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* @var array|Cluster[]
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*/
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private $clusters = null;
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/**
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* @var Space
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*/
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private $space;
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/**
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* @var array|float[][]
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*/
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private $membership;
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/**
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* @var float
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*/
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private $fuzziness;
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/**
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* @var float
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*/
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private $epsilon;
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/**
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* @var int
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*/
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private $maxIterations;
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/**
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* @var int
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*/
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private $sampleCount;
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/**
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* @var array
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*/
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private $samples;
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/**
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* @param int $clustersNumber
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*
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* @throws InvalidArgumentException
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*/
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public function __construct(int $clustersNumber, float $fuzziness = 2.0, float $epsilon = 1e-2, int $maxIterations = 100)
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{
|
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if ($clustersNumber <= 0) {
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throw InvalidArgumentException::invalidClustersNumber();
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}
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$this->clustersNumber = $clustersNumber;
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$this->fuzziness = $fuzziness;
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$this->epsilon = $epsilon;
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$this->maxIterations = $maxIterations;
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}
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protected function initClusters()
|
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{
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// Membership array is a matrix of cluster number by sample counts
|
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// We initilize the membership array with random values
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$dim = $this->space->getDimension();
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$this->generateRandomMembership($dim, $this->sampleCount);
|
||||
$this->updateClusters();
|
||||
}
|
||||
|
||||
/**
|
||||
* @param int $rows
|
||||
* @param int $cols
|
||||
*/
|
||||
protected function generateRandomMembership(int $rows, int $cols)
|
||||
{
|
||||
$this->membership = [];
|
||||
for ($i=0; $i < $rows; $i++) {
|
||||
$row = [];
|
||||
$total = 0.0;
|
||||
for ($k=0; $k < $cols; $k++) {
|
||||
$val = rand(1, 5) / 10.0;
|
||||
$row[] = $val;
|
||||
$total += $val;
|
||||
}
|
||||
$this->membership[] = array_map(function ($val) use ($total) {
|
||||
return $val / $total;
|
||||
}, $row);
|
||||
}
|
||||
}
|
||||
|
||||
protected function updateClusters()
|
||||
{
|
||||
$dim = $this->space->getDimension();
|
||||
if (! $this->clusters) {
|
||||
$this->clusters = [];
|
||||
for ($i=0; $i<$this->clustersNumber; $i++) {
|
||||
$this->clusters[] = new Cluster($this->space, array_fill(0, $dim, 0.0));
|
||||
}
|
||||
}
|
||||
|
||||
for ($i=0; $i<$this->clustersNumber; $i++) {
|
||||
$cluster = $this->clusters[$i];
|
||||
$center = $cluster->getCoordinates();
|
||||
for ($k=0; $k<$dim; $k++) {
|
||||
$a = $this->getMembershipRowTotal($i, $k, true);
|
||||
$b = $this->getMembershipRowTotal($i, $k, false);
|
||||
$center[$k] = $a / $b;
|
||||
}
|
||||
$cluster->setCoordinates($center);
|
||||
}
|
||||
}
|
||||
|
||||
protected function getMembershipRowTotal(int $row, int $col, bool $multiply)
|
||||
{
|
||||
$sum = 0.0;
|
||||
for ($k = 0; $k < $this->sampleCount; $k++) {
|
||||
$val = pow($this->membership[$row][$k], $this->fuzziness);
|
||||
if ($multiply) {
|
||||
$val *= $this->samples[$k][$col];
|
||||
}
|
||||
$sum += $val;
|
||||
}
|
||||
return $sum;
|
||||
}
|
||||
|
||||
protected function updateMembershipMatrix()
|
||||
{
|
||||
for ($i = 0; $i < $this->clustersNumber; $i++) {
|
||||
for ($k = 0; $k < $this->sampleCount; $k++) {
|
||||
$distCalc = $this->getDistanceCalc($i, $k);
|
||||
$this->membership[$i][$k] = 1.0 / $distCalc;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
*
|
||||
* @param int $row
|
||||
* @param int $col
|
||||
* @return float
|
||||
*/
|
||||
protected function getDistanceCalc(int $row, int $col)
|
||||
{
|
||||
$sum = 0.0;
|
||||
$distance = new Euclidean();
|
||||
$dist1 = $distance->distance(
|
||||
$this->clusters[$row]->getCoordinates(),
|
||||
$this->samples[$col]);
|
||||
for ($j = 0; $j < $this->clustersNumber; $j++) {
|
||||
$dist2 = $distance->distance(
|
||||
$this->clusters[$j]->getCoordinates(),
|
||||
$this->samples[$col]);
|
||||
$val = pow($dist1 / $dist2, 2.0 / ($this->fuzziness - 1));
|
||||
$sum += $val;
|
||||
}
|
||||
return $sum;
|
||||
}
|
||||
|
||||
/**
|
||||
* The objective is to minimize the distance between all data points
|
||||
* and all cluster centers. This method returns the summation of all
|
||||
* these distances
|
||||
*/
|
||||
protected function getObjective()
|
||||
{
|
||||
$sum = 0.0;
|
||||
$distance = new Euclidean();
|
||||
for ($i = 0; $i < $this->clustersNumber; $i++) {
|
||||
$clust = $this->clusters[$i]->getCoordinates();
|
||||
for ($k = 0; $k < $this->sampleCount; $k++) {
|
||||
$point = $this->samples[$k];
|
||||
$sum += $distance->distance($clust, $point);
|
||||
}
|
||||
}
|
||||
return $sum;
|
||||
}
|
||||
|
||||
/**
|
||||
* @return array
|
||||
*/
|
||||
public function getMembershipMatrix()
|
||||
{
|
||||
return $this->membership;
|
||||
}
|
||||
|
||||
/**
|
||||
* @param array|Point[] $samples
|
||||
* @return array
|
||||
*/
|
||||
public function cluster(array $samples)
|
||||
{
|
||||
// Initialize variables, clusters and membership matrix
|
||||
$this->sampleCount = count($samples);
|
||||
$this->samples =& $samples;
|
||||
$this->space = new Space(count($samples[0]));
|
||||
$this->initClusters();
|
||||
|
||||
// Our goal is minimizing the objective value while
|
||||
// executing the clustering steps at a maximum number of iterations
|
||||
$lastObjective = 0.0;
|
||||
$difference = 0.0;
|
||||
$iterations = 0;
|
||||
do {
|
||||
// Update the membership matrix and cluster centers, respectively
|
||||
$this->updateMembershipMatrix();
|
||||
$this->updateClusters();
|
||||
|
||||
// Calculate the new value of the objective function
|
||||
$objectiveVal = $this->getObjective();
|
||||
$difference = abs($lastObjective - $objectiveVal);
|
||||
$lastObjective = $objectiveVal;
|
||||
} while ($difference > $this->epsilon && $iterations++ <= $this->maxIterations);
|
||||
|
||||
// Attach (hard cluster) each data point to the nearest cluster
|
||||
for ($k=0; $k<$this->sampleCount; $k++) {
|
||||
$column = array_column($this->membership, $k);
|
||||
arsort($column);
|
||||
reset($column);
|
||||
$i = key($column);
|
||||
$cluster = $this->clusters[$i];
|
||||
$cluster->attach(new Point($this->samples[$k]));
|
||||
}
|
||||
|
||||
// Return grouped samples
|
||||
$grouped = [];
|
||||
foreach ($this->clusters as $cluster) {
|
||||
$grouped[] = $cluster->getPoints();
|
||||
}
|
||||
return $grouped;
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,60 @@
|
|||
<?php
|
||||
|
||||
declare(strict_types=1);
|
||||
|
||||
namespace tests\Classification;
|
||||
|
||||
use Phpml\Classification\DecisionTree;
|
||||
|
||||
class DecisionTreeTest extends \PHPUnit_Framework_TestCase
|
||||
{
|
||||
public $data = [
|
||||
['sunny', 85, 85, 'false', 'Dont_play' ],
|
||||
['sunny', 80, 90, 'true', 'Dont_play' ],
|
||||
['overcast', 83, 78, 'false', 'Play' ],
|
||||
['rain', 70, 96, 'false', 'Play' ],
|
||||
['rain', 68, 80, 'false', 'Play' ],
|
||||
['rain', 65, 70, 'true', 'Dont_play' ],
|
||||
['overcast', 64, 65, 'true', 'Play' ],
|
||||
['sunny', 72, 95, 'false', 'Dont_play' ],
|
||||
['sunny', 69, 70, 'false', 'Play' ],
|
||||
['rain', 75, 80, 'false', 'Play' ],
|
||||
['sunny', 75, 70, 'true', 'Play' ],
|
||||
['overcast', 72, 90, 'true', 'Play' ],
|
||||
['overcast', 81, 75, 'false', 'Play' ],
|
||||
['rain', 71, 80, 'true', 'Dont_play' ]
|
||||
];
|
||||
|
||||
public function getData()
|
||||
{
|
||||
static $data = null, $targets = null;
|
||||
if ($data == null) {
|
||||
$data = $this->data;
|
||||
$targets = array_column($data, 4);
|
||||
array_walk($data, function (&$v) {
|
||||
array_splice($v, 4, 1);
|
||||
});
|
||||
}
|
||||
return [$data, $targets];
|
||||
}
|
||||
|
||||
public function testPredictSingleSample()
|
||||
{
|
||||
list($data, $targets) = $this->getData();
|
||||
$classifier = new DecisionTree(5);
|
||||
$classifier->train($data, $targets);
|
||||
$this->assertEquals('Dont_play', $classifier->predict(['sunny', 78, 72, 'false']));
|
||||
$this->assertEquals('Play', $classifier->predict(['overcast', 60, 60, 'false']));
|
||||
$this->assertEquals('Dont_play', $classifier->predict(['rain', 60, 60, 'true']));
|
||||
|
||||
return $classifier;
|
||||
}
|
||||
|
||||
public function testTreeDepth()
|
||||
{
|
||||
list($data, $targets) = $this->getData();
|
||||
$classifier = new DecisionTree(5);
|
||||
$classifier->train($data, $targets);
|
||||
$this->assertTrue(5 >= $classifier->actualDepth);
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,43 @@
|
|||
<?php
|
||||
declare(strict_types=1);
|
||||
|
||||
namespace tests\Clustering;
|
||||
|
||||
use Phpml\Clustering\FuzzyCMeans;
|
||||
|
||||
class FuzzyCMeansTest extends \PHPUnit_Framework_TestCase
|
||||
{
|
||||
public function testFCMSamplesClustering()
|
||||
{
|
||||
$samples = [[1, 1], [8, 7], [1, 2], [7, 8], [2, 1], [8, 9]];
|
||||
$fcm = new FuzzyCMeans(2);
|
||||
$clusters = $fcm->cluster($samples);
|
||||
$this->assertCount(2, $clusters);
|
||||
foreach ($samples as $index => $sample) {
|
||||
if (in_array($sample, $clusters[0]) || in_array($sample, $clusters[1])) {
|
||||
unset($samples[$index]);
|
||||
}
|
||||
}
|
||||
$this->assertCount(0, $samples);
|
||||
return $fcm;
|
||||
}
|
||||
|
||||
public function testMembershipMatrix()
|
||||
{
|
||||
$fcm = $this->testFCMSamplesClustering();
|
||||
$clusterCount = 2;
|
||||
$sampleCount = 6;
|
||||
$matrix = $fcm->getMembershipMatrix();
|
||||
$this->assertCount($clusterCount, $matrix);
|
||||
foreach ($matrix as $row) {
|
||||
$this->assertCount($sampleCount, $row);
|
||||
}
|
||||
// Transpose of the matrix
|
||||
array_unshift($matrix, null);
|
||||
$matrix = call_user_func_array('array_map', $matrix);
|
||||
// All column totals should be equal to 1 (100% membership)
|
||||
foreach ($matrix as $col) {
|
||||
$this->assertEquals(1, array_sum($col));
|
||||
}
|
||||
}
|
||||
}
|
||||
Loading…
Reference in New Issue