dbscan

DBSCAN (go package)

DBSCAN (Density-based spatial clustering) clustering optimized for multicore processing.

Idea

If the distance of two points in any dimension is more than eps, than the total distance is more than eps

1. Calculate variance for each dimension (in parallel), find & store dimension with max variance

2. Sort by the dimension with max variance

3. Build a neighborhood map in parallel (Euclidean distance)

• Slide through sorted data, from lowest to highest. Sliding performed until neighbor_value <= curr_value + eps

• Use array / indices to store neighbors lists; ConcurrentLinkedQueue holds density reachable points.

1. Use DFS (Depth First Search) to find clusters

Example explaining how it works

Consider the following points:

Name => { X, Y }
"0" => { 2, 4 }
"1" => { 7, 3 }
"2" => { 3, 5 }
"3" => { 5, 3 }
"4" => { 7, 4 }
"5" => { 6, 8 }
"6" => { 6, 5 }
"7" => { 8, 4 }
"8" => { 2, 5 }
"9" => { 3, 7 }

Let eps = 2.0, minPts = 2:

  Y|
   |
  8|                       x <- Noise
   |
  7|           x
   |           |
  6|           | <- Points are density connected (from [3,5])
   |           |
  5|       x---x           x
   |         /               \
  4|       x                   x---x
   |                           |
  3|                   x-------x
   |                        /\
  2|                   Points are density reachable
   |
  1|
___|___________________________________
  0|   1   2   3   4   5   6   7   8  X

If we'll consider only X dimension, points sorted by this dimension will look like:

X  0  1  2  3  4  5  6  7  8  9
P        o  o     o  o  o  o

"0": 2.0, "8": 2.0, "2": 3.0, "9": 3.0, "3": 5.0, "5": 6.0, "6": 6.0, "1": 7.0, "4": 7.0, "7": 8.0
or
"0": [2.0, 4.0], "8": [2.0, 5.0], "2": [3.0, 5.0], "9": [3.0, 7.0], "3": [5.0, 3.0], "5": [6.0, 8.0], "6": [6.0, 5.0], "1": [7.0, 3.0], "4": [7.0, 4.0], "7": [8.0, 4.0]

We build neighborhood map (array containing concurrent non-blocking queues of density connected points' indices), by considering forward points, which are reachable by eps:

                       0    1    2    3    4    5    6    7    8    9
Sorted data points: [ "0", "8", "2", "9", "3", "5", "6", "1", "4", "7" ]

Point "0": 2.0, sees 3 points in range dimensionValue + eps - "8": 2.0, "2": 3.0, "9": 3.0
(e.g. 2.0 + 2.0 =4 - every point with X dimension value above 4 is definitely not reachable)
Then we check if they are reachable with Euclidean distance and add to neighbors.
Point "9": [3.0, 7.0] isn't density reachable to point "0": [2.0, 4.0]

Neighborhood map:
0: [ 1, 2 ]
1: [ 0 ]
2: [ 0 ]

Point "8": 2.0, sees "2": 3.0, "9": 3.0; but point "9": [3.0, 7.0] isn't density reachable
Neighborhood map:
0: [ 1, 2 ]
1: [ 0, 2 ]
2: [ 0, 1 ]

Point "2": 3.0, sees "9": 3.0, "3": 5.0; but point "3": [5.0, 3.0] isn't density reachable
Neighborhood map:
0: [ 1, 2 ]
1: [ 0, 2 ]
2: [ 0, 1, 3 ]
3: [ 2 ]

Note that we slide only forward, thus also add back-references to self index. Concurrent non-blocking queue allows to add in parallel (order doesn't matter).

Finally neighborhood map:

0: [0, 1, 2]
1: [0, 1, 2]
2: [0, 2, 3, 1]
3: [3, 2]
4: [4, 7]
5: [5]
6: [6, 8]
7: [7, 8, 9, 4]
8: [6, 8, 9, 7]
9: [8, 9, 7]

Now its easy to traverse and find clusters with Depth First Search (or BFS)

Cluster size: 4
 Point: 0, [2.0, 4.0]
 Point: 2, [3.0, 5.0]
 Point: 8, [2.0, 5.0]
 Point: 9, [3.0, 7.0]
Cluster size: 5
 Point: 3, [5.0, 3.0]
 Point: 1, [7.0, 3.0]
 Point: 7, [8.0, 4.0]
 Point: 4, [7.0, 4.0]
 Point: 6, [6.0, 5.0]