From 9938cf29113d8797a58a9d2f526f286d8c65f53d Mon Sep 17 00:00:00 2001
From: Yuji Uchiyama <y.uchiyama.1015@gmail.com>
Date: Tue, 9 Jan 2018 18:53:02 +0900
Subject: [PATCH] Rewrite DBSCAN (#185)

* Add testcases to DBSCAN

* Fix DBSCAN implementation

* Refactoring DBSCAN implementation

* Fix coding style
---
 src/Phpml/Clustering/DBSCAN.php       | 112 ++++++++++++++++----------
 tests/Phpml/Clustering/DBSCANTest.php |  34 ++++++++
 2 files changed, 103 insertions(+), 43 deletions(-)

diff --git a/src/Phpml/Clustering/DBSCAN.php b/src/Phpml/Clustering/DBSCAN.php
index 3546ebf..e96c5ff 100644
--- a/src/Phpml/Clustering/DBSCAN.php
+++ b/src/Phpml/Clustering/DBSCAN.php
@@ -4,12 +4,13 @@ declare(strict_types=1);
 
 namespace Phpml\Clustering;
 
-use array_merge;
 use Phpml\Math\Distance;
 use Phpml\Math\Distance\Euclidean;
 
 class DBSCAN implements Clusterer
 {
+    private const NOISE = -1;
+
     /**
      * @var float
      */
@@ -38,57 +39,82 @@ class DBSCAN implements Clusterer
 
     public function cluster(array $samples): array
     {
-        $clusters = [];
-        $visited = [];
+        $labels = [];
+        $n = 0;
 
         foreach ($samples as $index => $sample) {
-            if (isset($visited[$index])) {
+            if (isset($labels[$index])) {
                 continue;
             }
 
-            $visited[$index] = true;
+            $neighborIndices = $this->getIndicesInRegion($sample, $samples);
 
-            $regionSamples = $this->getSamplesInRegion($sample, $samples);
-            if (count($regionSamples) >= $this->minSamples) {
-                $clusters[] = $this->expandCluster($regionSamples, $visited);
+            if (count($neighborIndices) < $this->minSamples) {
+                $labels[$index] = self::NOISE;
+
+                continue;
             }
+
+            $labels[$index] = $n;
+
+            $this->expandCluster($samples, $neighborIndices, $labels, $n);
+
+            ++$n;
+        }
+
+        return $this->groupByCluster($samples, $labels, $n);
+    }
+
+    private function expandCluster(array $samples, array $seeds, array &$labels, int $n): void
+    {
+        while (($index = array_pop($seeds)) !== null) {
+            if (isset($labels[$index])) {
+                if ($labels[$index] === self::NOISE) {
+                    $labels[$index] = $n;
+                }
+
+                continue;
+            }
+
+            $labels[$index] = $n;
+
+            $sample = $samples[$index];
+            $neighborIndices = $this->getIndicesInRegion($sample, $samples);
+
+            if (count($neighborIndices) >= $this->minSamples) {
+                $seeds = array_unique(array_merge($seeds, $neighborIndices));
+            }
+        }
+    }
+
+    private function getIndicesInRegion(array $center, array $samples): array
+    {
+        $indices = [];
+
+        foreach ($samples as $index => $sample) {
+            if ($this->distanceMetric->distance($center, $sample) < $this->epsilon) {
+                $indices[] = $index;
+            }
+        }
+
+        return $indices;
+    }
+
+    private function groupByCluster(array $samples, array $labels, int $n): array
+    {
+        $clusters = array_fill(0, $n, []);
+
+        foreach ($samples as $index => $sample) {
+            if ($labels[$index] !== self::NOISE) {
+                $clusters[$labels[$index]][$index] = $sample;
+            }
+        }
+
+        // Reindex (i.e. to 0, 1, 2, ...) integer indices for backword compatibility
+        foreach ($clusters as $index => $cluster) {
+            $clusters[$index] = array_merge($cluster, []);
         }
 
         return $clusters;
     }
-
-    private function getSamplesInRegion(array $localSample, array $samples): array
-    {
-        $region = [];
-
-        foreach ($samples as $index => $sample) {
-            if ($this->distanceMetric->distance($localSample, $sample) < $this->epsilon) {
-                $region[$index] = $sample;
-            }
-        }
-
-        return $region;
-    }
-
-    private function expandCluster(array $samples, array &$visited): array
-    {
-        $cluster = [];
-
-        $clusterMerge = [[]];
-        foreach ($samples as $index => $sample) {
-            if (!isset($visited[$index])) {
-                $visited[$index] = true;
-                $regionSamples = $this->getSamplesInRegion($sample, $samples);
-                if (count($regionSamples) > $this->minSamples) {
-                    $clusterMerge[] = $regionSamples;
-                }
-            }
-
-            $cluster[$index] = $sample;
-        }
-
-        $cluster = array_merge($cluster, ...$clusterMerge);
-
-        return $cluster;
-    }
 }
diff --git a/tests/Phpml/Clustering/DBSCANTest.php b/tests/Phpml/Clustering/DBSCANTest.php
index c0d0401..3c6d08d 100644
--- a/tests/Phpml/Clustering/DBSCANTest.php
+++ b/tests/Phpml/Clustering/DBSCANTest.php
@@ -59,4 +59,38 @@ class DBSCANTest extends TestCase
 
         $this->assertEquals($clustered, $dbscan->cluster($samples));
     }
+
+    public function testClusterEpsilonSmall(): void
+    {
+        $samples = [[0], [1], [2]];
+        $clustered = [
+        ];
+
+        $dbscan = new DBSCAN($epsilon = 0.5, $minSamples = 2);
+
+        $this->assertEquals($clustered, $dbscan->cluster($samples));
+    }
+
+    public function testClusterEpsilonBoundary(): void
+    {
+        $samples = [[0], [1], [2]];
+        $clustered = [
+        ];
+
+        $dbscan = new DBSCAN($epsilon = 1.0, $minSamples = 2);
+
+        $this->assertEquals($clustered, $dbscan->cluster($samples));
+    }
+
+    public function testClusterEpsilonLarge(): void
+    {
+        $samples = [[0], [1], [2]];
+        $clustered = [
+            [[0], [1], [2]],
+        ];
+
+        $dbscan = new DBSCAN($epsilon = 1.5, $minSamples = 2);
+
+        $this->assertEquals($clustered, $dbscan->cluster($samples));
+    }
 }