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DecisionTree and Fuzzy C Means classifiers (#35)

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* 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 2017-01-31 21:27:15 +02:00 committed by Arkadiusz Kondas
parent 95fc139170
commit 87396ebe58
6 changed files with 740 additions and 27 deletions
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274
src/Phpml/Classification/DecisionTree.php Normal file
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<?php
declare(strict_types=1);
namespace Phpml\Classification;
use Phpml\Helper\Predictable;
use Phpml\Helper\Trainable;
use Phpml\Math\Statistic\Mean;
use Phpml\Classification\DecisionTree\DecisionTreeLeaf;
class DecisionTree implements Classifier
{
use Trainable, Predictable;
const CONTINUOS = 1;
const NOMINAL = 2;
/**
* @var array
*/
private $samples = array();
/**
* @var array
*/
private $columnTypes;
/**
* @var array
*/
private $labels = array();
/**
* @var int
*/
private $featureCount = 0;
/**
* @var DecisionTreeLeaf
*/
private $tree = null;
/**
* @var int
*/
private $maxDepth;
/**
* @var int
*/
public $actualDepth = 0;
/**
* @param int $maxDepth
*/
public function __construct($maxDepth = 10)
{
$this->maxDepth = $maxDepth;
}
/**
* @param array $samples
* @param array $targets
*/
public function train(array $samples, array $targets)
{
$this->featureCount = count($samples[0]);
$this->columnTypes = $this->getColumnTypes($samples);
$this->samples = $samples;
$this->targets = $targets;
$this->labels = array_keys(array_count_values($targets));
$this->tree = $this->getSplitLeaf(range(0, count($samples) - 1));
}
protected function getColumnTypes(array $samples)
{
$types = [];
for ($i=0; $i<$this->featureCount; $i++) {
$values = array_column($samples, $i);
$isCategorical = $this->isCategoricalColumn($values);
$types[] = $isCategorical ? self::NOMINAL : self::CONTINUOS;
}
return $types;
}
/**
* @param null|array $records
* @return DecisionTreeLeaf
*/
protected function getSplitLeaf($records, $depth = 0)
{
$split = $this->getBestSplit($records);
$split->level = $depth;
if ($this->actualDepth < $depth) {
$this->actualDepth = $depth;
}
$leftRecords = [];
$rightRecords= [];
$remainingTargets = [];
$prevRecord = null;
$allSame = true;
foreach ($records as $recordNo) {
$record = $this->samples[$recordNo];
if ($prevRecord && $prevRecord != $record) {
$allSame = false;
}
$prevRecord = $record;
if ($split->evaluate($record)) {
$leftRecords[] = $recordNo;
} else {
$rightRecords[]= $recordNo;
}
$target = $this->targets[$recordNo];
if (! in_array($target, $remainingTargets)) {
$remainingTargets[] = $target;
}
}
if (count($remainingTargets) == 1 || $allSame || $depth >= $this->maxDepth) {
$split->isTerminal = 1;
$classes = array_count_values($remainingTargets);
arsort($classes);
$split->classValue = key($classes);
} else {
if ($leftRecords) {
$split->leftLeaf = $this->getSplitLeaf($leftRecords, $depth + 1);
}
if ($rightRecords) {
$split->rightLeaf= $this->getSplitLeaf($rightRecords, $depth + 1);
}
}
return $split;
}
/**
* @param array $records
* @return DecisionTreeLeaf[]
*/
protected function getBestSplit($records)
{
$targets = array_intersect_key($this->targets, array_flip($records));
$samples = array_intersect_key($this->samples, array_flip($records));
$samples = array_combine($records, $this->preprocess($samples));
$bestGiniVal = 1;
$bestSplit = null;
for ($i=0; $i<$this->featureCount; $i++) {
$colValues = [];
$baseValue = null;
foreach ($samples as $index => $row) {
$colValues[$index] = $row[$i];
if ($baseValue === null) {
$baseValue = $row[$i];
}
}
$gini = $this->getGiniIndex($baseValue, $colValues, $targets);
if ($bestSplit == null || $bestGiniVal > $gini) {
$split = new DecisionTreeLeaf();
$split->value = $baseValue;
$split->giniIndex = $gini;
$split->columnIndex = $i;
$split->records = $records;
$bestSplit = $split;
$bestGiniVal = $gini;
}
}
return $bestSplit;
}
/**
* @param string $baseValue
* @param array $colValues
* @param array $targets
*/
public function getGiniIndex($baseValue, $colValues, $targets)
{
$countMatrix = [];
foreach ($this->labels as $label) {
$countMatrix[$label] = [0, 0];
}
foreach ($colValues as $index => $value) {
$label = $targets[$index];
$rowIndex = $value == $baseValue ? 0 : 1;
$countMatrix[$label][$rowIndex]++;
}
$giniParts = [0, 0];
for ($i=0; $i<=1; $i++) {
$part = 0;
$sum = array_sum(array_column($countMatrix, $i));
if ($sum > 0) {
foreach ($this->labels as $label) {
$part += pow($countMatrix[$label][$i] / floatval($sum), 2);
}
}
$giniParts[$i] = (1 - $part) * $sum;
}
return array_sum($giniParts) / count($colValues);
}
/**
* @param array $samples
* @return array
*/
protected function preprocess(array $samples)
{
// Detect and convert continuous data column values into
// discrete values by using the median as a threshold value
$columns = array();
for ($i=0; $i<$this->featureCount; $i++) {
$values = array_column($samples, $i);
if ($this->columnTypes[$i] == self::CONTINUOS) {
$median = Mean::median($values);
foreach ($values as &$value) {
if ($value <= $median) {
$value = "<= $median";
} else {
$value = "> $median";
}
}
}
$columns[] = $values;
}
// Below method is a strange yet very simple & efficient method
// to get the transpose of a 2D array
return array_map(null, ...$columns);
}
/**
* @param array $columnValues
* @return bool
*/
protected function isCategoricalColumn(array $columnValues)
{
$count = count($columnValues);
// There are two main indicators that *may* show whether a
// column is composed of discrete set of values:
// 1- Column may contain string values
// 2- Number of unique values in the column is only a small fraction of
// all values in that column (Lower than or equal to %20 of all values)
$numericValues = array_filter($columnValues, 'is_numeric');
if (count($numericValues) != $count) {
return true;
}
$distinctValues = array_count_values($columnValues);
if (count($distinctValues) <= $count / 5) {
return true;
}
return false;
}
/**
* @return string
*/
public function getHtml()
{
return $this->tree->__toString();
}
/**
* @param array $sample
* @return mixed
*/
protected function predictSample(array $sample)
{
$node = $this->tree;
do {
if ($node->isTerminal) {
break;
}
if ($node->evaluate($sample)) {
$node = $node->leftLeaf;
} else {
$node = $node->rightLeaf;
}
} while ($node);
return $node->classValue;
}
}

106
src/Phpml/Classification/DecisionTree/DecisionTreeLeaf.php Normal file
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<?php
declare(strict_types=1);
namespace Phpml\Classification\DecisionTree;
class DecisionTreeLeaf
{
const OPERATOR_EQ = '=';
/**
* @var string
*/
public $value;
/**
* @var int
*/
public $columnIndex;
/**
* @var DecisionTreeLeaf
*/
public $leftLeaf = null;
/**
* @var DecisionTreeLeaf
*/
public $rightLeaf= null;
/**
* @var array
*/
public $records = [];
/**
* Class value represented by the leaf, this value is non-empty
* only for terminal leaves
*
* @var string
*/
public $classValue = '';
/**
* @var bool
*/
public $isTerminal = false;
/**
* @var float
*/
public $giniIndex = 0;
/**
* @var int
*/
public $level = 0;
/**
* @param array $record
* @return bool
*/
public function evaluate($record)
{
$recordField = $record[$this->columnIndex];
if (preg_match("/^([<>=]{1,2})\s*(.*)/", $this->value, $matches)) {
$op = $matches[1];
$value= floatval($matches[2]);
$recordField = strval($recordField);
eval("\$result = $recordField $op $value;");
return $result;
}
return $recordField == $this->value;
}
public function __toString()
{
if ($this->isTerminal) {
$value = "<b>$this->classValue</b>";
} else {
$value = $this->value;
$col = "col_$this->columnIndex";
if (! preg_match("/^[<>=]{1,2}/", $value)) {
$value = "=$value";
}
$value = "<b>$col $value</b><br>Gini: ". number_format($this->giniIndex, 2);
}
$str = "<table ><tr><td colspan=3 align=center style='border:1px solid;'>
$value</td></tr>";
if ($this->leftLeaf || $this->rightLeaf) {
$str .='<tr>';
if ($this->leftLeaf) {
$str .="<td valign=top><b>| Yes</b><br>$this->leftLeaf</td>";
} else {
$str .='<td></td>';
}
$str .='<td>&nbsp;</td>';
if ($this->rightLeaf) {
$str .="<td valign=top align=right><b>No |</b><br>$this->rightLeaf</td>";
} else {
$str .='<td></td>';
}
$str .= '</tr>';
}
$str .= '</table>';
return $str;
}
}

42
src/Phpml/Classification/NaiveBayes.php
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@ -68,8 +68,8 @@ class NaiveBayes implements Classifier
$this->sampleCount = count($samples);
$this->featureCount = count($samples[0]);
$this->labels = $targets;
array_unique($this->labels);
$labelCounts = array_count_values($targets);
$this->labels = array_keys($labelCounts);
foreach ($this->labels as $label) {
$samples = $this->getSamplesByLabel($label);
$this->p[$label] = count($samples) / $this->sampleCount;
@ -165,32 +165,20 @@ class NaiveBayes implements Classifier
*/
protected function predictSample(array $sample)
{
$isArray = is_array($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;
// 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 += $Plf;
}
arsort($predictions, SORT_NUMERIC);
reset($predictions);
$samplePredictions[] = key($predictions);
$predictions[$label] = $p;
}
if (! $isArray) {
return $samplePredictions[0];
}
return $samplePredictions;
arsort($predictions, SORT_NUMERIC);
reset($predictions);
return key($predictions);
}
}

242
src/Phpml/Clustering/FuzzyCMeans.php Normal file
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<?php
declare(strict_types=1);
namespace Phpml\Clustering;
use Phpml\Clustering\KMeans\Point;
use Phpml\Clustering\KMeans\Cluster;
use Phpml\Clustering\KMeans\Space;
use Phpml\Math\Distance\Euclidean;
class FuzzyCMeans implements Clusterer
{
/**
* @var int
*/
private $clustersNumber;
/**
* @var array|Cluster[]
*/
private $clusters = null;
/**
* @var Space
*/
private $space;
/**
* @var array|float[][]
*/
private $membership;
/**
* @var float
*/
private $fuzziness;
/**
* @var float
*/
private $epsilon;
/**
* @var int
*/
private $maxIterations;
/**
* @var int
*/
private $sampleCount;
/**
* @var array
*/
private $samples;
/**
* @param int $clustersNumber
*
* @throws InvalidArgumentException
*/
public function __construct(int $clustersNumber, float $fuzziness = 2.0, float $epsilon = 1e-2, int $maxIterations = 100)
{
if ($clustersNumber <= 0) {
throw InvalidArgumentException::invalidClustersNumber();
}
$this->clustersNumber = $clustersNumber;
$this->fuzziness = $fuzziness;
$this->epsilon = $epsilon;
$this->maxIterations = $maxIterations;
}
protected function initClusters()
{
// Membership array is a matrix of cluster number by sample counts
// We initilize the membership array with random values
$dim = $this->space->getDimension();
$this->generateRandomMembership($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;
}
}

60
tests/Phpml/Classification/DecisionTreeTest.php Normal file
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<?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);
}
}

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tests/Phpml/Clustering/FuzzyCMeansTest.php Normal file
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<?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));
}
}
}