158:
strategies then in use could all be related to each other: all five use formulas for the distance between clusters that vary only in the weights of certain numerical coefficients. This unification allowed the coefficients to be chosen based on their effect on the overall clustering rather than, as
170:
between pairs of points normalised by dividing by the total
Manhattan distance of the points from the origin. The normalisation makes this distance measure particularly suited for data sets in which some data values may significantly differ from the rest.
120:. A year later, Williams moved to CSIRO himself, at the same time becoming an Australian citizen. He worked in CSIRO's Division of Computing Research in Canberra from 1966 to 1968, and then transferred to the Division of Tropical Pastures in
550:
147:. However, while at Southampton he became interested in more mathematical and statistical research topics such as the spatial distribution of plants. At the same time, he began writing software for his statistical analysis, using the
75:, also in London, from which he earned a bachelor's degree 1933, a PhD and diploma in 1940, and a D.Sc. in 1956. While studying for his PhD, Williams taught at Imperial College from 1933 to 1936, and at
113:
203:
Long a self-taught piano player, Williams took lessons after moving to
Australia, earned a credential, and taught piano himself. He also organised the first North Queensland Piano Competition.
540:
510:
216:
505:
194:
puzzle "The Little Pigley Farm" (also known as Dog's Mead, Little Pigley, Little Piggly Farm, Little Pigsby, Pilgrims' Plot, or Dog Days) which he first published in 1935 in
174:
Recognizing the general applicability of these methods, Williams went on at CSIRO to apply them to problems other than plant taxonomy, as well as to the classification of
402:
Studies in the
Numerical Analysis of Complex Rain-Forest Communities: III. The Analysis of Successional Data. Journal of Ecology, Vol. 57, No. 2, Jul., 1969, pp. 515-535
525:
151:
computer then available at
Southampton's computer centre. The centre's director, Godfrey Lance, was later to become a regular research collaborator of Williams.
535:
500:
485:
72:
95:
28:
545:
530:
495:
441:
71:, London, England, the only child of a Welsh coal miner. He went to the Stationers' Company's School in London and then to the
362:
Lance, G. N.; Williams, W. T. (1966), "Computer programs for hierarchical polythetic classification ("similarity analyses")",
490:
76:
98:. He enlisted as a private (neglecting to inform the military about his degrees) but eventually reached the rank of major.
37:
333:
Lance, G. N.; Williams, W. T. (1967), "A general theory of classificatory sorting strategies. I. Hierarchical systems",
555:
220:
40:
480:
179:
106:
91:
212:
102:
392:
155:
520:
515:
196:
117:
154:
Williams' most heavily cited research work, with Lance, makes the observation that five different
17:
406:
167:
56:
163:
371:
342:
315:
148:
140:
109:, where he was professor of botany and head of the department of botany from 1951 to 1965.
303:
87:
450:
131:. During his retirement he continued to work as a consultant for several institutions.
112:
In 1965, Williams' former
Southampton colleague Godfrey Lance invited him to visit the
48:
474:
256:
Walker, Rosanne (2006), "Biographical Entry: Williams, William Thomas (1913–1995)",
396:
191:
83:
190:
Williams was an avid composer of mathematical puzzles; for instance, he wrote the
424:
175:
128:
127:
Williams retired from CSIRO in 1973, at which point he moved from
Brisbane to
347:
376:
159:
had been done before, selecting the clustering strategy on an ad hoc basis.
52:
257:
319:
121:
44:
410:
400:
178:
and grasses. In this work, he viewed numerical taxonomy as a form of
68:
551:
Military personnel from the London
Borough of Hammersmith and Fulham
144:
143:, and more specifically on leaf expansion and the function of the
182:, intended more to generate new hypotheses than to confirm them.
43:(18 April 1913 – 15 October 1995) was an English and Australian
215:
awarded
Williams an honorary doctorate. He was elected as a
114:
Commonwealth
Scientific and Industrial Research Organisation
105:, where he stayed from 1946 to 1951. He then moved to the
541:Royal Electrical and Mechanical Engineers officers
443:On crossnumber puzzles and the Lucas–Bonaccio farm
405:, Journal of Ecology, British Ecological Society,
219:in 1978, and in 1980 he became an officer of the
8:
511:Fellows of the Australian Academy of Science
217:fellow of the Australian Academy of Science
506:Academics of the University of Southampton
73:Imperial College of Science and Technology
375:
346:
96:Royal Electrical and Mechanical Engineers
308:Historical Records of Australian Science
297:
295:
293:
291:
289:
231:
162:Williams and Lance also introduced the
101:After the war, he became a lecturer at
526:British Army personnel of World War II
287:
285:
283:
281:
279:
277:
275:
273:
271:
269:
251:
249:
247:
245:
243:
241:
239:
237:
235:
124:, where he worked from 1968 to 1973.
7:
304:"William Thomas Williams 1913–1995"
67:Williams was born 18 April 1913 in
536:Royal Army Ordnance Corps soldiers
259:Encyclopedia of Australian Science
25:
18:William Thomas Williams (botanist)
501:Alumni of Imperial College London
486:20th-century Australian botanists
391:Williams, W. T.; Lance, G. N.;
77:Sir John Cass Technical College
546:British emigrants to Australia
1:
139:Williams' early work was on
221:Order of the British Empire
572:
26:
180:exploratory data analysis
107:University of Southampton
103:Bedford College for Women
92:Royal Army Ordnance Corps
531:Royal Artillery soldiers
496:Australian statisticians
440:Sit, William Y. (1998),
302:Clifford, H. T. (1998),
213:University of Queensland
51:, known for his work on
156:hierarchical clustering
35:William Thomas Williams
29:William Thomas Williams
426:The Little Pigley Farm
348:10.1093/comjnl/9.4.373
491:English statisticians
377:10.1093/comjnl/9.1.60
364:The Computer Journal
335:The Computer Journal
320:10.1071/HR9981210099
27:For other uses, see
197:The Strand Magazine
118:Canberra, Australia
86:, he served in the
79:from 1936 to 1940.
556:People from Fulham
207:Awards and honours
168:Manhattan distance
57:numerical taxonomy
481:English botanists
456:on 26 August 2011
423:Pomerantz, Joel,
164:Canberra distance
16:(Redirected from
563:
466:
464:
463:
461:
455:
449:, archived from
448:
437:
431:
429:
420:
414:
413:
388:
382:
380:
379:
359:
353:
351:
350:
330:
324:
322:
299:
264:
262:
253:
186:Other activities
149:Ferranti Pegasus
141:plant physiology
49:plant taxonomist
21:
571:
570:
566:
565:
564:
562:
561:
560:
471:
470:
469:
459:
457:
453:
446:
439:
438:
434:
422:
421:
417:
390:
389:
385:
361:
360:
356:
332:
331:
327:
301:
300:
267:
255:
254:
233:
229:
209:
188:
137:
88:Royal Artillery
65:
32:
23:
22:
15:
12:
11:
5:
569:
567:
559:
558:
553:
548:
543:
538:
533:
528:
523:
518:
513:
508:
503:
498:
493:
488:
483:
473:
472:
468:
467:
432:
415:
383:
354:
341:(4): 373–380,
325:
265:
230:
228:
225:
208:
205:
187:
184:
136:
133:
64:
61:
24:
14:
13:
10:
9:
6:
4:
3:
2:
568:
557:
554:
552:
549:
547:
544:
542:
539:
537:
534:
532:
529:
527:
524:
522:
519:
517:
514:
512:
509:
507:
504:
502:
499:
497:
494:
492:
489:
487:
484:
482:
479:
478:
476:
452:
445:
444:
436:
433:
428:
427:
419:
416:
412:
408:
404:
403:
398:
397:Tracey, J. G.
394:
387:
384:
378:
373:
369:
365:
358:
355:
349:
344:
340:
336:
329:
326:
321:
317:
314:(1): 99–118,
313:
309:
305:
298:
296:
294:
292:
290:
288:
286:
284:
282:
280:
278:
276:
274:
272:
270:
266:
261:
260:
252:
250:
248:
246:
244:
242:
240:
238:
236:
232:
226:
224:
222:
218:
214:
211:In 1973, the
206:
204:
201:
199:
198:
193:
185:
183:
181:
177:
172:
169:
165:
160:
157:
152:
150:
146:
142:
134:
132:
130:
125:
123:
119:
115:
110:
108:
104:
99:
97:
93:
89:
85:
80:
78:
74:
70:
62:
60:
58:
54:
50:
46:
42:
39:
36:
30:
19:
460:13 September
458:, retrieved
451:the original
442:
435:
425:
418:
401:
386:
370:(1): 60–64,
367:
363:
357:
338:
334:
328:
311:
307:
258:
210:
202:
195:
192:cross-figure
189:
173:
166:, a form of
161:
153:
138:
126:
111:
100:
84:World War II
81:
66:
34:
33:
521:1995 deaths
516:1913 births
393:Webb, L. J.
176:angiosperms
116:(CSIRO) in
475:Categories
227:References
129:Townsville
53:algorithms
63:Biography
399:(1969),
135:Research
122:Brisbane
45:botanist
411:2258396
145:Stomata
82:During
409:
94:, and
69:Fulham
454:(PDF)
447:(PDF)
407:JSTOR
462:2011
55:for
47:and
372:doi
343:doi
316:doi
41:OBE
38:FAA
477::
395:;
366:,
337:,
312:12
310:,
306:,
268:^
234:^
223:.
200:.
90:,
59:.
465:.
430:.
381:.
374::
368:9
352:.
345::
339:9
323:.
318::
263:.
31:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.