Fuzzy Clustering

近幾天在寫某個版本的 fuzzy clustering，過程就是不斷更新由各式各樣的 summations 串出來的數值，因此在 Haskell 之下只要 list comprehension + map + zipWith + sum 就乾淨地解決了，沒做任何 optimisations 速度也不太差（當然也可能是因為助教提供的 dataset 偏小的關係）。詳細數式請看〈Active semi-supervised fuzzy clustering〉。"Semi-supervised" 的意思就是使用者可以提供一些分類資訊，目前我還沒寫 supervisory input，但數式已經全部寫進去，所以程式差不多算寫完了。數式裡帶有一些參數，此類 paper 的慣例似乎總是寫「如果參數挑得好的話，結果相當振奮人心」這種話，而那前提其實相當難達成。似乎經驗是不二法門，調久了之後甚至有種「參數變成旋鈕」的直覺，會期待這個鈕轉一下、那個鈕撥一下應該對結果產生什麼樣的修正。目前已經偶爾跑得出滿正確的結果，例如可以看出下面的 raw data 分成三群、各 50 點：

-- Iteration 64, # of clusters = 3
ClusteringData {rawData = [((4 |> [5.1,3.5,1.4,0.2],1),1),((4 |> [4.9,3.0,1.4,0.
2],2),1),((4 |> [4.7,3.2,1.3,0.2],3),1),((4 |> [4.6,3.1,1.5,0.2],4),1),((4 |> [5
.0,3.6,1.4,0.2],5),1),((4 |> [5.4,3.9,1.7,0.4],6),1),((4 |> [4.6,3.4,1.4,0.3],7)
,1),((4 |> [5.0,3.4,1.5,0.2],8),1),((4 |> [4.4,2.9,1.4,0.2],9),1),((4 |> [4.9,3.
1,1.5,0.1],10),1),((4 |> [5.4,3.7,1.5,0.2],11),1),((4 |> [4.8,3.4,1.6,0.2],12),1
),((4 |> [4.8,3.0,1.4,0.1],13),1),((4 |> [4.3,3.0,1.1,0.1],14),1),((4 |> [5.8,4.
0,1.2,0.2],15),1),((4 |> [5.7,4.4,1.5,0.4],16),1),((4 |> [5.4,3.9,1.3,0.4],17),1
),((4 |> [5.1,3.5,1.4,0.3],18),1),((4 |> [5.7,3.8,1.7,0.3],19),1),((4 |> [5.1,3.
8,1.5,0.3],20),1),((4 |> [5.4,3.4,1.7,0.2],21),1),((4 |> [5.1,3.7,1.5,0.4],22),1
),((4 |> [4.6,3.6,1.0,0.2],23),1),((4 |> [5.1,3.3,1.7,0.5],24),1),((4 |> [4.8,3.
4,1.9,0.2],25),1),((4 |> [5.0,3.0,1.6,0.2],26),1),((4 |> [5.0,3.4,1.6,0.4],27),1
),((4 |> [5.2,3.5,1.5,0.2],28),1),((4 |> [5.2,3.4,1.4,0.2],29),1),((4 |> [4.7,3.
2,1.6,0.2],30),1),((4 |> [4.8,3.1,1.6,0.2],31),1),((4 |> [5.4,3.4,1.5,0.4],32),1
),((4 |> [5.2,4.1,1.5,0.1],33),1),((4 |> [5.5,4.2,1.4,0.2],34),1),((4 |> [4.9,3.
1,1.5,0.2],35),1),((4 |> [5.0,3.2,1.2,0.2],36),1),((4 |> [5.5,3.5,1.3,0.2],37),1
),((4 |> [4.9,3.6,1.4,0.1],38),1),((4 |> [4.4,3.0,1.3,0.2],39),1),((4 |> [5.1,3.
4,1.5,0.2],40),1),((4 |> [5.0,3.5,1.3,0.3],41),1),((4 |> [4.5,2.3,1.3,0.3],42),1
),((4 |> [4.4,3.2,1.3,0.2],43),1),((4 |> [5.0,3.5,1.6,0.6],44),1),((4 |> [5.1,3.
8,1.9,0.4],45),1),((4 |> [4.8,3.0,1.4,0.3],46),1),((4 |> [5.1,3.8,1.6,0.2],47),1
),((4 |> [4.6,3.2,1.4,0.2],48),1),((4 |> [5.3,3.7,1.5,0.2],49),1),((4 |> [5.0,3.
3,1.4,0.2],50),1),((4 |> [7.0,3.2,4.7,1.4],51),2),((4 |> [6.4,3.2,4.5,1.5],52),2
),((4 |> [6.9,3.1,4.9,1.5],53),2),((4 |> [5.5,2.3,4.0,1.3],54),2),((4 |> [6.5,2.
8,4.6,1.5],55),2),((4 |> [5.7,2.8,4.5,1.3],56),2),((4 |> [6.3,3.3,4.7,1.6],57),2
),((4 |> [4.9,2.4,3.3,1.0],58),2),((4 |> [6.6,2.9,4.6,1.3],59),2),((4 |> [5.2,2.
7,3.9,1.4],60),2),((4 |> [5.0,2.0,3.5,1.0],61),2),((4 |> [5.9,3.0,4.2,1.5],62),2
),((4 |> [6.0,2.2,4.0,1.0],63),2),((4 |> [6.1,2.9,4.7,1.4],64),2),((4 |> [5.6,2.
9,3.6,1.3],65),2),((4 |> [6.7,3.1,4.4,1.4],66),2),((4 |> [5.6,3.0,4.5,1.5],67),2
),((4 |> [5.8,2.7,4.1,1.0],68),2),((4 |> [6.2,2.2,4.5,1.5],69),2),((4 |> [5.6,2.
5,3.9,1.1],70),2),((4 |> [5.9,3.2,4.8,1.8],71),2),((4 |> [6.1,2.8,4.0,1.3],72),2
),((4 |> [6.3,2.5,4.9,1.5],73),2),((4 |> [6.1,2.8,4.7,1.2],74),2),((4 |> [6.4,2.
9,4.3,1.3],75),2),((4 |> [6.6,3.0,4.4,1.4],76),2),((4 |> [6.8,2.8,4.8,1.4],77),2
),((4 |> [6.7,3.0,5.0,1.7],78),2),((4 |> [6.0,2.9,4.5,1.5],79),2),((4 |> [5.7,2.
6,3.5,1.0],80),2),((4 |> [5.5,2.4,3.8,1.1],81),2),((4 |> [5.5,2.4,3.7,1.0],82),2
),((4 |> [5.8,2.7,3.9,1.2],83),2),((4 |> [6.0,2.7,5.1,1.6],84),2),((4 |> [5.4,3.
0,4.5,1.5],85),2),((4 |> [6.0,3.4,4.5,1.6],86),2),((4 |> [6.7,3.1,4.7,1.5],87),2
),((4 |> [6.3,2.3,4.4,1.3],88),2),((4 |> [5.6,3.0,4.1,1.3],89),2),((4 |> [5.5,2.
5,4.0,1.3],90),2),((4 |> [5.5,2.6,4.4,1.2],91),2),((4 |> [6.1,3.0,4.6,1.4],92),2
),((4 |> [5.8,2.6,4.0,1.2],93),2),((4 |> [5.0,2.3,3.3,1.0],94),2),((4 |> [5.6,2.
7,4.2,1.3],95),2),((4 |> [5.7,3.0,4.2,1.2],96),2),((4 |> [5.7,2.9,4.2,1.3],97),2
),((4 |> [6.2,2.9,4.3,1.3],98),2),((4 |> [5.1,2.5,3.0,1.1],99),2),((4 |> [5.7,2.
8,4.1,1.3],100),2),((4 |> [6.3,3.3,6.0,2.5],101),3),((4 |> [5.8,2.7,5.1,1.9],102
),3),((4 |> [7.1,3.0,5.9,2.1],103),3),((4 |> [6.3,2.9,5.6,1.8],104),3),((4 |> [6
.5,3.0,5.8,2.2],105),3),((4 |> [7.6,3.0,6.6,2.1],106),3),((4 |> [4.9,2.5,4.5,1.7
],107),3),((4 |> [7.3,2.9,6.3,1.8],108),3),((4 |> [6.7,2.5,5.8,1.8],109),3),((4 
|> [7.2,3.6,6.1,2.5],110),3),((4 |> [6.5,3.2,5.1,2.0],111),3),((4 |> [6.4,2.7,5.
3,1.9],112),3),((4 |> [6.8,3.0,5.5,2.1],113),3),((4 |> [5.7,2.5,5.0,2.0],114),3)
,((4 |> [5.8,2.8,5.1,2.4],115),3),((4 |> [6.4,3.2,5.3,2.3],116),3),((4 |> [6.5,3
.0,5.5,1.8],117),3),((4 |> [7.7,3.8,6.7,2.2],118),3),((4 |> [7.7,2.6,6.9,2.3],11
9),3),((4 |> [6.0,2.2,5.0,1.5],120),3),((4 |> [6.9,3.2,5.7,2.3],121),3),((4 |> [
5.6,2.8,4.9,2.0],122),3),((4 |> [7.7,2.8,6.7,2.0],123),3),((4 |> [6.3,2.7,4.9,1.
8],124),3),((4 |> [6.7,3.3,5.7,2.1],125),3),((4 |> [7.2,3.2,6.0,1.8],126),3),((4
 |> [6.2,2.8,4.8,1.8],127),3),((4 |> [6.1,3.0,4.9,1.8],128),3),((4 |> [6.4,2.8,5
.6,2.1],129),3),((4 |> [7.2,3.0,5.8,1.6],130),3),((4 |> [7.4,2.8,6.1,1.9],131),3
),((4 |> [7.9,3.8,6.4,2.0],132),3),((4 |> [6.4,2.8,5.6,2.2],133),3),((4 |> [6.3,
2.8,5.1,1.5],134),3),((4 |> [6.1,2.6,5.6,1.4],135),3),((4 |> [7.7,3.0,6.1,2.3],1
36),3),((4 |> [6.3,3.4,5.6,2.4],137),3),((4 |> [6.4,3.1,5.5,1.8],138),3),((4 |> 
[6.0,3.0,4.8,1.8],139),3),((4 |> [6.9,3.1,5.4,2.1],140),3),((4 |> [6.7,3.1,5.6,2
.4],141),3),((4 |> [6.9,3.1,5.1,2.3],142),3),((4 |> [5.8,2.7,5.1,1.9],143),3),((
4 |> [6.8,3.2,5.9,2.3],144),3),((4 |> [6.7,3.3,5.7,2.5],145),3),((4 |> [6.7,3.0,
5.2,2.3],146),3),((4 |> [6.3,2.5,5.0,1.9],147),3),((4 |> [6.5,3.0,5.2,2.0],148),
3),((4 |> [6.2,3.4,5.4,2.3],149),3),((4 |> [5.9,3.0,5.1,1.8],150),3)], nData = 1
50, prototypes = [((4 |> [5.013888853100183,3.437742055000191,1.4653680472369688
,0.24413569908981225],1),49.273748971572665),((4 |> [6.113058187123257,2.8026095
070502457,4.489826484038653,1.3965685861695043],2),52.62732004865611),((4 |> [6.
410685936607242,2.9739386945180994,5.32095635913265,2.0187917825743362],3),48.09
893097977119)], memberships = array ((1,1),(3,150)) [((1,1),0.9952403769488021),
((1,2),0.957852051241039),((1,3),0.9798905556204084),((1,4),0.96806374876768),((
1,5),0.9919591608994238),((1,6),0.962710558774297),((1,7),0.9458955112432162),((
1,8),0.9952866519095965),((1,9),0.9343931456056512),((1,10),0.949246345036193),(
(1,11),0.9796535338502901),((1,12),0.9709101481519239),((1,13),0.949726999953223
),((1,14),0.9022715529866884),((1,15),0.9300777665122273),((1,16),0.942918121412
5627),((1,17),0.9433551251952859),((1,18),0.9902022618698284),((1,19),0.94992582
79607329),((1,20),0.9806705723421719),((1,21),0.934477082320783),((1,22),0.96401
1129580819),((1,23),0.900986314960819),((1,24),0.8869352488363349),((1,25),0.881
1520004614971),((1,26),0.9334892886853143),((1,27),0.9618572804577499),((1,28),0
.9895703200978919),((1,29),0.9823516224961432),((1,30),0.9646209830863363),((1,3
1),0.9661221619461772),((1,32),0.9306356003734213),((1,33),0.938577365072229),((
1,34),0.9610787974560411),((1,35),0.9766005961180397),((1,36),0.9532291148957966
),((1,37),0.9388982470572855),((1,38),0.9677496121418085),((1,39),0.937048531631
9951),((1,40),0.9919288341366196),((1,41),0.9768609531839877),((1,42),0.71403344
43879821),((1,43),0.9343620265176544),((1,44),0.8271247078457762),((1,45),0.9098
200412319813),((1,46),0.9484299698270311),((1,47),0.9688054875451735),((1,48),0.
9745303683672146),((1,49),0.9861767704585206),((1,50),0.9924071332142961),((1,51
),2.8987022806985903e-2),((1,52),1.5242243066212134e-2),((1,53),1.30344278296570
06e-2),((1,54),2.5446064078978932e-2),((1,55),1.0870818000752645e-2),((1,56),1.8
79331019400933e-2),((1,57),1.6778767543446163e-2),((1,58),5.190611102387584e-2),
((1,59),1.5129944458907075e-2),((1,60),3.163199471284373e-2),((1,61),6.755059001
961151e-2),((1,62),1.8798548625505788e-2),((1,63),5.0634440593271796e-2),((1,64)
,6.884417931445846e-3),((1,65),4.279161523745877e-2),((1,66),2.7022552660506332e
-2),((1,67),2.0566162095190816e-2),((1,68),4.244155287795546e-2),((1,69),3.65704
12566095736e-2),((1,70),1.566020957203388e-2),((1,71),1.725962365483938e-2),((1,
72),1.7470417612353555e-2),((1,73),9.488040355779735e-3),((1,74),2.6565793582218
993e-2),((1,75),1.3545424347935996e-2),((1,76),2.001637196445928e-2),((1,77),1.4
9514145241289e-2),((1,78),8.573318483398217e-3),((1,79),5.253976970870509e-3),((
1,80),3.675932520059246e-2),((1,81),1.9208681341979828e-2),((1,82),2.97178484278
30623e-2),((1,83),7.366616641822843e-3),((1,84),9.388767526109728e-3),((1,85),3.
0010941238666176e-2),((1,86),3.2711886972967875e-2),((1,87),1.2133261880835541e-
2),((1,88),2.978317859247903e-2),((1,89),2.296915585523545e-2),((1,90),1.4149053
40587315e-2),((1,91),2.855094052020725e-2),((1,92),7.671169057755277e-3),((1,93)
,6.389335725903479e-3),((1,94),4.964625330439047e-2),((1,95),9.108749441468089e-
3),((1,96),3.195647441885316e-2),((1,97),1.24640058757178e-2),((1,98),5.79723286
0495821e-3),((1,99),9.696543353396248e-2),((1,100),6.022697411220746e-3),((1,101
),1.7985934505122904e-2),((1,102),1.070522258676711e-2),((1,103),6.8083158168920
37e-3),((1,104),1.0444810261073585e-2),((1,105),5.666240787420569e-3),((1,106),1
.3076827874200045e-2),((1,107),4.322351489368876e-2),((1,108),1.5376364946573665
e-2),((1,109),1.4557468033237635e-2),((1,110),1.4611011089552102e-2),((1,111),8.
316550280249529e-3),((1,112),5.249380118596008e-3),((1,113),3.3894798677162946e-
3),((1,114),2.183587627251873e-2),((1,115),2.595421293678265e-2),((1,116),7.4192
85136544786e-3),((1,117),6.0240924508249884e-3),((1,118),2.1552615432697944e-2),
((1,119),2.4123242041180933e-2),((1,120),2.2820683271400976e-2),((1,121),4.76266
895472512e-3),((1,122),1.4943029815230704e-2),((1,123),1.7805069640206464e-2),((
1,124),8.731510249478217e-3),((1,125),7.40659043168889e-3),((1,126),1.1297598045
534001e-2),((1,127),7.634116096134396e-3),((1,128),5.761714812930143e-3),((1,129
),5.80919814308978e-3),((1,130),1.551012127428524e-2),((1,131),1.266096215966396
9e-2),((1,132),2.4123313905433697e-2),((1,133),7.164891595845435e-3),((1,134),7.
5258859983678905e-3),((1,135),3.814161541838403e-2),((1,136),1.9410140330655423e
-2),((1,137),1.4094354679920386e-2),((1,138),9.138359718871504e-3),((1,139),7.75
7538399356827e-3),((1,140),7.585592590252757e-3),((1,141),6.8145597116487985e-3)
,((1,142),2.978604574680067e-2),((1,143),1.070522258676711e-2),((1,144),4.730290
909270292e-3),((1,145),8.965211058128e-3),((1,146),1.776244400882234e-2),((1,147
),1.8026522207250203e-2),((1,148),2.033941834348376e-3),((1,149),1.5110886440024
096e-2),((1,150),1.0650798907488625e-2),((2,1),3.4210032703757467e-3),((2,2),3.1
60037275850999e-2),((2,3),1.4900359314249463e-2),((2,4),2.3377424655255132e-2),(
(2,5),5.718134331824047e-3),((2,6),2.6376525932533756e-2),((2,7),3.9597754263287
176e-2),((2,8),3.3855927134941303e-3),((2,9),4.930553075311585e-2),((2,10),3.627
583376611837e-2),((2,11),1.4315370390148035e-2),((2,12),2.0498625821451462e-2),(
(2,13),3.663077816422032e-2),((2,14),7.25597528101397e-2),((2,15),4.883758063970
4635e-2),((2,16),3.936370260370368e-2),((2,17),4.053386713013177e-2),((2,18),7.1
6668505495424e-3),((2,19),3.5177805775085315e-2),((2,20),1.3678735153709399e-2),
((2,21),4.6370017594938695e-2),((2,22),2.607156717978128e-2),((2,23),7.167846331
524959e-2),((2,24),8.55002477563547e-2),((2,25),7.948221759937557e-2),((2,26),4.
907780658129206e-2),((2,27),2.8337561444328304e-2),((2,28),7.445665763400736e-3)
,((2,29),1.2788421693578824e-2),((2,30),2.5372058490319257e-2),((2,31),2.4683268
164989936e-2),((2,32),5.1201236697198706e-2),((2,33),4.079551707134192e-2),((2,3
4),2.664225356095243e-2),((2,35),1.7270481076472312e-2),((2,36),3.47751889396684
25e-2),((2,37),4.3917355820290264e-2),((2,38),2.2298041652924757e-2),((2,39),4.7
258617343711444e-2),((2,40),5.806598802736592e-3),((2,41),1.6987066358020112e-2)
,((2,42),0.22617718979438933),((2,43),4.81105828746244e-2),((2,44),0.12837541302
158806),((2,45),6.277081515286613e-2),((2,46),3.948423742677633e-2),((2,47),2.14
11115462803557e-2),((2,48),1.8646824522623683e-2),((2,49),9.717297220986932e-3),
((2,50),5.55018766670349e-3),((2,51),0.7337166903314236),((2,52),0.7987180911592
069),((2,53),0.7847469601102202),((2,54),0.7061655894354258),((2,55),0.763458275
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12),((3,112),0.8445168359879037),((3,113),0.930585065820211),((3,114),0.76672433
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0),0.4291693746324294),((3,121),0.9314844383357174),((3,122),0.837690818228908),
((3,123),0.3965390115437441),((3,124),0.7808718309203859),((3,125),0.79129804631
69716),((3,126),0.34484302377053316),((3,127),0.8167532140270747),((3,128),0.816
5316163573697),((3,129),0.8818434724099179),((3,130),0.37537463186528564),((3,13
1),0.4353585603972815),((3,132),0.33324241012004985),((3,133),0.8943229025786503
),((3,134),0.3260086535035433),((3,135),0.5244262879916373),((3,136),0.705854022
095231),((3,137),0.8619302145444536),((3,138),0.5345557358212287),((3,139),0.802
8648412348194),((3,140),0.866408884413472),((3,141),0.9331427316790457),((3,142)
,0.7994204903940182),((3,143),0.8057890517203751),((3,144),0.9142007935511516),(
(3,145),0.9188463896793009),((3,146),0.8629774876749744),((3,147),0.739419570654
2976),((3,148),0.9578271130867587),((3,149),0.848684448425652),((3,150),0.710299
2206798279)], mustLink = [], nMustLink = 0, cannotLink = [], nCannotLink = 0, dp
Dim = 4, eta0 = 0.181, t0 = 25, tau = 1.09, tolerance = 1.0e-20, threshold = 1.0
e-2}

除了第一行以外，輸出完全是 Haskell 的 deriving Show 做出來的，對於程式員已經相當足夠。

--
感覺上這東西最有學問的部份是調參數 XD。