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Hierarchical clustering

Agglomorative clustering seeks to pair up nearest points (according to a chosen distance measurement) into a cluster, progressively merging clusters into a hierarchy, until there only is a single cluster left.

Worked Example

As before, using the date example, we need the distance and average functions as defined previously:

(require '[clustering.core.hierarchical :as hier])
(require '[clustering.data-viz.image :refer :all])
(require '[clustering.data-viz.dendrogram :as dendrogram])
(require '[clj-time.core :refer [after? date-time interval in-days])
(require '[clj-time.format :refer [unparse formatters])
(require '[clj-time.coerce :refer [to-long from-long])

(def test-dataset
  (hash-set
    (date-time 2013 7 21)
    (date-time 2013 7 25)
    ...)))

(defn distance [dt-a dt-b]
   ...)

(defn average [dates]
   ...)

Rather than returning a vector of clusters, hierarchical clustering returns a single cluster object with left and right sub-parts that require recursive traversal, most easily demonstrated with a suitable data visualization, such as a dendrogram:

(def groups (hier/cluster distance average test-dataset))

(write-png
  "doc/dendrogram.png"
  (dendrogram/->img group fmt))

(spit
  "doc/dendrogram.svg"
  (dendrogram/->svg group fmt))

dendrogram

More Examples

Further examples can be found in the https://github.com/rm-hull/clustering/tree/main/test/clustering/examples directory.

Word Similaries

Taking a list of sampled dictionary words and using the Levenshtein distance to cluster, the hierarchical clustering algorithm produce the following dendrogram:

word-similarities

Substituting different distance metrics (see clj-fuzzy) would give different (and maybe more interesting) cluster clumps.

Baseball: Team & League Standard Batting

baseball-reference.com has lots of interesting historical statistics for all major league games, one of which is the 2015 National League:

Tm #Bat BatAge R/G G PA AB R H 2B 3B HR RBI SB CS BB SO BA OBP SLG OPS OPS+ TB GDP HBP SH SF IBB LOB
ARI 50 26.6 4.44 162 6276 5649 720 1494 289 48 154 680 132 44 490 1312 .264 .324 .414 .738 96 2341 134 33 46 57 40 1153
ATL 60 28.8 3.54 162 6034 5420 573 1361 251 18 100 548 69 33 471 1107 .251 .314 .359 .674 88 1948 148 44 67 31 39 1145
CHC 50 26.9 4.25 162 6200 5491 689 1341 272 30 171 657 95 37 567 1518 .244 .321 .398 .719 97 2186 101 74 32 35 47 1165
CIN 50 29.5 3.95 162 6196 5571 640 1382 257 27 167 613 134 38 496 1255 .248 .312 .394 .706 92 2194 112 42 47 40 38 1148
COL 51 28.0 4.55 162 6071 5572 737 1479 274 49 186 702 97 43 388 1283 .265 .315 .432 .748 89 2409 114 33 44 34 47 1016
LAD 55 29.6 4.12 162 6090 5385 667 1346 263 26 187 638 59 34 563 1258 .250 .326 .413 .739 107 2222 135 60 49 30 31 1121
MIA 51 27.9 3.78 162 5988 5463 613 1420 236 40 120 575 112 45 375 1150 .260 .310 .384 .694 91 2096 133 39 71 40 30 1059
MIL 49 28.1 4.04 162 6024 5480 655 1378 274 34 145 624 84 29 412 1299 .251 .307 .393 .700 90 2155 130 41 55 34 35 1026
NYM 49 28.5 4.22 162 6145 5527 683 1351 295 17 177 654 51 25 488 1290 .244 .312 .400 .712 98 2211 130 68 29 32 42 1098
PHI 50 28.0 3.86 162 6053 5529 626 1374 272 37 130 586 88 32 387 1274 .249 .303 .382 .684 86 2110 119 54 53 29 20 1066
PIT 46 28.2 4.30 162 6285 5631 697 1462 292 27 140 661 98 45 461 1322 .260 .323 .396 .719 98 2228 115 89 63 41 46 1166
SDP 46 27.7 4.01 162 6019 5457 650 1324 260 36 148 623 82 29 426 1327 .243 .300 .385 .685 92 2100 108 40 52 42 22 1028
SFG 48 28.9 4.30 162 6153 5565 696 1486 288 39 136 663 93 36 457 1159 .267 .326 .406 .732 102 2260 142 49 45 37 30 1130
STL 46 28.4 3.99 162 6139 5484 647 1386 288 39 137 619 69 38 506 1267 .253 .321 .394 .716 95 2163 128 66 39 42 47 1152
WSN 44 28.4 4.34 162 6117 5428 703 1363 265 13 177 665 57 23 539 1344 .251 .321 .403 .724 95 2185 129 44 55 51 38 1114
LgAvg 48 28.2 4.11 162 6119 5510 666 1396 272 32 152 634 88 35 468 1278 .253 .316 .397 .713 94 2187 125 52 50 38 37 1106 714 28.2 4.11 2430 91790 82652 9996 20947 4076 480 2275 9508 1320 531 7026 19165 .253 .316 .397 .713 94 32808 1878 776 747 575 552 16587

Using the Euclidean distance function, this yields the following dendrogram:

baseball-nl2015