Hi Cole,

The Dunn index seems to work fairly well with this set of data. It may of course fail miserably with similar but different data. Need to experiment with the various options FindClusters provides and see what works best. You should also try removing the {0, 0} point. Clustering algorithms avoid clusters of one point so it is going to get pulled into the closest cluster and can potentially impact other clusters.

clusterDunn =  FindClusters[points, PerformanceGoal -> "Quality", CriterionFunction -> "Dunn"];

ListPlot[clusterDunn, PlotMarkers -> {Automatic, 12}]

Hi Rohit,

Table is listed below. Note that this is a subset of an array that has {x, y, z} coordinates. Here I've just added the x,y coordinates for simplicity. Also, note that (0,0) is an artificial point that I used to clean up the points the fall in between the groups.

{{0, 0}, {1, 4}, {1, 8}, {1, 9}, {1, 10}, {1, 11}, {1, 12}, {1, 
  16}, {1, 17}, {1, 18}, {2, 10}, {2, 11}, {2, 12}, {2, 16}, {2, 
  17}, {2, 18}, {3, 1}, {3, 11}, {3, 12}, {3, 13}, {3, 16}, {3, 
  17}, {3, 18}, {3, 19}, {3, 20}, {3, 21}, {4, 1}, {4, 2}, {4, 6}, {4,
   7}, {4, 13}, {4, 17}, {4, 18}, {4, 19}, {4, 20}, {4, 21}, {5, 
  1}, {5, 2}, {5, 3}, {5, 6}, {5, 7}, {5, 8}, {5, 19}, {5, 20}, {5, 
  21}, {6, 1}, {6, 2}, {6, 3}, {6, 6}, {6, 7}, {6, 8}, {6, 9}, {6, 
  10}, {6, 14}, {6, 21}, {7, 1}, {7, 2}, {7, 3}, {7, 7}, {7, 8}, {7, 
  9}, {7, 10}, {7, 11}, {7, 14}, {7, 15}, {7, 16}, {8, 3}, {8, 8}, {8,
   9}, {8, 10}, {8, 11}, {8, 14}, {8, 15}, {8, 16}, {8, 17}, {8, 
  18}, {9, 10}, {9, 11}, {9, 14}, {9, 15}, {9, 16}, {9, 17}, {9, 
  18}, {9, 19}, {9, 20}, {9, 21}, {10, 5}, {10, 11}, {10, 16}, {10, 
  17}, {10, 18}, {10, 19}, {10, 20}, {10, 21}, {11, 1}, {11, 5}, {11, 
  6}, {11, 7}, {11, 18}, {11, 19}, {11, 20}, {11, 21}, {12, 1}, {12, 
  2}, {12, 5}, {12, 6}, {12, 7}, {12, 8}, {12, 13}, {12, 19}, {12, 
  20}, {12, 21}, {13, 1}, {13, 2}, {13, 5}, {13, 6}, {13, 7}, {13, 
  8}, {13, 9}, {13, 13}, {13, 14}, {13, 15}, {14, 1}, {14, 2}, {14, 
  5}, {14, 6}, {14, 7}, {14, 8}, {14, 9}, {14, 10}, {14, 13}, {14, 
  14}, {14, 15}, {14, 16}, {15, 1}, {15, 2}, {15, 7}, {15, 8}, {15, 
  9}, {15, 10}, {15, 13}, {15, 14}, {15, 15}, {15, 16}, {15, 17}, {15,
   18}, {15, 21}, {16, 1}, {16, 2}, {16, 8}, {16, 9}, {16, 10}, {16, 
  13}, {16, 14}, {16, 15}, {16, 16}, {16, 17}, {16, 18}, {16, 
  21}, {17, 1}, {17, 2}, {17, 9}, {17, 10}, {17, 15}, {17, 16}, {17, 
  17}, {17, 18}, {17, 21}, {18, 5}, {18, 16}, {18, 17}, {18, 18}, {19,
   5}, {19, 6}, {19, 12}, {19, 17}, {19, 18}, {20, 5}, {20, 6}, {20, 
  7}, {20, 8}, {20, 12}, {20, 13}, {21, 1}, {21, 5}, {21, 6}, {21, 
  7}, {21, 8}, {21, 9}, {21, 12}, {21, 13}, {21, 14}, {21, 20}, {21, 
  21}}

Are all of your datasets on an exact integer-valued grid?