id sid tid token lemma pos fcis-2488 1 1 frontiers frontier NOUN fcis-2488 1 2 in in ADP fcis-2488 1 3 computing computing NOUN fcis-2488 1 4 and and CCONJ fcis-2488 1 5 intelligent intelligent ADJ fcis-2488 1 6 systems system NOUN fcis-2488 1 7 issn issn VERB fcis-2488 1 8 : : PUNCT fcis-2488 1 9 2832 2832 NUM fcis-2488 1 10 - - SYM fcis-2488 1 11 6024 6024 NUM fcis-2488 1 12 | | NOUN fcis-2488 1 13 vol vol NOUN fcis-2488 1 14 . . PROPN fcis-2488 2 1 2 2 NUM fcis-2488 2 2 , , PUNCT fcis-2488 2 3 no no INTJ fcis-2488 2 4 . . NOUN fcis-2488 2 5 1 1 NUM fcis-2488 2 6 , , PUNCT fcis-2488 2 7 2022 2022 NUM fcis-2488 2 8 23 23 NUM fcis-2488 2 9 initial initial ADJ fcis-2488 2 10 cluster cluster NOUN fcis-2488 2 11 centers center NOUN fcis-2488 2 12 based base VERB fcis-2488 2 13 on on ADP fcis-2488 2 14 moving move VERB fcis-2488 2 15 two two NUM fcis-2488 2 16 lines line NOUN fcis-2488 2 17 approximation approximation NOUN fcis-2488 2 18 in in ADP fcis-2488 2 19 k k ADJ fcis-2488 2 20 - - PUNCT fcis-2488 2 21 means means NOUN fcis-2488 2 22 algorithm algorithm NOUN fcis-2488 2 23 wenyue wenyue PROPN fcis-2488 2 24 feng feng PROPN fcis-2488 2 25 , , PUNCT fcis-2488 2 26 shuangxia shuangxia PROPN fcis-2488 2 27 xuan xuan PROPN fcis-2488 2 28 anhui anhui PROPN fcis-2488 2 29 university university PROPN fcis-2488 2 30 of of ADP fcis-2488 2 31 finance finance NOUN fcis-2488 2 32 and and CCONJ fcis-2488 2 33 economics economic NOUN fcis-2488 2 34 , , PUNCT fcis-2488 2 35 bengbu bengbu NOUN fcis-2488 2 36 233030 233030 NUM fcis-2488 2 37 , , PUNCT fcis-2488 2 38 china china PROPN fcis-2488 2 39 abstract abstract PROPN fcis-2488 2 40 : : PUNCT fcis-2488 2 41 the the DET fcis-2488 2 42 main main ADJ fcis-2488 2 43 shortcoming shortcoming NOUN fcis-2488 2 44 of of ADP fcis-2488 2 45 k k NOUN fcis-2488 2 46 - - PUNCT fcis-2488 2 47 means mean VERB fcis-2488 2 48 clustering clustering ADJ fcis-2488 2 49 algorithm algorithm NOUN fcis-2488 2 50 is be AUX fcis-2488 2 51 its its PRON fcis-2488 2 52 great great ADJ fcis-2488 2 53 dependence dependence NOUN fcis-2488 2 54 on on ADP fcis-2488 2 55 the the DET fcis-2488 2 56 initial initial ADJ fcis-2488 2 57 cluster cluster NOUN fcis-2488 2 58 center center NOUN fcis-2488 2 59 point point NOUN fcis-2488 2 60 . . PUNCT fcis-2488 3 1 based base VERB fcis-2488 3 2 on on ADP fcis-2488 3 3 the the DET fcis-2488 3 4 moving move VERB fcis-2488 3 5 two two NUM fcis-2488 3 6 lines line NOUN fcis-2488 3 7 approximation approximation NOUN fcis-2488 3 8 model model NOUN fcis-2488 3 9 , , PUNCT fcis-2488 3 10 this this DET fcis-2488 3 11 paper paper NOUN fcis-2488 3 12 gives give VERB fcis-2488 3 13 a a DET fcis-2488 3 14 method method NOUN fcis-2488 3 15 to to PART fcis-2488 3 16 pick pick VERB fcis-2488 3 17 the the DET fcis-2488 3 18 initial initial ADJ fcis-2488 3 19 cluster cluster NOUN fcis-2488 3 20 center center NOUN fcis-2488 3 21 of of ADP fcis-2488 3 22 k k PROPN fcis-2488 3 23 - - PUNCT fcis-2488 3 24 means mean VERB fcis-2488 3 25 clustering clustering NOUN fcis-2488 3 26 . . PUNCT fcis-2488 4 1 numerical numerical ADJ fcis-2488 4 2 experiments experiment NOUN fcis-2488 4 3 and and CCONJ fcis-2488 4 4 comparison comparison NOUN fcis-2488 4 5 criteria criterion NOUN fcis-2488 4 6 show show VERB fcis-2488 4 7 that that SCONJ fcis-2488 4 8 this this DET fcis-2488 4 9 method method NOUN fcis-2488 4 10 can can AUX fcis-2488 4 11 get get VERB fcis-2488 4 12 better well ADJ fcis-2488 4 13 clustering clustering ADJ fcis-2488 4 14 effect effect NOUN fcis-2488 4 15 . . PUNCT fcis-2488 5 1 keywords keyword NOUN fcis-2488 5 2 : : PUNCT fcis-2488 5 3 initial initial ADJ fcis-2488 5 4 cluster cluster NOUN fcis-2488 5 5 centers center NOUN fcis-2488 5 6 ; ; PUNCT fcis-2488 5 7 moving move VERB fcis-2488 5 8 two two NUM fcis-2488 5 9 lines line NOUN fcis-2488 5 10 approximation approximation NOUN fcis-2488 5 11 ; ; PUNCT fcis-2488 5 12 k k X fcis-2488 5 13 - - PUNCT fcis-2488 5 14 means mean VERB fcis-2488 5 15 algorithm algorithm NOUN fcis-2488 5 16 . . PUNCT fcis-2488 6 1 1 1 X fcis-2488 6 2 . . X fcis-2488 6 3 introduction introduction NOUN fcis-2488 6 4 k k NOUN fcis-2488 6 5 - - PUNCT fcis-2488 6 6 means means NOUN fcis-2488 6 7 algorithm algorithm NOUN fcis-2488 6 8 is be AUX fcis-2488 6 9 a a DET fcis-2488 6 10 hard hard ADV fcis-2488 6 11 - - PUNCT fcis-2488 6 12 clustering cluster VERB fcis-2488 6 13 algorithm algorithm NOUN fcis-2488 6 14 and and CCONJ fcis-2488 6 15 a a DET fcis-2488 6 16 representative representative NOUN fcis-2488 6 17 of of ADP fcis-2488 6 18 typical typical ADJ fcis-2488 6 19 prototype prototype NOUN fcis-2488 6 20 based base VERB fcis-2488 6 21 clustering clustering ADJ fcis-2488 6 22 methods method NOUN fcis-2488 6 23 . . PUNCT fcis-2488 7 1 it it PRON fcis-2488 7 2 is be AUX fcis-2488 7 3 a a DET fcis-2488 7 4 certain certain ADJ fcis-2488 7 5 distance distance NOUN fcis-2488 7 6 between between ADP fcis-2488 7 7 the the DET fcis-2488 7 8 data data NOUN fcis-2488 7 9 points point NOUN fcis-2488 7 10 and and CCONJ fcis-2488 7 11 the the DET fcis-2488 7 12 prototype prototype NOUN fcis-2488 7 13 as as ADP fcis-2488 7 14 the the DET fcis-2488 7 15 objective objective ADJ fcis-2488 7 16 function function NOUN fcis-2488 7 17 of of ADP fcis-2488 7 18 optimization optimization NOUN fcis-2488 7 19 , , PUNCT fcis-2488 7 20 and and CCONJ fcis-2488 7 21 uses use VERB fcis-2488 7 22 the the DET fcis-2488 7 23 method method NOUN fcis-2488 7 24 of of ADP fcis-2488 7 25 finding find VERB fcis-2488 7 26 the the DET fcis-2488 7 27 extreme extreme ADJ fcis-2488 7 28 value value NOUN fcis-2488 7 29 of of ADP fcis-2488 7 30 the the DET fcis-2488 7 31 function function NOUN fcis-2488 7 32 to to PART fcis-2488 7 33 get get VERB fcis-2488 7 34 the the DET fcis-2488 7 35 adjustment adjustment NOUN fcis-2488 7 36 rules rule NOUN fcis-2488 7 37 of of ADP fcis-2488 7 38 iterative iterative ADJ fcis-2488 7 39 operation operation NOUN fcis-2488 7 40 . . PUNCT fcis-2488 8 1 k k X fcis-2488 8 2 - - PUNCT fcis-2488 8 3 means mean VERB fcis-2488 8 4 clustering clustering NOUN fcis-2488 8 5 maximizes maximize NOUN fcis-2488 8 6 the the DET fcis-2488 8 7 distance distance NOUN fcis-2488 8 8 between between ADP fcis-2488 8 9 objects object NOUN fcis-2488 8 10 within within ADP fcis-2488 8 11 a a DET fcis-2488 8 12 class class NOUN fcis-2488 8 13 , , PUNCT fcis-2488 8 14 while while SCONJ fcis-2488 8 15 minimizes minimize VERB fcis-2488 8 16 the the DET fcis-2488 8 17 distance distance NOUN fcis-2488 8 18 between between ADP fcis-2488 8 19 classes class NOUN fcis-2488 8 20 . . PUNCT fcis-2488 9 1 k k X fcis-2488 9 2 - - PUNCT fcis-2488 9 3 means mean VERB fcis-2488 9 4 clustering clustering ADJ fcis-2488 9 5 algorithm algorithm NOUN fcis-2488 9 6 is be AUX fcis-2488 9 7 highly highly ADV fcis-2488 9 8 dependent dependent ADJ fcis-2488 9 9 on on ADP fcis-2488 9 10 the the DET fcis-2488 9 11 selection selection NOUN fcis-2488 9 12 of of ADP fcis-2488 9 13 initial initial ADJ fcis-2488 9 14 values value NOUN fcis-2488 9 15 . . PUNCT fcis-2488 10 1 an an DET fcis-2488 10 2 inappropriate inappropriate ADJ fcis-2488 10 3 initial initial ADJ fcis-2488 10 4 value value NOUN fcis-2488 10 5 causes cause VERB fcis-2488 10 6 the the DET fcis-2488 10 7 algorithm algorithm NOUN fcis-2488 10 8 to to PART fcis-2488 10 9 converge converge VERB fcis-2488 10 10 to to ADP fcis-2488 10 11 a a DET fcis-2488 10 12 local local ADJ fcis-2488 10 13 minimum minimum NOUN fcis-2488 10 14 , , PUNCT fcis-2488 10 15 so so SCONJ fcis-2488 10 16 a a DET fcis-2488 10 17 lot lot NOUN fcis-2488 10 18 of of ADP fcis-2488 10 19 work work NOUN fcis-2488 10 20 has have AUX fcis-2488 10 21 been be AUX fcis-2488 10 22 done do VERB fcis-2488 10 23 on on ADP fcis-2488 10 24 the the DET fcis-2488 10 25 selection selection NOUN fcis-2488 10 26 of of ADP fcis-2488 10 27 initial initial ADJ fcis-2488 10 28 clustering clustering ADJ fcis-2488 10 29 centers center NOUN fcis-2488 10 30 . . PUNCT fcis-2488 11 1 fayyad fayyad PROPN fcis-2488 11 2 et et PROPN fcis-2488 11 3 al al PROPN fcis-2488 11 4 . . PUNCT fcis-2488 12 1 [ [ X fcis-2488 12 2 1 1 X fcis-2488 12 3 ] ] AUX fcis-2488 12 4 give give VERB fcis-2488 12 5 a a DET fcis-2488 12 6 fast fast ADJ fcis-2488 12 7 and and CCONJ fcis-2488 12 8 efficient efficient ADJ fcis-2488 12 9 algorithnm algorithnm NOUN fcis-2488 12 10 operated operate VERB fcis-2488 12 11 over over ADP fcis-2488 12 12 small small ADJ fcis-2488 12 13 subsamples subsample NOUN fcis-2488 12 14 of of ADP fcis-2488 12 15 a a DET fcis-2488 12 16 given give VERB fcis-2488 12 17 database database NOUN fcis-2488 12 18 for for ADP fcis-2488 12 19 refining refine VERB fcis-2488 12 20 an an DET fcis-2488 12 21 initial initial ADJ fcis-2488 12 22 starting starting NOUN fcis-2488 12 23 point point NOUN fcis-2488 12 24 . . PUNCT fcis-2488 13 1 using use VERB fcis-2488 13 2 the the DET fcis-2488 13 3 global global ADJ fcis-2488 13 4 optimization optimization NOUN fcis-2488 13 5 ability ability NOUN fcis-2488 13 6 of of ADP fcis-2488 13 7 genetic genetic ADJ fcis-2488 13 8 algorithm algorithm NOUN fcis-2488 13 9 to to PART fcis-2488 13 10 improve improve VERB fcis-2488 13 11 the the DET fcis-2488 13 12 traditional traditional ADJ fcis-2488 13 13 kmeans kmean NOUN fcis-2488 13 14 algorithm algorithm NOUN fcis-2488 13 15 to to PART fcis-2488 13 16 prevent prevent VERB fcis-2488 13 17 only only ADV fcis-2488 13 18 local local ADJ fcis-2488 13 19 optimal optimal ADJ fcis-2488 13 20 solutions solution NOUN fcis-2488 13 21 is be AUX fcis-2488 13 22 described describe VERB fcis-2488 13 23 in in ADP fcis-2488 13 24 [ [ X fcis-2488 13 25 2,3 2,3 NUM fcis-2488 13 26 ] ] PUNCT fcis-2488 13 27 . . PUNCT fcis-2488 14 1 likas likas PROPN fcis-2488 14 2 et et PROPN fcis-2488 14 3 al al PROPN fcis-2488 14 4 . . PROPN fcis-2488 15 1 present present VERB fcis-2488 15 2 the the DET fcis-2488 15 3 global global ADJ fcis-2488 15 4 k k PROPN fcis-2488 15 5 - - PUNCT fcis-2488 15 6 means means NOUN fcis-2488 15 7 algorithm algorithm NOUN fcis-2488 15 8 which which PRON fcis-2488 15 9 is be AUX fcis-2488 15 10 an an DET fcis-2488 15 11 incremental incremental ADJ fcis-2488 15 12 approach approach NOUN fcis-2488 15 13 to to ADP fcis-2488 15 14 clustering cluster VERB fcis-2488 15 15 that that PRON fcis-2488 15 16 dynamically dynamically ADV fcis-2488 15 17 adds add VERB fcis-2488 15 18 one one NUM fcis-2488 15 19 cluster cluster NOUN fcis-2488 15 20 center center NOUN fcis-2488 15 21 at at ADP fcis-2488 15 22 a a DET fcis-2488 15 23 time time NOUN fcis-2488 15 24 through through ADP fcis-2488 15 25 a a DET fcis-2488 15 26 deterministic deterministic ADJ fcis-2488 15 27 global global ADJ fcis-2488 15 28 search search NOUN fcis-2488 15 29 procedure procedure NOUN fcis-2488 15 30 [ [ X fcis-2488 15 31 4 4 NUM fcis-2488 15 32 ] ] PUNCT fcis-2488 15 33 . . PUNCT fcis-2488 16 1 kkan kkan PROPN fcis-2488 16 2 and and CCONJ fcis-2488 16 3 ahmad ahmad PROPN fcis-2488 16 4 propose propose VERB fcis-2488 16 5 an an DET fcis-2488 16 6 algorithm algorithm NOUN fcis-2488 16 7 to to PART fcis-2488 16 8 compute compute VERB fcis-2488 16 9 initial initial ADJ fcis-2488 16 10 cluster cluster NOUN fcis-2488 16 11 centers center NOUN fcis-2488 16 12 for for ADP fcis-2488 16 13 kmeans kmean NOUN fcis-2488 16 14 clustering cluster VERB fcis-2488 16 15 . . PUNCT fcis-2488 17 1 this this DET fcis-2488 17 2 algorithm algorithm NOUN fcis-2488 17 3 is be AUX fcis-2488 17 4 based base VERB fcis-2488 17 5 on on ADP fcis-2488 17 6 two two NUM fcis-2488 17 7 observations observation NOUN fcis-2488 17 8 that that PRON fcis-2488 17 9 some some PRON fcis-2488 17 10 of of ADP fcis-2488 17 11 the the DET fcis-2488 17 12 patterns pattern NOUN fcis-2488 17 13 are be AUX fcis-2488 17 14 very very ADV fcis-2488 17 15 similar similar ADJ fcis-2488 17 16 to to ADP fcis-2488 17 17 each each DET fcis-2488 17 18 other other ADJ fcis-2488 17 19 and and CCONJ fcis-2488 17 20 that that PRON fcis-2488 17 21 is be AUX fcis-2488 17 22 why why SCONJ fcis-2488 17 23 they they PRON fcis-2488 17 24 have have VERB fcis-2488 17 25 same same ADJ fcis-2488 17 26 cluster cluster NOUN fcis-2488 17 27 membership membership NOUN fcis-2488 17 28 irrespective irrespective ADV fcis-2488 17 29 to to ADP fcis-2488 17 30 the the DET fcis-2488 17 31 choice choice NOUN fcis-2488 17 32 of of ADP fcis-2488 17 33 initial initial ADJ fcis-2488 17 34 cluster cluster NOUN fcis-2488 17 35 centers center NOUN fcis-2488 17 36 [ [ X fcis-2488 17 37 5 5 NUM fcis-2488 17 38 ] ] PUNCT fcis-2488 17 39 . . PUNCT fcis-2488 18 1 in in ADP fcis-2488 18 2 order order NOUN fcis-2488 18 3 to to PART fcis-2488 18 4 get get VERB fcis-2488 18 5 the the DET fcis-2488 18 6 initial initial ADJ fcis-2488 18 7 cluster cluster NOUN fcis-2488 18 8 centers center NOUN fcis-2488 18 9 for for ADP fcis-2488 18 10 k k NOUN fcis-2488 18 11 - - PUNCT fcis-2488 18 12 means means NOUN fcis-2488 18 13 algorithm algorithm NOUN fcis-2488 18 14 , , PUNCT fcis-2488 18 15 cells cell NOUN fcis-2488 18 16 are be AUX fcis-2488 18 17 partitioned partition VERB fcis-2488 18 18 one one NUM fcis-2488 18 19 at at ADP fcis-2488 18 20 a a DET fcis-2488 18 21 time time NOUN fcis-2488 18 22 until until SCONJ fcis-2488 18 23 the the DET fcis-2488 18 24 number number NOUN fcis-2488 18 25 of of ADP fcis-2488 18 26 cells cell NOUN fcis-2488 18 27 equals equal VERB fcis-2488 18 28 to to ADP fcis-2488 18 29 the the DET fcis-2488 18 30 predefined predefine VERB fcis-2488 18 31 number number NOUN fcis-2488 18 32 of of ADP fcis-2488 18 33 clusters cluster NOUN fcis-2488 18 34 , , PUNCT fcis-2488 18 35 k. k. PROPN fcis-2488 19 1 the the DET fcis-2488 19 2 centers center NOUN fcis-2488 19 3 of of ADP fcis-2488 19 4 the the DET fcis-2488 19 5 k k PROPN fcis-2488 19 6 cells cell NOUN fcis-2488 19 7 become become VERB fcis-2488 19 8 the the DET fcis-2488 19 9 initial initial ADJ fcis-2488 19 10 cluster cluster NOUN fcis-2488 19 11 centers center NOUN fcis-2488 19 12 [ [ X fcis-2488 19 13 6 6 NUM fcis-2488 19 14 ] ] PUNCT fcis-2488 19 15 . . PUNCT fcis-2488 20 1 later later ADV fcis-2488 20 2 a a DET fcis-2488 20 3 new new ADJ fcis-2488 20 4 algorithm algorithm NOUN fcis-2488 20 5 for for ADP fcis-2488 20 6 initial initial ADJ fcis-2488 20 7 cluster cluster NOUN fcis-2488 20 8 centers center NOUN fcis-2488 20 9 in in ADP fcis-2488 20 10 k k NOUN fcis-2488 20 11 - - PUNCT fcis-2488 20 12 means means NOUN fcis-2488 20 13 algorithm algorithm NOUN fcis-2488 20 14 is be AUX fcis-2488 20 15 given give VERB fcis-2488 20 16 in in ADP fcis-2488 20 17 [ [ X fcis-2488 20 18 7 7 NUM fcis-2488 20 19 ] ] PUNCT fcis-2488 20 20 . . PUNCT fcis-2488 21 1 two two NUM fcis-2488 21 2 principal principal ADJ fcis-2488 21 3 variables variable NOUN fcis-2488 21 4 are be AUX fcis-2488 21 5 selected select VERB fcis-2488 21 6 according accord VERB fcis-2488 21 7 to to ADP fcis-2488 21 8 maximum maximum ADJ fcis-2488 21 9 coefficient coefficient NOUN fcis-2488 21 10 of of ADP fcis-2488 21 11 the the DET fcis-2488 21 12 variaton variaton NOUN fcis-2488 21 13 and and CCONJ fcis-2488 21 14 minimum minimum NOUN fcis-2488 21 15 absoute absoute ADJ fcis-2488 21 16 value value NOUN fcis-2488 21 17 of of ADP fcis-2488 21 18 the the DET fcis-2488 21 19 correlation correlation NOUN fcis-2488 21 20 . . PUNCT fcis-2488 22 1 the the DET fcis-2488 22 2 rest rest NOUN fcis-2488 22 3 of of ADP fcis-2488 22 4 this this DET fcis-2488 22 5 paper paper NOUN fcis-2488 22 6 is be AUX fcis-2488 22 7 organized organize VERB fcis-2488 22 8 as as SCONJ fcis-2488 22 9 follows follow VERB fcis-2488 22 10 . . PUNCT fcis-2488 23 1 section section NOUN fcis-2488 23 2 2 2 NUM fcis-2488 23 3 introduces introduce VERB fcis-2488 23 4 the the DET fcis-2488 23 5 initial initial ADJ fcis-2488 23 6 cluster cluster NOUN fcis-2488 23 7 centers center NOUN fcis-2488 23 8 computing computing NOUN fcis-2488 23 9 based base VERB fcis-2488 23 10 on on ADP fcis-2488 23 11 moving move VERB fcis-2488 23 12 two two NUM fcis-2488 23 13 lines line NOUN fcis-2488 23 14 approximation approximation NOUN fcis-2488 23 15 . . PUNCT fcis-2488 24 1 section section NOUN fcis-2488 24 2 3 3 NUM fcis-2488 24 3 introduces introduce VERB fcis-2488 24 4 the the DET fcis-2488 24 5 comparision comparision NOUN fcis-2488 24 6 criteria criterion NOUN fcis-2488 24 7 such such ADJ fcis-2488 24 8 as as ADP fcis-2488 24 9 error error NOUN fcis-2488 24 10 percentage percentage NOUN fcis-2488 24 11 and and CCONJ fcis-2488 24 12 rand rand NOUN fcis-2488 24 13 index index NOUN fcis-2488 24 14 . . PUNCT fcis-2488 25 1 section section NOUN fcis-2488 25 2 4 4 NUM fcis-2488 25 3 elaborates elaborate VERB fcis-2488 25 4 the the DET fcis-2488 25 5 implementation implementation NOUN fcis-2488 25 6 of of ADP fcis-2488 25 7 the the DET fcis-2488 25 8 algorithm algorithm NOUN fcis-2488 25 9 and and CCONJ fcis-2488 25 10 presents present VERB fcis-2488 25 11 experiments experiment NOUN fcis-2488 25 12 and and CCONJ fcis-2488 25 13 results result VERB fcis-2488 25 14 better well ADV fcis-2488 25 15 . . PUNCT fcis-2488 26 1 section section NOUN fcis-2488 26 2 4 4 NUM fcis-2488 26 3 concludes conclude VERB fcis-2488 26 4 the the DET fcis-2488 26 5 paper paper NOUN fcis-2488 26 6 . . PUNCT fcis-2488 27 1 2 2 X fcis-2488 27 2 . . X fcis-2488 27 3 initial initial ADJ fcis-2488 27 4 cluster cluster NOUN fcis-2488 27 5 centers center NOUN fcis-2488 27 6 computing computing NOUN fcis-2488 27 7 based base VERB fcis-2488 27 8 on on ADP fcis-2488 27 9 moving move VERB fcis-2488 27 10 two two NUM fcis-2488 27 11 lines line NOUN fcis-2488 27 12 approximation approximation NOUN fcis-2488 27 13 moving move VERB fcis-2488 27 14 multiple multiple ADJ fcis-2488 27 15 curves curve NOUN fcis-2488 27 16 approximation approximation NOUN fcis-2488 27 17 is be AUX fcis-2488 27 18 based base VERB fcis-2488 27 19 on on ADP fcis-2488 27 20 [ [ X fcis-2488 27 21 8 8 NUM fcis-2488 27 22 ] ] PUNCT fcis-2488 27 23 , , PUNCT fcis-2488 27 24 while while SCONJ fcis-2488 27 25 moving move VERB fcis-2488 27 26 two two NUM fcis-2488 27 27 lines line NOUN fcis-2488 27 28 approximation approximation NOUN fcis-2488 27 29 is be AUX fcis-2488 27 30 a a DET fcis-2488 27 31 particultiple particultiple ADJ fcis-2488 27 32 curves curve NOUN fcis-2488 27 33 approximation approximation NOUN fcis-2488 27 34 of of ADP fcis-2488 27 35 moving move VERB fcis-2488 27 36 multiple multiple ADJ fcis-2488 27 37 curves curve NOUN fcis-2488 27 38 approximation approximation NOUN fcis-2488 28 1 [ [ X fcis-2488 28 2 9 9 NUM fcis-2488 28 3 ] ] PUNCT fcis-2488 28 4 . . PUNCT fcis-2488 29 1 there there ADV fcis-2488 29 2 using use VERB fcis-2488 29 3 two two NUM fcis-2488 29 4 lines line NOUN fcis-2488 29 5 in in ADP fcis-2488 29 6 the the DET fcis-2488 29 7 moving move VERB fcis-2488 29 8 multiple multiple ADJ fcis-2488 29 9 curves curve NOUN fcis-2488 29 10 approximation approximation NOUN fcis-2488 29 11 model model NOUN fcis-2488 29 12 and and CCONJ fcis-2488 29 13 modify modify VERB fcis-2488 29 14 the the DET fcis-2488 29 15 model model NOUN fcis-2488 29 16 as as SCONJ fcis-2488 29 17 follows follow VERB fcis-2488 29 18 . . PUNCT fcis-2488 30 1 π‘šπ‘–π‘› π‘šπ‘–π‘› NOUN fcis-2488 30 2 βˆ‘ βˆ‘ PROPN fcis-2488 30 3 ( ( PUNCT fcis-2488 30 4 π‘Ž1π‘₯𝑖 π‘Ž1π‘₯𝑖 VERB fcis-2488 30 5 + + CCONJ fcis-2488 30 6 𝑏1𝑦𝑖 𝑏1𝑦𝑖 PUNCT fcis-2488 31 1 + + X fcis-2488 31 2 𝑐1)2(π‘Ž2π‘₯𝑖 𝑐1)2(π‘Ž2π‘₯𝑖 ADJ fcis-2488 31 3 + + CCONJ fcis-2488 31 4 𝑏2𝑦𝑖 𝑏2𝑦𝑖 X fcis-2488 31 5 + + NOUN fcis-2488 31 6 𝑛 𝑛 PRON fcis-2488 31 7 𝑖=1 𝑖=1 PROPN fcis-2488 31 8 𝑐2)2πœƒ(‖𝑃𝑖 𝑐2)2πœƒ(‖𝑃𝑖 NOUN fcis-2488 31 9 βˆ’ βˆ’ NOUN fcis-2488 31 10 𝑂π‘₯β€– 𝑂π‘₯β€– NOUN fcis-2488 31 11 ) ) PUNCT fcis-2488 31 12 𝑠. 𝑠. NOUN fcis-2488 31 13 𝑑. 𝑑. NOUN fcis-2488 31 14 π‘Ž1 π‘Ž1 NOUN fcis-2488 31 15 2 2 NUM fcis-2488 31 16 + + CCONJ fcis-2488 31 17 𝑏1 𝑏1 ADJ fcis-2488 31 18 2 2 NUM fcis-2488 31 19 = = SYM fcis-2488 31 20 1 1 NUM fcis-2488 31 21 π‘Ž2 π‘Ž2 NOUN fcis-2488 31 22 2 2 NUM fcis-2488 31 23 + + CCONJ fcis-2488 31 24 𝑏2 𝑏2 PROPN fcis-2488 31 25 2 2 NUM fcis-2488 31 26 = = SYM fcis-2488 31 27 1 1 NUM fcis-2488 31 28 ( ( PUNCT fcis-2488 31 29 1 1 NUM fcis-2488 31 30 ) ) PUNCT fcis-2488 31 31 where where SCONJ fcis-2488 31 32 π‘œπ‘₯ π‘œπ‘₯ PROPN fcis-2488 31 33 is be AUX fcis-2488 31 34 a a DET fcis-2488 31 35 projected project VERB fcis-2488 31 36 point point NOUN fcis-2488 31 37 of of ADP fcis-2488 31 38 𝑋on 𝑋on PROPN fcis-2488 31 39 an an DET fcis-2488 31 40 underlying underlie VERB fcis-2488 31 41 curve curve NOUN fcis-2488 31 42 and and CCONJ fcis-2488 31 43 𝑋 𝑋 NOUN fcis-2488 31 44 is be AUX fcis-2488 31 45 a a DET fcis-2488 31 46 fixed fix VERB fcis-2488 31 47 point point NOUN fcis-2488 31 48 called call VERB fcis-2488 31 49 a a DET fcis-2488 31 50 reference reference NOUN fcis-2488 31 51 point point NOUN fcis-2488 31 52 near near ADP fcis-2488 31 53 the the DET fcis-2488 31 54 underlying underlie VERB fcis-2488 31 55 shape shape NOUN fcis-2488 31 56 which which PRON fcis-2488 31 57 is be AUX fcis-2488 31 58 acquired acquire VERB fcis-2488 31 59 according accord VERB fcis-2488 31 60 to to ADP fcis-2488 31 61 partitioning partition VERB fcis-2488 31 62 the the DET fcis-2488 31 63 space space NOUN fcis-2488 31 64 occupied occupy VERB fcis-2488 31 65 by by ADP fcis-2488 31 66 { { PUNCT fcis-2488 31 67 𝑃𝑖}𝑖=1 𝑃𝑖}𝑖=1 PROPN fcis-2488 31 68 𝑛 𝑛 PROPN fcis-2488 31 69 . . PUNCT fcis-2488 32 1 ( ( PUNCT fcis-2488 32 2 π‘₯𝑖 π‘₯𝑖 PROPN fcis-2488 32 3 , , PUNCT fcis-2488 32 4 𝑦𝑖 𝑦𝑖 PROPN fcis-2488 32 5 ) ) PUNCT fcis-2488 32 6 is be AUX fcis-2488 32 7 the the DET fcis-2488 32 8 coordinate coordinate NOUN fcis-2488 32 9 of of ADP fcis-2488 32 10 , , PUNCT fcis-2488 32 11 𝑃𝑖 𝑃𝑖 ADP fcis-2488 32 12 , , PUNCT fcis-2488 32 13 𝑖 𝑖 NOUN fcis-2488 32 14 = = SYM fcis-2488 32 15 1,2 1,2 NUM fcis-2488 32 16 , , PUNCT fcis-2488 32 17 β‹― β‹― PROPN fcis-2488 32 18 , , PUNCT fcis-2488 32 19 𝑛 𝑛 PROPN fcis-2488 32 20 . . PUNCT fcis-2488 33 1 π‘Ž2π‘₯ π‘Ž2π‘₯ PROPN fcis-2488 33 2 + + CCONJ fcis-2488 33 3 𝑏2𝑦 𝑏2𝑦 PROPN fcis-2488 33 4 + + NUM fcis-2488 33 5 𝑐2 𝑐2 NOUN fcis-2488 33 6 = = SYM fcis-2488 33 7 0 0 NUM fcis-2488 33 8 are be AUX fcis-2488 33 9 algebraic algebraic ADJ fcis-2488 33 10 equations equation NOUN fcis-2488 33 11 of of ADP fcis-2488 33 12 two two NUM fcis-2488 33 13 lines line NOUN fcis-2488 33 14 . . PUNCT fcis-2488 34 1 π‘Ž1π‘₯𝑖 π‘Ž1π‘₯𝑖 PROPN fcis-2488 35 1 + + CCONJ fcis-2488 35 2 𝑏1𝑦𝑖 𝑏1𝑦𝑖 PUNCT fcis-2488 35 3 + + CCONJ fcis-2488 35 4 𝑐1 𝑐1 NOUN fcis-2488 35 5 and and CCONJ fcis-2488 35 6 π‘Ž2π‘₯𝑖 π‘Ž2π‘₯𝑖 X fcis-2488 35 7 + + CCONJ fcis-2488 35 8 𝑏2𝑦𝑖 𝑏2𝑦𝑖 ADP fcis-2488 35 9 + + NOUN fcis-2488 35 10 𝑐2 𝑐2 NOUN fcis-2488 35 11 are be AUX fcis-2488 35 12 two two NUM fcis-2488 35 13 algebraic algebraic ADJ fcis-2488 35 14 distance distance NOUN fcis-2488 35 15 from from ADP fcis-2488 35 16 𝑃𝑖. 𝑃𝑖. PROPN fcis-2488 35 17 and and CCONJ fcis-2488 35 18 πœƒ(‖𝑃𝑖 πœƒ(‖𝑃𝑖 NOUN fcis-2488 35 19 βˆ’ βˆ’ VERB fcis-2488 35 20 𝑂π‘₯β€– 𝑂π‘₯β€– NOUN fcis-2488 35 21 ) ) PUNCT fcis-2488 35 22 = = PUNCT fcis-2488 35 23 𝑒 𝑒 PROPN fcis-2488 35 24 βˆ’ βˆ’ PROPN fcis-2488 35 25 ||π‘ƒπ‘–βˆ’π‘‚π‘₯||2 ||π‘ƒπ‘–βˆ’π‘‚π‘₯||2 AUX fcis-2488 35 26 𝜌2 𝜌2 ADJ fcis-2488 35 27 βˆ‘ βˆ‘ PUNCT fcis-2488 35 28 𝑒 𝑒 PROPN fcis-2488 35 29 βˆ’ βˆ’ PROPN fcis-2488 35 30 ||π‘ƒπ‘–βˆ’π‘‚π‘₯||2 ||π‘ƒπ‘–βˆ’π‘‚π‘₯||2 AUX fcis-2488 35 31 𝜌2 𝜌2 ADJ fcis-2488 35 32 π‘ƒπ‘–βˆˆ{𝑃𝑖}𝑖=1 π‘ƒπ‘–βˆˆ{𝑃𝑖}𝑖=1 NOUN fcis-2488 35 33 𝑛 𝑛 PROPN fcis-2488 35 34 𝜌is 𝜌is VERB fcis-2488 35 35 a a DET fcis-2488 35 36 adjustment adjustment NOUN fcis-2488 35 37 parameter parameter NOUN fcis-2488 35 38 . . PUNCT fcis-2488 36 1 to to PART fcis-2488 36 2 reduce reduce VERB fcis-2488 36 3 the the DET fcis-2488 36 4 instability instability NOUN fcis-2488 36 5 and and CCONJ fcis-2488 36 6 expensive expensive ADJ fcis-2488 36 7 computation computation NOUN fcis-2488 36 8 , , PUNCT fcis-2488 36 9 moving move VERB fcis-2488 36 10 two two NUM fcis-2488 36 11 lines line NOUN fcis-2488 36 12 approximation approximation NOUN fcis-2488 36 13 ( ( PUNCT fcis-2488 36 14 1 1 X fcis-2488 36 15 ) ) PUNCT fcis-2488 36 16 is be AUX fcis-2488 36 17 rewrite rewrite VERB fcis-2488 36 18 as as ADP fcis-2488 36 19 ( ( PUNCT fcis-2488 36 20 2 2 NUM fcis-2488 36 21 ) ) PUNCT fcis-2488 36 22 . . PUNCT fcis-2488 37 1 π‘šπ‘–π‘› π‘šπ‘–π‘› NOUN fcis-2488 37 2 βˆ‘ βˆ‘ PROPN fcis-2488 37 3 ( ( PUNCT fcis-2488 37 4 π‘Ž1π‘₯𝑖 π‘Ž1π‘₯𝑖 VERB fcis-2488 37 5 + + CCONJ fcis-2488 37 6 𝑏1𝑦𝑖 𝑏1𝑦𝑖 PUNCT fcis-2488 38 1 + + X fcis-2488 38 2 𝑐1)2(π‘Ž2π‘₯𝑖 𝑐1)2(π‘Ž2π‘₯𝑖 ADJ fcis-2488 38 3 + + CCONJ fcis-2488 38 4 𝑏2𝑦𝑖 𝑏2𝑦𝑖 PUNCT fcis-2488 38 5 + + NOUN fcis-2488 38 6 𝑐2)2πœƒ(‖𝑃𝑖 𝑐2)2πœƒ(‖𝑃𝑖 NOUN fcis-2488 38 7 βˆ’π‘› βˆ’π‘› NOUN fcis-2488 38 8 𝑖=1 𝑖=1 PROPN fcis-2488 38 9 𝑋‖ 𝑋‖ PROPN fcis-2488 38 10 ) ) PUNCT fcis-2488 38 11 ( ( PUNCT fcis-2488 38 12 2 2 X fcis-2488 38 13 ) ) PUNCT fcis-2488 38 14 see see VERB fcis-2488 38 15 [ [ X fcis-2488 38 16 9 9 X fcis-2488 38 17 ] ] PUNCT fcis-2488 38 18 for for ADP fcis-2488 38 19 more more ADJ fcis-2488 38 20 details detail NOUN fcis-2488 38 21 . . PUNCT fcis-2488 39 1 3 3 X fcis-2488 39 2 . . X fcis-2488 39 3 comparision comparision NOUN fcis-2488 39 4 criteria criterion NOUN fcis-2488 39 5 to to PART fcis-2488 39 6 compare compare VERB fcis-2488 39 7 the the DET fcis-2488 39 8 clustering clustering ADJ fcis-2488 39 9 results result NOUN fcis-2488 39 10 , , PUNCT fcis-2488 39 11 two two NUM fcis-2488 39 12 clustering cluster VERB fcis-2488 39 13 criteria criterion NOUN fcis-2488 39 14 are be AUX fcis-2488 39 15 presented present VERB fcis-2488 39 16 here here ADV fcis-2488 39 17 . . PUNCT fcis-2488 40 1 one one NUM fcis-2488 40 2 is be AUX fcis-2488 40 3 error error NOUN fcis-2488 40 4 percentage percentage NOUN fcis-2488 40 5 [ [ X fcis-2488 40 6 7 7 NUM fcis-2488 40 7 ] ] PUNCT fcis-2488 40 8 and and CCONJ fcis-2488 40 9 another another PRON fcis-2488 40 10 is be AUX fcis-2488 40 11 the the DET fcis-2488 40 12 rand rand NOUN fcis-2488 40 13 index index NOUN fcis-2488 40 14 [ [ X fcis-2488 40 15 10 10 NUM fcis-2488 40 16 ] ] PUNCT fcis-2488 40 17 . . PUNCT fcis-2488 41 1 error error NOUN fcis-2488 41 2 percentage percentage NOUN fcis-2488 41 3 is be AUX fcis-2488 41 4 defined define VERB fcis-2488 41 5 as as SCONJ fcis-2488 41 6 follows follow VERB fcis-2488 41 7 πΈπ‘Ÿπ‘Ÿπ‘œπ‘Ÿ πΈπ‘Ÿπ‘Ÿπ‘œπ‘Ÿ PROPN fcis-2488 41 8 = = PUNCT fcis-2488 41 9 πœ€ πœ€ PROPN fcis-2488 41 10 𝑛 𝑛 PRON fcis-2488 41 11 Γ— Γ— NOUN fcis-2488 41 12 100 100 NUM fcis-2488 41 13 ( ( PUNCT fcis-2488 41 14 3 3 NUM fcis-2488 41 15 ) ) PUNCT fcis-2488 41 16 where where SCONJ fcis-2488 41 17 πœ€ πœ€ PROPN fcis-2488 41 18 is be AUX fcis-2488 41 19 misclassified misclassifie VERB fcis-2488 41 20 observations observation NOUN fcis-2488 41 21 and and CCONJ fcis-2488 41 22 𝑛 𝑛 PROPN fcis-2488 41 23 is be AUX fcis-2488 41 24 the the DET fcis-2488 41 25 total total ADJ fcis-2488 41 26 number number NOUN fcis-2488 41 27 of of ADP fcis-2488 41 28 observations observation NOUN fcis-2488 41 29 in in ADP fcis-2488 41 30 datasets dataset NOUN fcis-2488 41 31 . . PUNCT fcis-2488 42 1 the the PRON fcis-2488 42 2 higher high ADJ fcis-2488 42 3 the the DET fcis-2488 42 4 value value NOUN fcis-2488 42 5 of of ADP fcis-2488 42 6 error error NOUN fcis-2488 42 7 , , PUNCT fcis-2488 42 8 the the PRON fcis-2488 42 9 better well ADJ fcis-2488 42 10 the the DET fcis-2488 42 11 result result NOUN fcis-2488 42 12 . . PUNCT fcis-2488 43 1 suppose suppose VERB fcis-2488 43 2 𝑄1 𝑄1 NOUN fcis-2488 43 3 βŠ† βŠ† NUM fcis-2488 43 4 { { PUNCT fcis-2488 43 5 𝑃𝑖}𝑖=1 𝑃𝑖}𝑖=1 NOUN fcis-2488 43 6 𝑛 𝑛 PROPN fcis-2488 43 7 , , PUNCT fcis-2488 43 8 𝑄2 𝑄2 PROPN fcis-2488 43 9 βŠ† βŠ† NUM fcis-2488 43 10 { { PUNCT fcis-2488 43 11 𝑃𝑖}𝑖=1 𝑃𝑖}𝑖=1 NOUN fcis-2488 43 12 𝑛 𝑛 PROPN fcis-2488 43 13 represent represent VERB fcis-2488 43 14 partitions partition NOUN fcis-2488 43 15 of of ADP fcis-2488 43 16 { { PUNCT fcis-2488 43 17 𝑃𝑖}𝑖=1 𝑃𝑖}𝑖=1 NOUN fcis-2488 43 18 𝑛 𝑛 PROPN fcis-2488 43 19 by by ADP fcis-2488 43 20 k k ADJ fcis-2488 43 21 - - PUNCT fcis-2488 43 22 means means NOUN fcis-2488 43 23 algorithm algorithm NOUN fcis-2488 43 24 and and CCONJ fcis-2488 43 25 real real ADJ fcis-2488 43 26 cluster cluster NOUN fcis-2488 43 27 memberships membership NOUN fcis-2488 43 28 respectively respectively ADV fcis-2488 43 29 . . PUNCT fcis-2488 44 1 for for ADP fcis-2488 44 2 each each DET fcis-2488 44 3 object object NOUN fcis-2488 44 4 pair pair NOUN fcis-2488 44 5 { { PUNCT fcis-2488 44 6 𝑃𝑖 𝑃𝑖 ADP fcis-2488 44 7 , , PUNCT fcis-2488 44 8 𝑃𝑗 𝑃𝑗 NOUN fcis-2488 44 9 } } PUNCT fcis-2488 44 10 there there ADV fcis-2488 44 11 ， ， PROPN fcis-2488 44 12 0111 0111 NUM fcis-2488 44 13 = = PUNCT fcis-2488 44 14 + + ADJ fcis-2488 44 15 + + ADJ fcis-2488 44 16 cybxa cybxa ADJ fcis-2488 44 17 javascript javascript NOUN fcis-2488 44 18 : : PUNCT fcis-2488 44 19 ; ; PUNCT fcis-2488 44 20 24 24 NUM fcis-2488 44 21 are be AUX fcis-2488 44 22 four four NUM fcis-2488 44 23 possible possible ADJ fcis-2488 44 24 scenarios scenario NOUN fcis-2488 44 25 : : PUNCT fcis-2488 44 26 π‘Ž:𝑃𝑖 π‘Ž:𝑃𝑖 NOUN fcis-2488 44 27 and and CCONJ fcis-2488 44 28 𝑃𝑗 𝑃𝑗 PROPN fcis-2488 44 29 are be AUX fcis-2488 44 30 in in ADP fcis-2488 44 31 the the DET fcis-2488 44 32 same same ADJ fcis-2488 44 33 cluster cluster NOUN fcis-2488 44 34 in in ADP fcis-2488 44 35 𝑄1 𝑄1 NOUN fcis-2488 44 36 and and CCONJ fcis-2488 44 37 in in ADP fcis-2488 44 38 the the DET fcis-2488 44 39 same same ADJ fcis-2488 44 40 cluster cluster NOUN fcis-2488 44 41 in in ADP fcis-2488 44 42 𝑄2 𝑄2 PROPN fcis-2488 44 43 . . PROPN fcis-2488 45 1 𝑏:𝑃𝑖 𝑏:𝑃𝑖 AUX fcis-2488 45 2 and and CCONJ fcis-2488 45 3 𝑃𝑗 𝑃𝑗 PROPN fcis-2488 45 4 are be AUX fcis-2488 45 5 in in ADP fcis-2488 45 6 different different ADJ fcis-2488 45 7 cluster cluster NOUN fcis-2488 45 8 in in ADP fcis-2488 45 9 𝑄1 𝑄1 NOUN fcis-2488 45 10 but but CCONJ fcis-2488 45 11 in in ADP fcis-2488 45 12 the the DET fcis-2488 45 13 same same ADJ fcis-2488 45 14 cluster cluster NOUN fcis-2488 45 15 in in ADP fcis-2488 45 16 𝑄2 𝑄2 PROPN fcis-2488 45 17 . . PUNCT fcis-2488 46 1 𝑐 𝑐 NOUN fcis-2488 46 2 : : PUNCT fcis-2488 46 3 𝑃𝑖 𝑃𝑖 ADP fcis-2488 46 4 and and CCONJ fcis-2488 46 5 𝑃𝑗 𝑃𝑗 PROPN fcis-2488 46 6 are be AUX fcis-2488 46 7 in in ADP fcis-2488 46 8 the the DET fcis-2488 46 9 same same ADJ fcis-2488 46 10 cluster cluster NOUN fcis-2488 46 11 in in ADP fcis-2488 46 12 𝑄1 𝑄1 NOUN fcis-2488 46 13 but but CCONJ fcis-2488 46 14 in in ADP fcis-2488 46 15 different different ADJ fcis-2488 46 16 cluster cluster NOUN fcis-2488 46 17 in in ADP fcis-2488 46 18 𝑄2 𝑄2 PROPN fcis-2488 46 19 . . PROPN fcis-2488 46 20 𝑑:𝑃𝑖 𝑑:𝑃𝑖 PROPN fcis-2488 46 21 and and CCONJ fcis-2488 46 22 𝑃𝑗 𝑃𝑗 PROPN fcis-2488 46 23 are be AUX fcis-2488 46 24 in in ADP fcis-2488 46 25 different different ADJ fcis-2488 46 26 cluster cluster NOUN fcis-2488 46 27 in in ADP fcis-2488 46 28 𝑄1 𝑄1 NOUN fcis-2488 46 29 and and CCONJ fcis-2488 46 30 in in ADP fcis-2488 46 31 different different ADJ fcis-2488 46 32 cluster cluster NOUN fcis-2488 46 33 in in ADP fcis-2488 46 34 𝑄2 𝑄2 PROPN fcis-2488 46 35 . . PROPN fcis-2488 46 36 rand rand PROPN fcis-2488 46 37 index index NOUN fcis-2488 46 38 is be AUX fcis-2488 46 39 given give VERB fcis-2488 46 40 as as SCONJ fcis-2488 46 41 follows follow VERB fcis-2488 46 42 π‘Ÿπ‘Žπ‘›π‘‘ π‘Ÿπ‘Žπ‘›π‘‘ NOUN fcis-2488 46 43 = = SYM fcis-2488 46 44 π‘Ž+𝑑 π‘Ž+𝑑 NUM fcis-2488 46 45 π‘Ž+𝑏+𝑐+𝑑 π‘Ž+𝑏+𝑐+𝑑 X fcis-2488 46 46 ( ( PUNCT fcis-2488 46 47 4 4 NUM fcis-2488 46 48 ) ) PUNCT fcis-2488 46 49 and and CCONJ fcis-2488 46 50 the the PRON fcis-2488 46 51 lower low ADJ fcis-2488 46 52 the the DET fcis-2488 46 53 value value NOUN fcis-2488 46 54 of of ADP fcis-2488 46 55 rand rand NOUN fcis-2488 46 56 , , PUNCT fcis-2488 46 57 the the PRON fcis-2488 46 58 better well ADJ fcis-2488 46 59 the the DET fcis-2488 46 60 result result NOUN fcis-2488 46 61 . . PUNCT fcis-2488 47 1 4 4 X fcis-2488 47 2 . . X fcis-2488 47 3 experiments experiment NOUN fcis-2488 47 4 and and CCONJ fcis-2488 47 5 results result VERB fcis-2488 47 6 4.1 4.1 NUM fcis-2488 47 7 . . PUNCT fcis-2488 48 1 random random ADJ fcis-2488 48 2 initial initial ADJ fcis-2488 48 3 cluster cluster NOUN fcis-2488 48 4 centers center NOUN fcis-2488 48 5 we we PRON fcis-2488 48 6 consider consider VERB fcis-2488 48 7 the the DET fcis-2488 48 8 sampling sampling NOUN fcis-2488 48 9 points point NOUN fcis-2488 48 10 { { PUNCT fcis-2488 48 11 𝑃𝑖}𝑖=1 𝑃𝑖}𝑖=1 NOUN fcis-2488 48 12 𝑛 𝑛 PROPN fcis-2488 48 13 from from ADP fcis-2488 48 14 two two NUM fcis-2488 48 15 curves curve NOUN fcis-2488 48 16 𝐢1 𝐢1 VERB fcis-2488 48 17 : : PUNCT fcis-2488 48 18 𝑦 𝑦 NOUN fcis-2488 48 19 1 1 NUM fcis-2488 48 20 = = SYM fcis-2488 48 21 0.02 0.02 NUM fcis-2488 48 22 and and CCONJ fcis-2488 48 23 𝐢2 𝐢2 ADJ fcis-2488 48 24 : : PUNCT fcis-2488 48 25 𝑦 𝑦 NOUN fcis-2488 48 26 2 2 X fcis-2488 48 27 = = SYM fcis-2488 48 28 βˆ’0.02 βˆ’0.02 INTJ fcis-2488 48 29 , , PUNCT fcis-2488 48 30 see see VERB fcis-2488 48 31 the the DET fcis-2488 48 32 pink pink ADJ fcis-2488 48 33 circles circle NOUN fcis-2488 48 34 in in ADP fcis-2488 48 35 figure figure NOUN fcis-2488 48 36 1 1 NUM fcis-2488 48 37 , , PUNCT fcis-2488 48 38 figure figure NOUN fcis-2488 48 39 2 2 NUM fcis-2488 48 40 and and CCONJ fcis-2488 48 41 figure figure VERB fcis-2488 48 42 3 3 NUM fcis-2488 48 43 . . PUNCT fcis-2488 49 1 we we PRON fcis-2488 49 2 pick pick VERB fcis-2488 49 3 the the DET fcis-2488 49 4 initial initial ADJ fcis-2488 49 5 centers center NOUN fcis-2488 49 6 ( ( PUNCT fcis-2488 49 7 0.2,0 0.2,0 PROPN fcis-2488 49 8 ) ) PUNCT fcis-2488 49 9 , , PUNCT fcis-2488 49 10 ( ( PUNCT fcis-2488 49 11 0.3,0 0.3,0 ADV fcis-2488 49 12 ) ) PUNCT fcis-2488 49 13 in in ADP fcis-2488 49 14 figure figure NOUN fcis-2488 49 15 1 1 NUM fcis-2488 49 16 and and CCONJ fcis-2488 49 17 ( ( PUNCT fcis-2488 49 18 0.4,0.02 0.4,0.02 NUM fcis-2488 49 19 ) ) PUNCT fcis-2488 49 20 , , PUNCT fcis-2488 49 21 ( ( PUNCT fcis-2488 49 22 0.1 0.1 NUM fcis-2488 49 23 , , PUNCT fcis-2488 49 24 βˆ’0.02 βˆ’0.02 NOUN fcis-2488 49 25 ) ) PUNCT fcis-2488 49 26 in in ADP fcis-2488 49 27 figure figure NOUN fcis-2488 49 28 2 2 NUM fcis-2488 49 29 and and CCONJ fcis-2488 49 30 use use VERB fcis-2488 49 31 k k ADJ fcis-2488 49 32 - - PUNCT fcis-2488 49 33 means means NOUN fcis-2488 49 34 algorithm algorithm NOUN fcis-2488 49 35 to to ADP fcis-2488 49 36 cluster cluster NOUN fcis-2488 49 37 { { PUNCT fcis-2488 49 38 𝑃𝑖}𝑖=1 𝑃𝑖}𝑖=1 NOUN fcis-2488 49 39 𝑛 𝑛 PROPN fcis-2488 49 40 into into ADP fcis-2488 49 41 two two NUM fcis-2488 49 42 classes class NOUN fcis-2488 49 43 , , PUNCT fcis-2488 49 44 see see VERB fcis-2488 49 45 figure figure NOUN fcis-2488 49 46 1 1 NUM fcis-2488 49 47 ( ( PUNCT fcis-2488 49 48 b b NOUN fcis-2488 49 49 ) ) PUNCT fcis-2488 49 50 and and CCONJ fcis-2488 49 51 figure figure VERB fcis-2488 49 52 2 2 NUM fcis-2488 49 53 ( ( PUNCT fcis-2488 49 54 b b NOUN fcis-2488 49 55 ) ) PUNCT fcis-2488 49 56 . . PUNCT fcis-2488 50 1 both both PRON fcis-2488 50 2 of of ADP fcis-2488 50 3 them they PRON fcis-2488 50 4 are be AUX fcis-2488 50 5 unreasonable unreasonable ADJ fcis-2488 50 6 results result NOUN fcis-2488 50 7 . . PUNCT fcis-2488 51 1 we we PRON fcis-2488 51 2 want want VERB fcis-2488 51 3 the the DET fcis-2488 51 4 ones one NOUN fcis-2488 51 5 with with ADP fcis-2488 51 6 the the DET fcis-2488 51 7 ordinate ordinate NOUN fcis-2488 51 8 0.02 0.02 NUM fcis-2488 51 9 to to PART fcis-2488 51 10 be be AUX fcis-2488 51 11 one one NUM fcis-2488 51 12 class class NOUN fcis-2488 51 13 and and CCONJ fcis-2488 51 14 the the DET fcis-2488 51 15 ones one NOUN fcis-2488 51 16 with with ADP fcis-2488 51 17 the the DET fcis-2488 51 18 ordinate ordinate NOUN fcis-2488 51 19 -0.02 -0.02 NUM fcis-2488 51 20 to to PART fcis-2488 51 21 be be AUX fcis-2488 51 22 the the DET fcis-2488 51 23 other other ADJ fcis-2488 51 24 class class NOUN fcis-2488 51 25 . . PUNCT fcis-2488 52 1 ( ( PUNCT fcis-2488 52 2 a a X fcis-2488 52 3 ) ) PUNCT fcis-2488 52 4 ( ( PUNCT fcis-2488 52 5 b b X fcis-2488 52 6 ) ) PUNCT fcis-2488 52 7 figure figure NOUN fcis-2488 52 8 1 1 NUM fcis-2488 52 9 . . PUNCT fcis-2488 53 1 ( ( PUNCT fcis-2488 53 2 a a X fcis-2488 53 3 ) ) PUNCT fcis-2488 53 4 the the DET fcis-2488 53 5 pink pink ADJ fcis-2488 53 6 circles circle NOUN fcis-2488 53 7 are be AUX fcis-2488 53 8 original original ADJ fcis-2488 53 9 data datum NOUN fcis-2488 53 10 and and CCONJ fcis-2488 53 11 the the DET fcis-2488 53 12 red red PROPN fcis-2488 53 13 star star PROPN fcis-2488 53 14 and and CCONJ fcis-2488 53 15 green green PROPN fcis-2488 53 16 star star PROPN fcis-2488 53 17 are be AUX fcis-2488 53 18 ( ( PUNCT fcis-2488 53 19 0.2,0),(0.3,0 0.2,0),(0.3,0 PRON fcis-2488 53 20 ) ) PUNCT fcis-2488 53 21 respectively respectively ADV fcis-2488 53 22 , , PUNCT fcis-2488 53 23 which which PRON fcis-2488 53 24 are be AUX fcis-2488 53 25 random random ADJ fcis-2488 53 26 initial initial ADJ fcis-2488 53 27 centers center NOUN fcis-2488 53 28 . . PUNCT fcis-2488 54 1 ( ( PUNCT fcis-2488 54 2 b b X fcis-2488 54 3 ) ) PUNCT fcis-2488 54 4 based base VERB fcis-2488 54 5 on on ADP fcis-2488 54 6 ( ( PUNCT fcis-2488 54 7 0.2,0 0.2,0 PROPN fcis-2488 54 8 ) ) PUNCT fcis-2488 54 9 , , PUNCT fcis-2488 54 10 ( ( PUNCT fcis-2488 54 11 0.3,0 0.3,0 ADV fcis-2488 54 12 ) ) PUNCT fcis-2488 54 13 , , PUNCT fcis-2488 54 14 the the DET fcis-2488 54 15 result result NOUN fcis-2488 54 16 is be AUX fcis-2488 54 17 given give VERB fcis-2488 54 18 by by ADP fcis-2488 54 19 kmeans kmean NOUN fcis-2488 54 20 algorithm algorithm NOUN fcis-2488 54 21 , , PUNCT fcis-2488 54 22 there there PRON fcis-2488 54 23 is be VERB fcis-2488 54 24 a a DET fcis-2488 54 25 class class NOUN fcis-2488 54 26 in in ADP fcis-2488 54 27 red red ADJ fcis-2488 54 28 circle circle NOUN fcis-2488 54 29 and and CCONJ fcis-2488 54 30 a a DET fcis-2488 54 31 class class NOUN fcis-2488 54 32 in in ADP fcis-2488 54 33 green green PROPN fcis-2488 54 34 circle circle PROPN fcis-2488 54 35 , , PUNCT fcis-2488 54 36 the the DET fcis-2488 54 37 red red PROPN fcis-2488 54 38 star star PROPN fcis-2488 54 39 and and CCONJ fcis-2488 54 40 green green PROPN fcis-2488 54 41 star star PROPN fcis-2488 54 42 are be AUX fcis-2488 54 43 the the DET fcis-2488 54 44 final final ADJ fcis-2488 54 45 cluster cluster NOUN fcis-2488 54 46 centers center NOUN fcis-2488 54 47 . . PUNCT fcis-2488 55 1 4.2 4.2 NUM fcis-2488 55 2 . . PUNCT fcis-2488 55 3 initial initial ADJ fcis-2488 55 4 cluster cluster NOUN fcis-2488 55 5 center center NOUN fcis-2488 55 6 given give VERB fcis-2488 55 7 by by ADP fcis-2488 55 8 moving move VERB fcis-2488 55 9 two two NUM fcis-2488 55 10 lines line NOUN fcis-2488 55 11 approximation approximation NOUN fcis-2488 55 12 it it PRON fcis-2488 55 13 can can AUX fcis-2488 55 14 be be AUX fcis-2488 55 15 seen see VERB fcis-2488 55 16 from from ADP fcis-2488 55 17 the the DET fcis-2488 55 18 above above ADJ fcis-2488 55 19 results result NOUN fcis-2488 55 20 that that SCONJ fcis-2488 55 21 if if SCONJ fcis-2488 55 22 the the DET fcis-2488 55 23 initial initial ADJ fcis-2488 55 24 clustering clustering ADJ fcis-2488 55 25 center center NOUN fcis-2488 55 26 is be AUX fcis-2488 55 27 not not PART fcis-2488 55 28 appropriate appropriate ADJ fcis-2488 55 29 , , PUNCT fcis-2488 55 30 no no DET fcis-2488 55 31 good good ADJ fcis-2488 55 32 clustering clustering NOUN fcis-2488 55 33 result result NOUN fcis-2488 55 34 can can AUX fcis-2488 55 35 be be AUX fcis-2488 55 36 obtained obtain VERB fcis-2488 55 37 . . PUNCT fcis-2488 56 1 there there ADV fcis-2488 56 2 the the DET fcis-2488 56 3 initial initial ADJ fcis-2488 56 4 cluster cluster NOUN fcis-2488 56 5 center center NOUN fcis-2488 56 6 was be AUX fcis-2488 56 7 obtained obtain VERB fcis-2488 56 8 by by ADP fcis-2488 56 9 moving move VERB fcis-2488 56 10 two two NUM fcis-2488 56 11 lines line NOUN fcis-2488 56 12 approximation approximation NOUN fcis-2488 56 13 . . PUNCT fcis-2488 57 1 we we PRON fcis-2488 57 2 use use VERB fcis-2488 57 3 all all DET fcis-2488 57 4 the the DET fcis-2488 57 5 points point NOUN fcis-2488 57 6 { { PUNCT fcis-2488 57 7 𝑃𝑖}𝑖=1 𝑃𝑖}𝑖=1 NOUN fcis-2488 57 8 𝑛 𝑛 PROPN fcis-2488 57 9 in in ADP fcis-2488 57 10 the the DET fcis-2488 57 11 moving move VERB fcis-2488 57 12 two two NUM fcis-2488 57 13 lines line NOUN fcis-2488 57 14 approximation approximation NOUN fcis-2488 57 15 model model NOUN fcis-2488 57 16 ( ( PUNCT fcis-2488 57 17 2 2 NUM fcis-2488 57 18 ) ) PUNCT fcis-2488 57 19 without without ADP fcis-2488 57 20 partition partition NOUN fcis-2488 57 21 . . PUNCT fcis-2488 58 1 𝑋 𝑋 NOUN fcis-2488 58 2 is be AUX fcis-2488 58 3 the the DET fcis-2488 58 4 mean mean NOUN fcis-2488 58 5 of of ADP fcis-2488 58 6 { { PUNCT fcis-2488 58 7 𝑃𝑖}𝑖=1 𝑃𝑖}𝑖=1 PROPN fcis-2488 58 8 𝑛 𝑛 PROPN fcis-2488 58 9 , , PUNCT fcis-2488 58 10 denoted denote VERB fcis-2488 58 11 a a DET fcis-2488 58 12 pink pink ADJ fcis-2488 58 13 star star NOUN fcis-2488 58 14 in in ADP fcis-2488 58 15 figure figure NOUN fcis-2488 58 16 3 3 NUM fcis-2488 58 17 . . PUNCT fcis-2488 59 1 and and CCONJ fcis-2488 59 2 then then ADV fcis-2488 59 3 from from ADP fcis-2488 59 4 ( ( PUNCT fcis-2488 59 5 2 2 NUM fcis-2488 59 6 ) ) PUNCT fcis-2488 59 7 , , PUNCT fcis-2488 59 8 two two NUM fcis-2488 59 9 blue blue ADJ fcis-2488 59 10 lines line NOUN fcis-2488 59 11 are be AUX fcis-2488 59 12 obtained obtain VERB fcis-2488 59 13 showing show VERB fcis-2488 59 14 also also ADV fcis-2488 59 15 in in ADP fcis-2488 59 16 figure figure NOUN fcis-2488 59 17 3 3 NUM fcis-2488 59 18 . . PUNCT fcis-2488 60 1 the the DET fcis-2488 60 2 computed computed ADJ fcis-2488 60 3 two two NUM fcis-2488 60 4 blue blue ADJ fcis-2488 60 5 target target NOUN fcis-2488 60 6 points point NOUN fcis-2488 60 7 ( ( PUNCT fcis-2488 60 8 0.25,0.02 0.25,0.02 NUM fcis-2488 60 9 ) ) PUNCT fcis-2488 60 10 , , PUNCT fcis-2488 60 11 ( ( PUNCT fcis-2488 60 12 0.25,-0.02 0.25,-0.02 NUM fcis-2488 60 13 ) ) PUNCT fcis-2488 60 14 according accord VERB fcis-2488 60 15 to to ADP fcis-2488 60 16 ( ( PUNCT fcis-2488 60 17 2 2 NUM fcis-2488 60 18 ) ) PUNCT fcis-2488 60 19 are be AUX fcis-2488 60 20 considerd considerd ADJ fcis-2488 60 21 two two NUM fcis-2488 60 22 initial initial ADJ fcis-2488 60 23 centers center NOUN fcis-2488 60 24 of of ADP fcis-2488 60 25 k k NOUN fcis-2488 60 26 - - PUNCT fcis-2488 60 27 means mean NOUN fcis-2488 60 28 algorithm algorithm NOUN fcis-2488 60 29 , , PUNCT fcis-2488 60 30 see see VERB fcis-2488 60 31 figure figure NOUN fcis-2488 60 32 4(a 4(a NUM fcis-2488 60 33 ) ) PUNCT fcis-2488 60 34 . . PUNCT fcis-2488 61 1 depend depend VERB fcis-2488 61 2 on on ADP fcis-2488 61 3 the the DET fcis-2488 61 4 two two NUM fcis-2488 61 5 initial initial ADJ fcis-2488 61 6 centers center NOUN fcis-2488 61 7 from from ADP fcis-2488 61 8 ( ( PUNCT fcis-2488 61 9 2 2 NUM fcis-2488 61 10 ) ) PUNCT fcis-2488 61 11 , , PUNCT fcis-2488 61 12 we we PRON fcis-2488 61 13 get get VERB fcis-2488 61 14 a a DET fcis-2488 61 15 reasonable reasonable ADJ fcis-2488 61 16 clustering clustering NOUN fcis-2488 61 17 result result NOUN fcis-2488 61 18 , , PUNCT fcis-2488 61 19 see see VERB fcis-2488 61 20 figure figure NOUN fcis-2488 61 21 4 4 NUM fcis-2488 61 22 ( ( PUNCT fcis-2488 61 23 b b NOUN fcis-2488 61 24 ) ) PUNCT fcis-2488 61 25 . . PUNCT fcis-2488 62 1 besides besides SCONJ fcis-2488 62 2 , , PUNCT fcis-2488 62 3 with with ADP fcis-2488 62 4 the the DET fcis-2488 62 5 help help NOUN fcis-2488 62 6 of of ADP fcis-2488 62 7 formula formula NOUN fcis-2488 62 8 ( ( PUNCT fcis-2488 62 9 3 3 NUM fcis-2488 62 10 ) ) PUNCT fcis-2488 62 11 and and CCONJ fcis-2488 62 12 ( ( PUNCT fcis-2488 62 13 4 4 NUM fcis-2488 62 14 ) ) PUNCT fcis-2488 62 15 , , PUNCT fcis-2488 62 16 we we PRON fcis-2488 62 17 can can AUX fcis-2488 62 18 compute compute VERB fcis-2488 62 19 error error NOUN fcis-2488 62 20 percentage percentage NOUN fcis-2488 62 21 and and CCONJ fcis-2488 62 22 rand rand NOUN fcis-2488 62 23 index index NOUN fcis-2488 62 24 for for ADP fcis-2488 62 25 diffrent diffrent ADJ fcis-2488 62 26 initial initial ADJ fcis-2488 62 27 cluster cluster NOUN fcis-2488 62 28 centers center NOUN fcis-2488 62 29 , , PUNCT fcis-2488 62 30 see see VERB fcis-2488 62 31 table table NOUN fcis-2488 62 32 1 1 X fcis-2488 62 33 . . PUNCT fcis-2488 63 1 we we PRON fcis-2488 63 2 found find VERB fcis-2488 63 3 that that SCONJ fcis-2488 63 4 the the DET fcis-2488 63 5 initial initial ADJ fcis-2488 63 6 value value NOUN fcis-2488 63 7 from from ADP fcis-2488 63 8 the the DET fcis-2488 63 9 moving move VERB fcis-2488 63 10 two two NUM fcis-2488 63 11 lines line NOUN fcis-2488 63 12 approximation approximation NOUN fcis-2488 63 13 corresponds correspond VERB fcis-2488 63 14 to to ADP fcis-2488 63 15 the the DET fcis-2488 63 16 smallest small ADJ fcis-2488 63 17 error error NOUN fcis-2488 63 18 , , PUNCT fcis-2488 63 19 and and CCONJ fcis-2488 63 20 the the DET fcis-2488 63 21 maximum maximum ADJ fcis-2488 63 22 rand rand NOUN fcis-2488 63 23 index index NOUN fcis-2488 63 24 . . PUNCT fcis-2488 64 1 its its PRON fcis-2488 64 2 clustering cluster VERB fcis-2488 64 3 effect effect NOUN fcis-2488 64 4 is be AUX fcis-2488 64 5 the the DET fcis-2488 64 6 best good ADJ fcis-2488 64 7 . . PUNCT fcis-2488 65 1 figure figure NOUN fcis-2488 65 2 2 2 NUM fcis-2488 65 3 . . PUNCT fcis-2488 66 1 ( ( PUNCT fcis-2488 66 2 a a X fcis-2488 66 3 ) ) PUNCT fcis-2488 66 4 the the DET fcis-2488 66 5 pink pink ADJ fcis-2488 66 6 circles circle NOUN fcis-2488 66 7 are be AUX fcis-2488 66 8 original original ADJ fcis-2488 66 9 data datum NOUN fcis-2488 66 10 and and CCONJ fcis-2488 66 11 the the DET fcis-2488 66 12 two two NUM fcis-2488 66 13 blue blue ADJ fcis-2488 66 14 stars star NOUN fcis-2488 66 15 are be AUX fcis-2488 66 16 ( ( PUNCT fcis-2488 66 17 0.4,0.02),(0.1,-0.02 0.4,0.02),(0.1,-0.02 NOUN fcis-2488 66 18 ) ) PUNCT fcis-2488 66 19 respectively respectively ADV fcis-2488 66 20 , , PUNCT fcis-2488 66 21 which which PRON fcis-2488 66 22 are be AUX fcis-2488 66 23 initial initial ADJ fcis-2488 66 24 centers center NOUN fcis-2488 66 25 . . PUNCT fcis-2488 67 1 ( ( PUNCT fcis-2488 67 2 b b X fcis-2488 67 3 ) ) PUNCT fcis-2488 67 4 based base VERB fcis-2488 67 5 on on ADP fcis-2488 67 6 ( ( PUNCT fcis-2488 67 7 0.4,0.02),(0.1,-0.02 0.4,0.02),(0.1,-0.02 NUM fcis-2488 67 8 ) ) PUNCT fcis-2488 67 9 , , PUNCT fcis-2488 67 10 the the DET fcis-2488 67 11 result result NOUN fcis-2488 67 12 is be AUX fcis-2488 67 13 given give VERB fcis-2488 67 14 by by ADP fcis-2488 67 15 k k ADJ fcis-2488 67 16 - - PUNCT fcis-2488 67 17 means means NOUN fcis-2488 67 18 algorithm algorithm NOUN fcis-2488 67 19 . . PUNCT fcis-2488 68 1 there there PRON fcis-2488 68 2 is be VERB fcis-2488 68 3 a a DET fcis-2488 68 4 class class NOUN fcis-2488 68 5 in in ADP fcis-2488 68 6 red red ADJ fcis-2488 68 7 circle circle NOUN fcis-2488 68 8 and and CCONJ fcis-2488 68 9 a a DET fcis-2488 68 10 class class NOUN fcis-2488 68 11 in in ADP fcis-2488 68 12 green green PROPN fcis-2488 68 13 circle circle PROPN fcis-2488 68 14 . . PUNCT fcis-2488 69 1 the the DET fcis-2488 69 2 red red PROPN fcis-2488 69 3 star star PROPN fcis-2488 69 4 and and CCONJ fcis-2488 69 5 green green PROPN fcis-2488 69 6 star star PROPN fcis-2488 69 7 are be AUX fcis-2488 69 8 the the DET fcis-2488 69 9 final final ADJ fcis-2488 69 10 cluster cluster NOUN fcis-2488 69 11 centers center NOUN fcis-2488 69 12 . . PUNCT fcis-2488 70 1 figure figure VERB fcis-2488 70 2 3 3 NUM fcis-2488 70 3 . . PUNCT fcis-2488 71 1 based base VERB fcis-2488 71 2 on on ADP fcis-2488 71 3 moving move VERB fcis-2488 71 4 multiple multiple ADJ fcis-2488 71 5 curves curve NOUN fcis-2488 71 6 approximation approximation NOUN fcis-2488 71 7 , , PUNCT fcis-2488 71 8 we we PRON fcis-2488 71 9 compute compute VERB fcis-2488 71 10 two two NUM fcis-2488 71 11 lines line NOUN fcis-2488 71 12 and and CCONJ fcis-2488 71 13 the the DET fcis-2488 71 14 two two NUM fcis-2488 71 15 cluster cluster NOUN fcis-2488 71 16 initial initial ADJ fcis-2488 71 17 centers center NOUN fcis-2488 71 18 for for ADP fcis-2488 71 19 k k NOUN fcis-2488 71 20 - - PUNCT fcis-2488 71 21 means means NOUN fcis-2488 71 22 algorithm algorithm NOUN fcis-2488 71 23 . . PUNCT fcis-2488 72 1 the the DET fcis-2488 72 2 pink pink ADJ fcis-2488 72 3 star star NOUN fcis-2488 72 4 is be AUX fcis-2488 72 5 𝑋 𝑋 PROPN fcis-2488 72 6 in in ADP fcis-2488 72 7 ( ( PUNCT fcis-2488 72 8 2 2 NUM fcis-2488 72 9 ) ) PUNCT fcis-2488 72 10 . . PUNCT fcis-2488 73 1 figure figure VERB fcis-2488 73 2 4 4 NUM fcis-2488 73 3 . . PUNCT fcis-2488 74 1 ( ( PUNCT fcis-2488 74 2 a)the a)the DET fcis-2488 74 3 pink pink ADJ fcis-2488 74 4 circles circle NOUN fcis-2488 74 5 are be AUX fcis-2488 74 6 original original ADJ fcis-2488 74 7 data datum NOUN fcis-2488 74 8 and and CCONJ fcis-2488 74 9 the the DET fcis-2488 74 10 two two NUM fcis-2488 74 11 blue blue ADJ fcis-2488 74 12 stars star NOUN fcis-2488 74 13 are be AUX fcis-2488 74 14 ( ( PUNCT fcis-2488 74 15 0.25,0.02),(0.25,-0.02 0.25,0.02),(0.25,-0.02 NUM fcis-2488 74 16 ) ) PUNCT fcis-2488 74 17 , , PUNCT fcis-2488 74 18 which which PRON fcis-2488 74 19 are be AUX fcis-2488 74 20 initial initial ADJ fcis-2488 74 21 centers center NOUN fcis-2488 74 22 obtained obtain VERB fcis-2488 74 23 from from ADP fcis-2488 74 24 fig.3 fig.3 PROPN fcis-2488 74 25 ; ; PUNCT fcis-2488 74 26 ( ( PUNCT fcis-2488 74 27 b b X fcis-2488 74 28 ) ) PUNCT fcis-2488 74 29 the the DET fcis-2488 74 30 results result NOUN fcis-2488 74 31 given give VERB fcis-2488 74 32 by by ADP fcis-2488 74 33 k k ADJ fcis-2488 74 34 - - PUNCT fcis-2488 74 35 means means NOUN fcis-2488 74 36 algorithm algorithm NOUN fcis-2488 74 37 using use VERB fcis-2488 74 38 the the DET fcis-2488 74 39 initial initial ADJ fcis-2488 74 40 luster luster NOUN fcis-2488 74 41 centers center NOUN fcis-2488 74 42 from from ADP fcis-2488 74 43 ( ( PUNCT fcis-2488 74 44 a a X fcis-2488 74 45 ) ) PUNCT fcis-2488 74 46 , , PUNCT fcis-2488 74 47 there there PRON fcis-2488 74 48 is be VERB fcis-2488 74 49 a a DET fcis-2488 74 50 class class NOUN fcis-2488 74 51 in in ADP fcis-2488 74 52 red red ADJ fcis-2488 74 53 circle circle NOUN fcis-2488 74 54 and and CCONJ fcis-2488 74 55 a a DET fcis-2488 74 56 class class NOUN fcis-2488 74 57 in in ADP fcis-2488 74 58 green green PROPN fcis-2488 74 59 circle circle PROPN fcis-2488 74 60 . . PUNCT fcis-2488 75 1 the the DET fcis-2488 75 2 red red PROPN fcis-2488 75 3 star star PROPN fcis-2488 75 4 and and CCONJ fcis-2488 75 5 green green PROPN fcis-2488 75 6 star star PROPN fcis-2488 75 7 are be AUX fcis-2488 75 8 the the DET fcis-2488 75 9 final final ADJ fcis-2488 75 10 cluster cluster NOUN fcis-2488 75 11 centers center NOUN fcis-2488 75 12 . . PUNCT fcis-2488 76 1 table table NOUN fcis-2488 76 2 1 1 NUM fcis-2488 76 3 . . X fcis-2488 76 4 error error NOUN fcis-2488 76 5 percentage percentage NOUN fcis-2488 76 6 and and CCONJ fcis-2488 76 7 rand rand NOUN fcis-2488 76 8 index index NOUN fcis-2488 76 9 for for ADP fcis-2488 76 10 diffrent diffrent ADJ fcis-2488 76 11 datasets dataset NOUN fcis-2488 76 12 initial initial ADJ fcis-2488 76 13 cluster cluster NOUN fcis-2488 76 14 centers center NOUN fcis-2488 76 15 error error NOUN fcis-2488 76 16 percentage percentage NOUN fcis-2488 76 17 rand rand NOUN fcis-2488 76 18 index index NOUN fcis-2488 76 19 ( ( PUNCT fcis-2488 76 20 0.2,0 0.2,0 PROPN fcis-2488 76 21 ) ) PUNCT fcis-2488 76 22 , , PUNCT fcis-2488 76 23 ( ( PUNCT fcis-2488 76 24 0.3,0 0.3,0 ADV fcis-2488 76 25 ) ) PUNCT fcis-2488 76 26 50 50 NUM fcis-2488 76 27 0.4902 0.4902 NUM fcis-2488 76 28 ( ( PUNCT fcis-2488 76 29 0.4,0.02 0.4,0.02 NUM fcis-2488 76 30 ) ) PUNCT fcis-2488 76 31 , , PUNCT fcis-2488 76 32 ( ( PUNCT fcis-2488 76 33 0.1 0.1 NUM fcis-2488 76 34 , , PUNCT fcis-2488 76 35 -0.02 -0.02 NUM fcis-2488 76 36 ) ) PUNCT fcis-2488 76 37 50 50 NUM fcis-2488 76 38 0.4902 0.4902 NUM fcis-2488 76 39 ( ( PUNCT fcis-2488 76 40 0.25,0.02 0.25,0.02 NUM fcis-2488 76 41 ) ) PUNCT fcis-2488 76 42 , , PUNCT fcis-2488 76 43 ( ( PUNCT fcis-2488 76 44 0.25 0.25 NUM fcis-2488 76 45 , , PUNCT fcis-2488 76 46 0.02 0.02 NUM fcis-2488 76 47 ) ) PUNCT fcis-2488 76 48 0 0 NUM fcis-2488 76 49 1 1 NUM fcis-2488 76 50 5 5 NUM fcis-2488 76 51 . . PUNCT fcis-2488 77 1 conclusion conclusion NOUN fcis-2488 77 2 a a DET fcis-2488 77 3 new new ADJ fcis-2488 77 4 method method NOUN fcis-2488 77 5 to to PART fcis-2488 77 6 select select VERB fcis-2488 77 7 the the DET fcis-2488 77 8 initial initial ADJ fcis-2488 77 9 cluster cluster NOUN fcis-2488 77 10 center center NOUN fcis-2488 77 11 of of ADP fcis-2488 77 12 k k PROPN fcis-2488 77 13 - - PUNCT fcis-2488 77 14 means means NOUN fcis-2488 77 15 algorithm algorithm NOUN fcis-2488 77 16 , , PUNCT fcis-2488 77 17 that that ADV fcis-2488 77 18 is is ADV fcis-2488 77 19 , , PUNCT fcis-2488 77 20 moving move VERB fcis-2488 77 21 two two NUM fcis-2488 77 22 lines line NOUN fcis-2488 77 23 approximation approximation NOUN fcis-2488 77 24 have have AUX fcis-2488 77 25 provided provide VERB fcis-2488 77 26 in in ADP fcis-2488 77 27 this this DET fcis-2488 77 28 paper paper NOUN fcis-2488 77 29 . . PUNCT fcis-2488 78 1 moving move VERB fcis-2488 78 2 two two NUM fcis-2488 78 3 lines line NOUN fcis-2488 78 4 approximation approximation NOUN fcis-2488 78 5 is be AUX fcis-2488 78 6 a a DET fcis-2488 78 7 particular particular ADJ fcis-2488 78 8 case case NOUN fcis-2488 78 9 of of ADP fcis-2488 78 10 moving move VERB fcis-2488 78 11 multiple multiple ADJ fcis-2488 78 12 curves curve NOUN fcis-2488 78 13 approximation approximation NOUN fcis-2488 78 14 . . PUNCT fcis-2488 79 1 we we PRON fcis-2488 79 2 just just ADV fcis-2488 79 3 choose choose VERB fcis-2488 79 4 two two NUM fcis-2488 79 5 algebraic algebraic ADJ fcis-2488 79 6 equations equation NOUN fcis-2488 79 7 of of ADP fcis-2488 79 8 two two NUM fcis-2488 79 9 lines line NOUN fcis-2488 79 10 in in ADP fcis-2488 79 11 the the DET fcis-2488 79 12 model model NOUN fcis-2488 79 13 . . PUNCT fcis-2488 80 1 for for ADP fcis-2488 80 2 given give VERB fcis-2488 80 3 dataset dataset NOUN fcis-2488 80 4 , , PUNCT fcis-2488 80 5 by by ADP fcis-2488 80 6 moving move VERB fcis-2488 80 7 two two NUM fcis-2488 80 8 lines line NOUN fcis-2488 80 9 approximation approximation NOUN fcis-2488 80 10 , , PUNCT fcis-2488 80 11 we we PRON fcis-2488 80 12 can can AUX fcis-2488 80 13 find find VERB fcis-2488 80 14 better well ADJ fcis-2488 80 15 initial initial ADJ fcis-2488 80 16 center center NOUN fcis-2488 80 17 in in ADP fcis-2488 80 18 k k ADJ fcis-2488 80 19 - - PUNCT fcis-2488 80 20 means means NOUN fcis-2488 80 21 algorithm algorithm NOUN fcis-2488 80 22 for for ADP fcis-2488 80 23 given give VERB fcis-2488 80 24 observation observation NOUN fcis-2488 80 25 data datum NOUN fcis-2488 80 26 and and CCONJ fcis-2488 80 27 achieve achieve VERB fcis-2488 80 28 good good ADJ fcis-2488 80 29 clustering clustering ADJ fcis-2488 80 30 effect effect NOUN fcis-2488 80 31 than than ADP fcis-2488 80 32 javascript javascript NOUN fcis-2488 80 33 : : PUNCT fcis-2488 80 34 ; ; PUNCT fcis-2488 80 35 javascript javascript NOUN fcis-2488 80 36 : : PUNCT fcis-2488 80 37 ; ; PUNCT fcis-2488 80 38 25 25 NUM fcis-2488 80 39 random random ADJ fcis-2488 80 40 initial initial ADJ fcis-2488 80 41 cluster cluster NOUN fcis-2488 80 42 center center NOUN fcis-2488 80 43 . . PUNCT fcis-2488 81 1 here here ADV fcis-2488 81 2 , , PUNCT fcis-2488 81 3 only only ADV fcis-2488 81 4 moving move VERB fcis-2488 81 5 two two NUM fcis-2488 81 6 approximation approximation NOUN fcis-2488 81 7 is be AUX fcis-2488 81 8 used use VERB fcis-2488 81 9 to to PART fcis-2488 81 10 deal deal VERB fcis-2488 81 11 with with ADP fcis-2488 81 12 binary binary ADJ fcis-2488 81 13 classification classification NOUN fcis-2488 81 14 problems problem NOUN fcis-2488 81 15 . . PUNCT fcis-2488 82 1 in in ADP fcis-2488 82 2 the the DET fcis-2488 82 3 future future NOUN fcis-2488 82 4 , , PUNCT fcis-2488 82 5 moving move VERB fcis-2488 82 6 multiple multiple ADJ fcis-2488 82 7 curves curve NOUN fcis-2488 82 8 approximation approximation NOUN fcis-2488 82 9 can can AUX fcis-2488 82 10 be be AUX fcis-2488 82 11 considered consider VERB fcis-2488 82 12 to to PART fcis-2488 82 13 deal deal VERB fcis-2488 82 14 with with ADP fcis-2488 82 15 multiclassification multiclassification NOUN fcis-2488 82 16 problems problem NOUN fcis-2488 82 17 , , PUNCT fcis-2488 82 18 and and CCONJ fcis-2488 82 19 it it PRON fcis-2488 82 20 may may AUX fcis-2488 82 21 be be AUX fcis-2488 82 22 used use VERB fcis-2488 82 23 to to PART fcis-2488 82 24 deal deal VERB fcis-2488 82 25 with with ADP fcis-2488 82 26 practical practical ADJ fcis-2488 82 27 dataset dataset NOUN fcis-2488 82 28 . . PUNCT fcis-2488 83 1 acknowledgements acknowledgement NOUN fcis-2488 83 2 this this DET fcis-2488 83 3 work work NOUN fcis-2488 83 4 is be AUX fcis-2488 83 5 supported support VERB fcis-2488 83 6 by by ADP fcis-2488 83 7 the the DET fcis-2488 83 8 university university NOUN fcis-2488 83 9 - - PUNCT fcis-2488 83 10 level level NOUN fcis-2488 83 11 projects project NOUN fcis-2488 83 12 ( ( PUNCT fcis-2488 83 13 ackyc20050 ackyc20050 PROPN fcis-2488 83 14 ) ) PUNCT fcis-2488 83 15 . . PUNCT fcis-2488 84 1 references reference NOUN fcis-2488 84 2 [ [ X fcis-2488 84 3 1 1 NUM fcis-2488 84 4 ] ] PUNCT fcis-2488 84 5 fayyad fayyad NOUN fcis-2488 84 6 u u PROPN fcis-2488 84 7 , , PUNCT fcis-2488 84 8 reina reina PROPN fcis-2488 84 9 c c PROPN fcis-2488 84 10 , , PUNCT fcis-2488 84 11 bradley bradley PROPN fcis-2488 84 12 ps ps PROPN fcis-2488 84 13 : : PUNCT fcis-2488 84 14 initialization initialization NOUN fcis-2488 84 15 of of ADP fcis-2488 84 16 iterative iterative NOUN fcis-2488 84 17 refinement refinement NOUN fcis-2488 84 18 clustering clustering NOUN fcis-2488 84 19 algorithm algorithm NOUN fcis-2488 84 20 . . PUNCT fcis-2488 85 1 in in ADP fcis-2488 85 2 ： ： PUNCT fcis-2488 85 3 proc proc NOUN fcis-2488 85 4 of of ADP fcis-2488 85 5 the the DET fcis-2488 85 6 fourth fourth ADJ fcis-2488 85 7 international international ADJ fcis-2488 85 8 conference conference NOUN fcis-2488 85 9 on on ADP fcis-2488 85 10 knowledge knowledge NOUN fcis-2488 85 11 discovery discovery PROPN fcis-2488 85 12 and and CCONJ fcis-2488 85 13 data datum NOUN fcis-2488 85 14 mining mining NOUN fcis-2488 85 15 . . PUNCT fcis-2488 85 16 aaai，menlo aaai，menlo PROPN fcis-2488 85 17 park park NOUN fcis-2488 85 18 . . PUNCT fcis-2488 86 1 1998:194 1998:194 NUM fcis-2488 86 2 - - SYM fcis-2488 86 3 198 198 NUM fcis-2488 86 4 . . PUNCT fcis-2488 87 1 [ [ X fcis-2488 87 2 2 2 NUM fcis-2488 87 3 ] ] PUNCT fcis-2488 87 4 l. l. PROPN fcis-2488 87 5 x. x. PROPN fcis-2488 87 6 bang bang PROPN fcis-2488 87 7 , , PUNCT fcis-2488 87 8 j. j. PROPN fcis-2488 87 9 h. h. PROPN fcis-2488 87 10 yang yang PROPN fcis-2488 87 11 , , PUNCT fcis-2488 87 12 m.g m.g PROPN fcis-2488 87 13 . . PROPN fcis-2488 87 14 wang wang PROPN fcis-2488 87 15 : : PUNCT fcis-2488 87 16 using use VERB fcis-2488 87 17 genetic genetic ADJ fcis-2488 87 18 algorithm algorithm NOUN fcis-2488 87 19 to to PART fcis-2488 87 20 improve improve VERB fcis-2488 87 21 k k ADJ fcis-2488 87 22 - - PUNCT fcis-2488 87 23 means mean VERB fcis-2488 87 24 clustering cluster VERB fcis-2488 87 25 algorithm algorithm NOUN fcis-2488 87 26 in in ADP fcis-2488 87 27 clustering cluster VERB fcis-2488 87 28 analysis[j analysis[j PROPN fcis-2488 87 29 ] ] PUNCT fcis-2488 87 30 . . PUNCT fcis-2488 88 1 mathematical mathematical ADJ fcis-2488 88 2 statistics statistic NOUN fcis-2488 88 3 and and CCONJ fcis-2488 88 4 applied apply VERB fcis-2488 88 5 probability probability NOUN fcis-2488 88 6 , , PUNCT fcis-2488 88 7 1997 1997 NUM fcis-2488 88 8 , , PUNCT fcis-2488 88 9 1 1 NUM fcis-2488 88 10 2(4):350β€”356 2(4):350β€”356 NUM fcis-2488 88 11 . . PUNCT fcis-2488 89 1 ( ( PUNCT fcis-2488 89 2 in in ADP fcis-2488 89 3 chinese chinese PROPN fcis-2488 89 4 ) ) PUNCT fcis-2488 90 1 [ [ X fcis-2488 90 2 3 3 X fcis-2488 90 3 ] ] X fcis-2488 90 4 krishma krishma PROPN fcis-2488 90 5 k k PROPN fcis-2488 90 6 , , PUNCT fcis-2488 90 7 murty murty PROPN fcis-2488 90 8 mn mn PROPN fcis-2488 90 9 : : PUNCT fcis-2488 90 10 genetic genetic ADJ fcis-2488 90 11 k k NOUN fcis-2488 90 12 - - PUNCT fcis-2488 90 13 means means NOUN fcis-2488 90 14 algorithm[j algorithm[j PROPN fcis-2488 90 15 ] ] PUNCT fcis-2488 90 16 . . PUNCT fcis-2488 91 1 ieee ieee NOUN fcis-2488 91 2 transactions transaction NOUN fcis-2488 91 3 on on ADP fcis-2488 91 4 system system NOUN fcis-2488 91 5 , , PUNCT fcis-2488 91 6 man man NOUN fcis-2488 91 7 and and CCONJ fcis-2488 91 8 cybemetics cybemetic NOUN fcis-2488 91 9 , , PUNCT fcis-2488 91 10 part part PROPN fcis-2488 91 11 b. b. PROPN fcis-2488 91 12 1999 1999 NUM fcis-2488 91 13 . . PUNCT fcis-2488 92 1 29(3 29(3 NUM fcis-2488 92 2 ): ): PUNCT fcis-2488 92 3 433 433 NUM fcis-2488 92 4 - - PUNCT fcis-2488 92 5 439． 439． NOUN fcis-2488 92 6 [ [ X fcis-2488 92 7 4 4 NUM fcis-2488 92 8 ] ] X fcis-2488 92 9 likas likas X fcis-2488 92 10 , , PUNCT fcis-2488 92 11 a. a. NOUN fcis-2488 92 12 , , PUNCT fcis-2488 92 13 vlassis vlassis NOUN fcis-2488 92 14 , , PUNCT fcis-2488 92 15 n. n. NOUN fcis-2488 92 16 , , PUNCT fcis-2488 92 17 jakob jakob PROPN fcis-2488 92 18 , , PUNCT fcis-2488 92 19 j.v j.v PROPN fcis-2488 92 20 . . PROPN fcis-2488 92 21 : : PUNCT fcis-2488 93 1 the the DET fcis-2488 93 2 global global ADJ fcis-2488 93 3 k k PROPN fcis-2488 93 4 - - PUNCT fcis-2488 93 5 means mean VERB fcis-2488 93 6 algorithm algorithm NOUN fcis-2488 93 7 algorithm algorithm NOUN fcis-2488 93 8 . . PUNCT fcis-2488 94 1 pattern pattern NOUN fcis-2488 94 2 recognition recognition NOUN fcis-2488 94 3 2003 2003 NUM fcis-2488 94 4 , , PUNCT fcis-2488 94 5 36 36 NUM fcis-2488 94 6 , , PUNCT fcis-2488 94 7 451–461 451–461 NUM fcis-2488 94 8 . . PUNCT fcis-2488 95 1 [ [ X fcis-2488 95 2 5 5 NUM fcis-2488 95 3 ] ] X fcis-2488 95 4 khan khan PROPN fcis-2488 95 5 , , PUNCT fcis-2488 95 6 s.s s.s PROPN fcis-2488 95 7 . . PROPN fcis-2488 95 8 , , PUNCT fcis-2488 95 9 ahmad ahmad PROPN fcis-2488 95 10 , , PUNCT fcis-2488 95 11 a. a. NOUN fcis-2488 95 12 : : PUNCT fcis-2488 95 13 cluster cluster NOUN fcis-2488 95 14 center center NOUN fcis-2488 95 15 initialization initialization NOUN fcis-2488 95 16 algorithm algorithm NOUN fcis-2488 95 17 for for ADP fcis-2488 95 18 k k NOUN fcis-2488 95 19 - - PUNCT fcis-2488 95 20 means means NOUN fcis-2488 95 21 clustering clustering NOUN fcis-2488 95 22 . . PUNCT fcis-2488 96 1 pattern pattern NOUN fcis-2488 96 2 recognition recognition PROPN fcis-2488 96 3 lett lett PROPN fcis-2488 96 4 . . PUNCT fcis-2488 97 1 2004 2004 NUM fcis-2488 97 2 , , PUNCT fcis-2488 97 3 25 25 NUM fcis-2488 97 4 , , PUNCT fcis-2488 97 5 1293–1302 1293–1302 NUM fcis-2488 97 6 . . PUNCT fcis-2488 98 1 [ [ X fcis-2488 98 2 6 6 NUM fcis-2488 98 3 ] ] PUNCT fcis-2488 98 4 deelers deeler NOUN fcis-2488 98 5 , , PUNCT fcis-2488 98 6 s. s. PROPN fcis-2488 98 7 , , PUNCT fcis-2488 98 8 auwatanamongkol auwatanamongkol PROPN fcis-2488 98 9 , , PUNCT fcis-2488 98 10 s. s. PROPN fcis-2488 98 11 : : PUNCT fcis-2488 98 12 enhancing enhance VERB fcis-2488 98 13 k k PROPN fcis-2488 98 14 - - PUNCT fcis-2488 98 15 means means NOUN fcis-2488 98 16 algorithm algorithm NOUN fcis-2488 98 17 with with ADP fcis-2488 98 18 initial initial ADJ fcis-2488 98 19 cluster cluster NOUN fcis-2488 98 20 centers center NOUN fcis-2488 98 21 derived derive VERB fcis-2488 98 22 from from ADP fcis-2488 98 23 data datum NOUN fcis-2488 98 24 partitioning partition VERB fcis-2488 98 25 along along ADP fcis-2488 98 26 the the DET fcis-2488 98 27 data datum NOUN fcis-2488 98 28 axis axis NOUN fcis-2488 98 29 with with ADP fcis-2488 98 30 the the DET fcis-2488 98 31 highest high ADJ fcis-2488 98 32 variance variance NOUN fcis-2488 98 33 . . PUNCT fcis-2488 99 1 internat internat PROPN fcis-2488 99 2 . . PUNCT fcis-2488 100 1 j. j. PROPN fcis-2488 100 2 comput comput PROPN fcis-2488 100 3 . . PUNCT fcis-2488 101 1 sci sci PROPN fcis-2488 101 2 . . PROPN fcis-2488 101 3 2007 2007 NUM fcis-2488 101 4 , , PUNCT fcis-2488 101 5 2 2 NUM fcis-2488 101 6 , , PUNCT fcis-2488 101 7 247–252 247–252 NUM fcis-2488 101 8 . . PUNCT fcis-2488 102 1 [ [ X fcis-2488 102 2 7 7 X fcis-2488 102 3 ] ] X fcis-2488 102 4 murat murat PROPN fcis-2488 102 5 erisoglu erisoglu PROPN fcis-2488 102 6 , , PUNCT fcis-2488 102 7 nazif nazif X fcis-2488 102 8 calis cali NOUN fcis-2488 102 9 , , PUNCT fcis-2488 102 10 sadullahsakallioglu sadullahsakallioglu ADJ fcis-2488 102 11 : : PUNCT fcis-2488 102 12 a a DET fcis-2488 102 13 new new ADJ fcis-2488 102 14 algorithm algorithm NOUN fcis-2488 102 15 for for ADP fcis-2488 102 16 initial initial ADJ fcis-2488 102 17 cluster cluster NOUN fcis-2488 102 18 centers center NOUN fcis-2488 102 19 in in ADP fcis-2488 102 20 k k ADJ fcis-2488 102 21 - - PUNCT fcis-2488 102 22 means means NOUN fcis-2488 102 23 algorithm algorithm NOUN fcis-2488 102 24 . . PUNCT fcis-2488 103 1 pattern pattern NOUN fcis-2488 103 2 recognition recognition PROPN fcis-2488 103 3 lett lett PROPN fcis-2488 103 4 . . PUNCT fcis-2488 104 1 32 32 NUM fcis-2488 104 2 , , PUNCT fcis-2488 104 3 1701–1705 1701–1705 NUM fcis-2488 104 4 . . PUNCT fcis-2488 105 1 [ [ X fcis-2488 105 2 8 8 NUM fcis-2488 105 3 ] ] X fcis-2488 105 4 yang yang PROPN fcis-2488 105 5 z z PROPN fcis-2488 105 6 , , PUNCT fcis-2488 105 7 kim kim PROPN fcis-2488 105 8 t t PROPN fcis-2488 105 9 : : PUNCT fcis-2488 105 10 moving move VERB fcis-2488 105 11 parabolic parabolic ADJ fcis-2488 105 12 approximation approximation NOUN fcis-2488 105 13 of of ADP fcis-2488 105 14 point point NOUN fcis-2488 105 15 clouds[j clouds[j PROPN fcis-2488 105 16 ] ] PUNCT fcis-2488 105 17 . . PUNCT fcis-2488 106 1 computer computer NOUN fcis-2488 106 2 - - PUNCT fcis-2488 106 3 aided aid VERB fcis-2488 106 4 design design NOUN fcis-2488 106 5 , , PUNCT fcis-2488 106 6 2007 2007 NUM fcis-2488 106 7 , , PUNCT fcis-2488 106 8 39(12 39(12 NUM fcis-2488 106 9 ): ): PUNCT fcis-2488 106 10 1091 1091 NUM fcis-2488 106 11 - - SYM fcis-2488 106 12 1112 1112 NUM fcis-2488 106 13 . . PUNCT fcis-2488 107 1 [ [ X fcis-2488 107 2 9 9 NUM fcis-2488 107 3 ] ] PUNCT fcis-2488 107 4 w. w. PROPN fcis-2488 107 5 y. y. PROPN fcis-2488 107 6 feng feng PROPN fcis-2488 107 7 , , PUNCT fcis-2488 107 8 z. z. PROPN fcis-2488 107 9 w.yang w.yang PROPN fcis-2488 107 10 , , PUNCT fcis-2488 107 11 j. j. PROPN fcis-2488 107 12 s. s. PROPN fcis-2488 107 13 deng deng PROPN fcis-2488 107 14 : : PUNCT fcis-2488 107 15 moving move VERB fcis-2488 107 16 multiple multiple ADJ fcis-2488 107 17 curves curve NOUN fcis-2488 107 18 / / SYM fcis-2488 107 19 surfaces surface NOUN fcis-2488 107 20 approximation approximation NOUN fcis-2488 107 21 of of ADP fcis-2488 107 22 mixed mixed ADJ fcis-2488 107 23 point point NOUN fcis-2488 107 24 clouds[j clouds[j PROPN fcis-2488 107 25 ] ] PUNCT fcis-2488 107 26 . . PUNCT fcis-2488 108 1 communications communication NOUN fcis-2488 108 2 in in ADP fcis-2488 108 3 mathematics mathematic NOUN fcis-2488 108 4 and and CCONJ fcis-2488 108 5 statistics statistic NOUN fcis-2488 108 6 , , PUNCT fcis-2488 108 7 2014 2014 NUM fcis-2488 108 8 , , PUNCT fcis-2488 108 9 2(1 2(1 NUM fcis-2488 108 10 ): ): PUNCT fcis-2488 108 11 107 107 NUM fcis-2488 108 12 - - SYM fcis-2488 108 13 124 124 NUM fcis-2488 108 14 . . PUNCT fcis-2488 109 1 [ [ X fcis-2488 109 2 10 10 NUM fcis-2488 109 3 ] ] X fcis-2488 109 4 rand rand NOUN fcis-2488 109 5 , , PUNCT fcis-2488 109 6 w.m w.m PROPN fcis-2488 109 7 . . PROPN fcis-2488 109 8 : : PUNCT fcis-2488 109 9 objective objective ADJ fcis-2488 109 10 criteria criterion NOUN fcis-2488 109 11 for for ADP fcis-2488 109 12 the the DET fcis-2488 109 13 evaluation evaluation NOUN fcis-2488 109 14 of of ADP fcis-2488 109 15 clustering clustering ADJ fcis-2488 109 16 methods method NOUN fcis-2488 109 17 . . PUNCT fcis-2488 110 1 j. j. PROPN fcis-2488 110 2 amer amer PROPN fcis-2488 110 3 . . PUNCT fcis-2488 110 4 statist statist PROPN fcis-2488 110 5 . . PUNCT fcis-2488 111 1 assoc assoc PROPN fcis-2488 111 2 . . PUNCT fcis-2488 112 1 1971 1971 NUM fcis-2488 112 2 , , PUNCT fcis-2488 112 3 66 66 NUM fcis-2488 112 4 , , PUNCT fcis-2488 112 5 846–850 846–850 NUM fcis-2488 112 6 . . PUNCT fcis-2488 113 1 https://www.sciencedirect.com/science/article/abs/pii/s0167865511002248 https://www.sciencedirect.com/science/article/abs/pii/s0167865511002248 NOUN fcis-2488 113 2 # # NOUN fcis-2488 113 3 ! ! PUNCT fcis-2488 114 1 https://www.sciencedirect.com/science/article/abs/pii/s0167865511002248 https://www.sciencedirect.com/science/article/abs/pii/s0167865511002248 NOUN fcis-2488 114 2 # # NOUN fcis-2488 114 3 ! ! PUNCT