Reconhecimento de padrões

Trabalho 3
Algoritmos de indução de árvore de decisão e pré-processamento de dados


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Sobre o dataset

https://www.kaggle.com/alihussain1993/lower-back-pain-symptoms-datasetlabelled
O dataset escolhido contém dados numéricos sobre a coluna do paciente e usa esses dados para classificar a condição da coluna como normal ou anormal. Ele contém 310 exemplos que foram usados para treinar os algoritmos mostrados a seguir.
Sobre os parâmetros que foram utilizados no weka: o fator de confiança foi de 0.25 (como sugerido) e o número mínimo de objetos (necessários para se considerar uma resposta) foi 2, também como sugerido pelo software.
pelvic_incidence pelvic_tilt lumbar_lordosis_angle sacral_slope pelvic_radius degree_spondylolisthesis pelvic_slope direct_tilt thoracic_slope cervical_tilt sacrum_angle scoliosis_slope Class_att
63.0278175 22.55258597 39.60911701 40.47523153 98.67291675 -0.254399986 0.744503464 12.5661 14.5386 15.30468 -28.658501 43.5123 Abnormal
39.05695098 10.06099147 25.01537822 28.99595951 114.4054254 4.564258645 0.415185678 12.8874 17.5323 16.78486 -25.530607 16.1102 Abnormal
68.83202098 22.21848205 50.09219357 46.61353893 105.9851355 -3.530317314 0.474889164 26.8343 17.4861 16.65897 -29.031888 19.2221 Abnormal
69.29700807 24.65287791 44.31123813 44.64413017 101.8684951 11.21152344 0.369345264 23.5603 12.7074 11.42447 -30.470246 18.8329 Abnormal
49.71285934 9.652074879 28.317406 40.06078446 108.1687249 7.918500615 0.543360472 35.494 15.9546 8.87237 -16.378376 24.9171 Abnormal
40.25019968 13.92190658 25.1249496 26.32829311 130.3278713 2.230651729 0.789992856 29.323 12.0036 10.40462 -1.512209 9.6548 Abnormal
53.43292815 15.86433612 37.16593387 37.56859203 120.5675233 5.988550702 0.198919573 13.8514 10.7146 11.37832 -20.510434 25.9477 Abnormal
45.36675362 10.75561143 29.03834896 34.61114218 117.2700675 -10.67587083 0.131972555 28.8165 7.7676 7.60961 -25.111459 26.3543 Abnormal
43.79019026 13.5337531 42.69081398 30.25643716 125.0028927 13.28901817 0.190407626 22.7085 11.4234 10.59188 -20.020075 40.0276 Abnormal
36.68635286 5.010884121 41.9487509 31.67546874 84.24141517 0.664437117 0.367700139 26.2011 8.738 14.91416 -1.702097 21.432 Abnormal
49.70660953 13.04097405 31.33450009 36.66563548 108.6482654 -7.825985755 0.6880095 31.3502 16.5097 15.17645 -0.502127 18.3437 Abnormal
31.23238734 17.71581923 15.5 13.51656811 120.0553988 0.499751446 0.608342758 21.4356 9.2589 14.76412 -21.724559 36.4449 Abnormal
48.91555137 19.96455616 40.26379358 28.95099521 119.321358 8.028894629 0.139478165 32.7916 7.2049 8.61882 -1.215542 27.3713 Abnormal
53.5721702 20.46082824 33.1 33.11134196 110.9666978 7.044802938 0.081930993 15.058 12.8127 12.00109 -1.734117 15.6205 Abnormal
57.30022656 24.1888846 46.99999999 33.11134196 116.8065868 5.766946943 0.416721511 16.5158 18.6222 8.51898 -33.441303 13.2498 Abnormal
44.31890674 12.53799164 36.098763 31.78091509 124.1158358 5.415825143 0.664040876 9.5021 19.1756 7.25707 -32.893911 19.5695 Abnormal
63.83498162 20.36250706 54.55243367 43.47247456 112.3094915 -0.622526643 0.560675371 10.769 16.8116 11.41344 2.676002 17.3859 Abnormal
31.27601184 3.14466948 32.56299592 28.13134236 129.0114183 3.623020073 0.534481238 31.1641 18.6089 8.4402 4.482424 24.6513 Abnormal
38.69791243 13.44474904 31 25.25316339 123.1592507 1.429185758 0.30658054 28.3015 17.9575 14.75417 -14.252676 24.9361 Abnormal
41.72996308 12.25407408 30.12258646 29.475889 116.5857056 -1.244402488 0.468525928 28.5598 12.4637 14.1961 -20.392538 33.0265 Abnormal
43.92283983 14.17795853 37.8325467 29.7448813 134.4610156 6.451647637 0.280446206 12.4719 16.8965 10.32658 -4.986668 22.4667 Abnormal
54.91944259 21.06233245 42.19999999 33.85711014 125.2127163 2.432561437 0.175244572 23.0791 14.2195 14.14196 3.780394 24.9278 Abnormal
63.07361096 24.41380271 53.99999999 38.65980825 106.4243295 15.77969683 0.666388008 11.9696 17.6891 7.63771 -14.183602 44.2338 Abnormal
45.54078988 13.06959759 30.29832059 32.47119229 117.9808303 -4.987129618 0.567450078 23.8889 9.1019 7.70987 -19.37903 20.3649 Abnormal
36.12568347 22.75875277 29 13.3669307 115.5771163 -3.237562489 0.126473707 25.6206 15.7438 11.5561 -18.108941 24.1151 Abnormal
54.12492019 26.65048856 35.32974693 27.47443163 121.447011 1.571204816 0.928687869 14.6686 13.57 16.12951 -17.630363 28.1902 Abnormal
26.14792141 10.75945357 14 15.38846783 125.2032956 -10.09310817 0.391971136 9.871 8.6406 15.78046 -19.650163 43.955 Abnormal
43.58096394 16.5088837 46.99999999 27.07208024 109.271634 8.992815727 0.594175694 30.4577 17.97 10.79356 -25.180777 18.3196 Abnormal
44.5510115 21.93114655 26.78591597 22.61986495 111.0729197 2.652320636 0.527891438 32.4275 10.2244 11.71324 -28.506125 28.047 Abnormal
66.87921138 24.89199889 49.27859673 41.9872125 113.4770183 -2.005891748 0.677267795 12.4271 8.2495 7.58784 -3.963385 27.3587 Abnormal
50.81926781 15.40221253 42.52893886 35.41705528 112.192804 10.86956554 0.678987086 7.1103 7.2481 9.94785 -17.379206 14.7187 Abnormal
46.39026008 11.07904664 32.13655345 35.31121344 98.77454633 6.386831648 0.064872511 14.2826 7.4515 7.30184 -24.360827 28.2366 Abnormal
44.93667457 17.44383762 27.78057555 27.49283695 117.9803245 5.569619587 0.81674803 27.5218 13.8357 13.54721 -2.925586 36.0452 Abnormal
38.66325708 12.98644139 39.99999999 25.67681568 124.914118 2.703008052 0.815941481 30.2045 7.5284 9.28229 -2.817753 31.5193 Abnormal
59.59554032 31.99824445 46.56025198 27.59729587 119.3303537 1.474285836 0.477087978 8.6051 8.3058 8.537 -0.029028 40.5823 Abnormal
31.48421834 7.82622134 24.28481815 23.657997 113.8331446 4.393080498 0.713153407 9.7107 8.1003 11.85555 -26.650369 12.6599 Abnormal
32.09098679 6.989378081 35.99819848 25.10160871 132.264735 6.413427708 0.872719252 24.4626 11.6395 11.00446 -16.407275 38.8912 Abnormal
35.70345781 19.44325311 20.7 16.26020471 137.5406125 -0.263489651 0.882807309 32.5864 12.7274 9.53575 -14.695641 38.7458 Abnormal
55.84328595 28.84744756 47.69054322 26.99583839 123.3118449 2.812426855 0.142325313 12.6634 8.855 10.55193 -16.404668 15.2954 Abnormal
52.41938511 19.01156052 35.87265953 33.40782459 116.5597709 1.694705102 0.059106366 30.0191 18.9113 16.64731 -26.32863 39.2753 Abnormal
35.49244617 11.7016723 15.59036345 23.79077387 106.9388517 -3.460357991 0.743812023 15.3987 9.3239 16.71638 -2.488862 20.0076 Abnormal
46.44207842 8.39503589 29.0372302 38.04704253 115.4814047 2.045475795 0.80691143 27.8754 12.2285 9.55731 -22.35809 14.3317 Abnormal
53.85479842 19.23064334 32.77905978 34.62415508 121.6709148 5.329843204 0.417637339 9.3514 11.5243 12.37699 -24.199605 11.3375 Abnormal
66.28539377 26.32784484 47.49999999 39.95754893 121.2196839 -0.799624469 0.647625866 9.0466 10.2636 13.50349 1.138079 34.3683 Abnormal
56.03021778 16.2979149 62.27527456 39.73230287 114.0231172 -2.325683841 0.072901223 24.861 12.2345 14.16436 -30.035767 22.4654 Abnormal
50.91244034 23.01516931 46.99999999 27.89727103 117.4222591 -2.526701511 0.319204878 30.6389 18.6181 15.55901 2.537043 9.431 Abnormal
48.332638 22.22778399 36.18199318 26.10485401 117.3846251 6.481709096 0.062276845 23.5538 11.0942 13.15072 -4.200276 20.0348 Abnormal
41.35250407 16.57736351 30.70619135 24.77514057 113.2666746 -4.497957556 0.982250408 29.2557 16.7065 16.38754 -3.494359 14.5269 Abnormal
40.55735663 17.97778407 34 22.57957256 121.0462458 -1.537383074 0.011971076 31.6694 8.2526 7.88212 -9.567871 11.9238 Abnormal
41.76773173 17.89940172 20.0308863 23.86833001 118.3633889 2.062962549 0.371350889 21.1136 7.1646 9.82029 -6.841914 11.6156 Abnormal
55.28585178 20.44011836 34 34.84573342 115.8770174 3.558372358 0.680654711 16.711 15.9714 14.37627 4.779509 43.261 Abnormal
74.43359316 41.55733141 27.7 32.87626175 107.9493045 5.000088788 0.606767772 32.6283 9.8062 11.62142 -10.028289 9.3141 Abnormal
50.20966979 29.76012218 36.10400731 20.44954761 128.2925148 5.740614083 0.031139167 36.1431 13.9907 12.90967 -30.430498 31.6999 Abnormal
30.14993632 11.91744524 34 18.23249108 112.6841408 11.46322327 0.659772403 12.0969 10.7071 16.18484 -4.763914 26.8917 Abnormal
41.17167989 17.32120599 33.46940277 23.85047391 116.3778894 -9.569249858 0.302179133 9.2518 12.8432 8.09991 -17.401155 22.8036 Abnormal
47.65772963 13.27738491 36.67998541 34.38034472 98.24978071 6.273012173 0.972555636 18.2046 16.9817 12.32724 -26.375211 14.1334 Abnormal
43.34960621 7.467468964 28.06548279 35.88213725 112.7761866 5.753277458 0.592034449 14.3377 14.2176 9.64034 -12.480751 13.0244 Abnormal
46.85578065 15.35151393 38 31.50426672 116.2509174 1.662705589 0.121465407 30.283 14.6233 8.75046 4.334375 16.8302 Abnormal
43.20318499 19.66314572 35 23.54003927 124.8461088 -2.919075955 0.016747113 26.8235 16.2905 14.76132 -24.294191 23.8843 Abnormal
48.10923638 14.93072472 35.56468278 33.17851166 124.0564518 7.947904861 0.623275382 33.5947 14.1761 15.86896 2.50245 23.0762 Abnormal
74.37767772 32.05310438 78.77201304 42.32457334 143.5606905 56.12590603 0.159377926 35.9529 15.3975 11.71169 -18.628293 22.5623 Abnormal
89.68056731 32.70443487 83.13073216 56.97613244 129.9554764 92.02727682 0.527584239 26.3756 18.6012 16.09596 -18.70133 35.8729 Abnormal
44.529051 9.433234213 51.99999999 35.09581679 134.7117723 29.10657504 0.11662693 22.0548 13.7595 16.77905 -7.146471 13.5143 Abnormal
77.69057712 21.38064464 64.42944191 56.30993248 114.818751 26.93184095 0.046225827 24.5548 15.3209 11.10896 -23.279118 16.1132 Abnormal
76.1472121 21.93618556 82.96150249 54.21102654 123.9320096 10.43197194 0.252796128 21.5934 7.8098 11.07095 -34.89766 43.1487 Abnormal
83.93300857 41.28630543 61.99999999 42.64670314 115.012334 26.58810016 0.61476653 8.8345 7.2405 9.79573 -20.130727 22.4032 Abnormal
78.49173027 22.1817978 59.99999999 56.30993248 118.5303266 27.38321314 0.008485564 7.5647 12.6737 8.03422 -22.037558 32.0972 Abnormal
75.64973136 19.33979889 64.14868477 56.30993248 95.9036288 69.55130292 0.687091535 24.1004 13.3444 15.75602 -0.550516 18.2915 Abnormal
72.07627839 18.94617604 50.99999999 53.13010236 114.2130126 1.01004051 0.084621266 12.6031 9.6504 10.87581 -16.918585 14.0322 Abnormal
58.59952852 -0.261499046 51.49999999 58.86102756 102.0428116 28.05969711 0.356359455 11.4299 15.3124 15.06436 -8.393927 30.7765 Abnormal
72.56070163 17.38519079 51.99999999 55.17551084 119.1937238 32.10853735 0.267291991 26.9716 18.3111 13.67428 -19.605044 22.759 Abnormal
86.90079431 32.9281677 47.79434664 53.97262661 135.0753635 101.7190919 0.459674217 25.0986 8.7655 8.9351 -21.31896 12.8518 Abnormal
84.97413208 33.02117462 60.85987263 51.95295747 125.6595336 74.33340864 0.600115713 25.6364 17.7501 7.886 4.442569 13.4605 Abnormal
55.512212 20.09515673 43.99999999 35.41705528 122.648753 34.55294641 0.672041297 35.0909 8.6569 14.35843 -33.990906 25.5218 Abnormal
72.2223343 23.07771056 90.99999999 49.14462374 137.7366546 56.80409277 0.826532439 32.3379 7.4437 16.44128 -9.487619 9.6867 Abnormal
70.22145219 39.82272448 68.11840309 30.39872771 148.5255624 145.3781432 0.946610646 10.384 9.5742 11.22353 4.641629 9.8472 Abnormal
86.75360946 36.04301632 69.22104479 50.71059314 139.414504 110.8607824 0.640487619 16.5571 17.3635 12.70134 -15.088499 7.0079 Abnormal
58.78254775 7.667044186 53.33894082 51.11550357 98.50115697 51.58412476 0.06039077 26.0645 11.7696 9.99732 -0.622813 24.3675 Abnormal
67.41253785 17.44279712 60.14464036 49.96974073 111.12397 33.15764573 0.855643425 18.9972 12.8779 11.82259 -14.55007 42.2698 Abnormal
47.74467877 12.08935067 38.99999999 35.6553281 117.5120039 21.68240136 0.652596503 23.2067 14.7577 8.43155 -33.338734 22.7226 Abnormal
77.10657122 30.46999418 69.48062839 46.63657704 112.1516 70.75908308 0.156502675 10.849 13.2216 11.55132 -1.860646 18.6033 Abnormal
74.00554124 21.12240192 57.37950226 52.88313932 120.2059626 74.55516588 0.406965314 10.5895 12.5946 15.87462 -10.624659 31.9699 Abnormal
88.62390839 29.08945331 47.56426247 59.53445508 121.7647796 51.80589921 0.770613922 13.1962 13.659 15.27164 -4.208953 32.934 Abnormal
81.10410039 24.79416792 77.88702048 56.30993247 151.8398566 65.21461611 0.972005589 10.5715 11.2339 13.29506 -12.139219 11.8487 Abnormal
76.32600187 42.39620445 57.19999999 33.92979742 124.267007 50.12745689 0.583098014 33.1635 8.383 13.75752 -32.106343 18.6868 Abnormal
45.44374959 9.906071798 44.99999999 35.53767779 163.0710405 20.31531532 0.345234838 31.8795 15.0011 15.89311 -10.750511 22.7075 Abnormal
59.78526526 17.87932332 59.20646143 41.90594194 119.3191109 22.12386874 0.374705546 23.3173 15.0648 8.89121 -32.248563 40.3949 Abnormal
44.91414916 10.21899563 44.63091389 34.69515353 130.0756599 37.36453993 0.690088008 18.0873 18.1846 15.62397 -22.670743 37.0558 Abnormal
56.60577127 16.80020017 41.99999999 39.80557109 127.2945222 24.0185747 0.793168976 19.5456 8.7779 16.40308 -35.287375 31.6243 Abnormal
71.18681115 23.89620111 43.6966651 47.29061004 119.8649383 27.28398451 0.402241133 9.1296 16.7172 7.0306 -4.667443 14.5344 Abnormal
81.65603206 28.74886935 58.23282055 52.9071627 114.7698556 30.60914842 0.832811085 23.1811 11.2491 11.69024 -25.011107 21.918 Abnormal
70.95272771 20.15993121 62.85910914 50.7927965 116.1779325 32.522331 0.054842915 7.3173 16.3676 12.21365 -5.091336 17.2601 Abnormal
85.35231529 15.84491006 71.66865979 69.50740523 124.4197875 76.0206034 0.046938967 26.0497 11.7878 14.39722 -12.551344 39.8494 Abnormal
58.10193455 14.83763914 79.64983825 43.26429541 113.5876551 50.23787808 0.951361122 33.904 11.6354 12.20428 -22.326717 19.5797 Abnormal
94.17482232 15.38076983 67.70572132 78.79405249 114.8901128 53.25522004 0.199874982 12.1048 19.1837 8.97829 -3.549557 7.3222 Abnormal
57.52235608 33.64707522 50.90985841 23.87528085 140.9817119 148.7537109 0.597457003 21.5943 7.5666 7.81812 -27.570464 17.8768 Abnormal
96.65731511 19.46158117 90.21149828 77.19573393 120.6730408 64.08099841 0.623388207 21.5013 13.0551 11.35399 -14.093301 20.818 Abnormal
74.72074622 19.75694203 82.73535954 54.96380419 109.3565941 33.30606685 0.558833102 7.027 7.8697 13.97269 -5.115515 20.6402 Abnormal
77.65511874 22.4329501 93.89277881 55.22216863 123.0557067 61.2111866 0.924902858 14.9502 15.0493 7.57722 0.307904 33.7201 Abnormal
58.52162283 13.92228609 41.46785522 44.59933674 115.514798 30.3879839 0.401084706 34.6931 10.3564 10.64403 -26.05199 10.4338 Abnormal
84.5856071 30.36168482 65.47948563 54.22392228 108.0102185 25.11847846 0.341664609 30.4108 15.7092 11.58279 -1.273566 29.6399 Abnormal
79.93857026 18.7740711 63.31183486 61.16449915 114.787107 38.53874133 0.708886697 11.2935 10.922 7.17197 -34.653679 28.1835 Abnormal
70.39930842 13.46998624 61.19999999 56.92932218 102.3375244 25.53842852 0.974400946 30.9297 9.5431 12.34978 6.089565 34.9908 Abnormal
49.78212054 6.46680486 52.99999999 43.31531568 110.8647831 25.33564729 0.334657138 17.6515 11.704 16.26239 -0.89559 38.4719 Abnormal
77.40933294 29.39654543 63.23230243 48.0127875 118.4507311 93.56373734 0.37528738 11.2385 12.9197 13.82148 6.079425 11.8698 Abnormal
65.00796426 27.60260762 50.94751899 37.40535663 116.5811088 7.015977884 0.867324121 12.1292 13.8536 11.95397 -20.735613 9.7675 Abnormal
65.01377322 9.838262375 57.73583722 55.17551084 94.73852542 49.69695462 0.151993641 14.3986 8.9024 10.84295 6.573829 35.1025 Abnormal
78.42595126 33.42595126 76.27743927 45 138.5541111 77.15517241 0.580604336 36.6285 16.6264 7.96524 -19.123087 16.1431 Abnormal
63.17298709 6.330910974 62.99999999 56.84207612 110.6440206 42.60807567 0.23433535 24.5629 11.073 16.30352 -4.447261 41.326 Abnormal
68.61300092 15.0822353 63.01469619 53.53076561 123.4311742 39.49798659 0.249350536 27.0646 17.7171 7.1822 -20.883262 17.113 Abnormal
63.90063261 13.7062037 62.12433389 50.19442891 114.1292425 41.42282844 0.715779422 24.8714 16.645 16.46184 -1.682575 13.9094 Abnormal
84.99895554 29.61009772 83.35219438 55.38885782 126.9129899 71.32117542 0.998826684 7.0551 9.0119 9.85541 -19.314135 43.0086 Abnormal
42.02138603 -6.554948347 67.89999999 48.57633437 111.5857819 27.33867086 0.986271547 15.6365 10.8504 16.20134 0.043299 20.6529 Abnormal
69.75666532 19.27929659 48.49999999 50.47736873 96.49136982 51.1696403 0.797662594 9.6196 17.4517 7.24562 -7.96908 33.678 Abnormal
80.98807441 36.84317181 86.96060151 44.1449026 141.0881494 85.87215224 0.496180717 27.5223 13.5136 11.60893 -13.600284 34.3656 Abnormal
129.8340406 8.404475005 48.38405705 121.4295656 107.690466 418.5430821 0.860222868 18.5943 11.1514 11.36543 -34.202073 27.5144 Abnormal
70.48410444 12.48948765 62.41714208 57.99461679 114.1900488 56.90244779 0.823630076 13.5572 10.4727 11.19482 -1.999994 26.1908 Abnormal
86.04127982 38.75066978 47.87140494 47.29061004 122.0929536 61.98827709 0.035210491 27.5499 12.008 9.6275 5.603229 36.2899 Abnormal
65.53600255 24.15748726 45.77516991 41.3785153 136.4403015 16.37808564 0.377683884 25.067 13.7801 14.63875 -15.898046 19.5298 Abnormal
60.7538935 15.7538935 43.19915768 45 113.0533309 31.69354839 0.822344641 26.2469 17.3268 12.46333 -17.516477 22.9375 Abnormal
54.74177518 12.09507205 40.99999999 42.64670314 117.6432188 40.3823266 0.440722184 30.0719 19.2053 14.52239 -18.805512 33.1902 Abnormal
83.87994081 23.07742686 87.14151223 60.80251395 124.6460723 80.55560527 0.436932625 7.2994 11.1917 16.2815 -8.553212 24.8562 Abnormal
80.07491418 48.06953097 52.40343873 32.00538321 110.7099121 67.72731595 0.099940503 20.2822 10.3082 15.89258 -14.15607 39.973 Abnormal
65.66534698 10.54067533 56.48913545 55.12467166 109.1627768 53.93202006 0.184438017 20.2044 11.528 16.41116 -24.064246 15.9787 Abnormal
74.71722805 14.32167879 32.5 60.39554926 107.1822176 37.01708012 0.979253427 25.3481 8.2316 12.17025 1.594477 31.4138 Abnormal
48.06062649 5.687032126 57.05716117 42.37359436 95.44375749 32.83587702 0.403799874 31.1599 11.5825 11.35088 -25.723134 40.82 Abnormal
70.67689818 21.70440224 59.18116082 48.97249594 103.0083545 27.8101478 0.039655293 15.7748 14.8568 11.45991 -18.475476 19.8407 Abnormal
80.43342782 16.998479 66.53601753 63.43494882 116.4389807 57.78125 0.09580622 26.778 18.2886 11.96597 -25.207568 21.545 Abnormal
90.51396072 28.27250132 69.8139423 62.2414594 100.8921596 58.82364821 0.881441257 13.5739 16.3289 16.52676 -10.917156 35.6543 Abnormal
77.23689752 16.73762214 49.77553438 60.49927538 110.6903772 39.7871542 0.707245245 22.5858 12.5804 7.61063 -32.87061 19.6294 Abnormal
50.06678595 9.120340183 32.16846267 40.94644577 99.71245318 26.76669655 0.710450644 21.9074 18.8412 9.1785 5.120515 18.8581 Abnormal
69.78100617 13.77746531 57.99999999 56.00354085 118.9306656 17.91456046 0.668562821 24.2342 8.7164 7.96714 -15.682309 34.906 Abnormal
69.62628302 21.12275138 52.76659472 48.50353164 116.8030913 54.81686729 0.286894092 18.5916 15.4963 15.92252 1.320769 34.8665 Abnormal
81.75441933 20.12346562 70.56044038 61.63095371 119.4250857 55.50688907 0.265889494 15.379 18.1885 14.66728 -3.994716 33.2091 Abnormal
52.20469309 17.21267289 78.09496877 34.9920202 136.9725168 54.93913416 0.006128311 20.3617 8.5783 12.06379 -2.974064 24.2895 Abnormal
77.12134424 30.3498745 77.48108264 46.77146974 110.6111484 82.09360704 0.278327565 21.9069 17.0071 16.22809 -0.05579 27.6595 Abnormal
88.0244989 39.84466878 81.77447308 48.17983012 116.6015376 56.76608323 0.238984543 14.6182 12.1692 7.39996 -11.029157 40.7572 Abnormal
83.39660609 34.31098931 78.42329287 49.08561678 110.4665164 49.67209559 0.771860278 24.9264 7.6245 13.236 -21.449617 16.2153 Abnormal
72.05403412 24.70073725 79.87401586 47.35329687 107.1723576 56.42615873 0.296152366 7.7545 10.8824 7.23178 -2.990023 29.9404 Abnormal
85.09550254 21.06989651 91.73479193 64.02560604 109.062312 38.03283108 0.481861846 17.1681 8.4727 11.9815 -25.387556 8.3163 Abnormal
69.56348614 15.4011391 74.43849743 54.16234705 105.0673556 29.70121083 0.003220264 13.3594 18.2659 15.38281 -2.504431 14.2555 Abnormal
89.5049473 48.90365265 72.0034229 40.60129465 134.6342912 118.3533701 0.039380359 19.8712 8.9861 14.77008 6.868423 29.1844 Abnormal
85.29017283 18.27888963 100.7442198 67.0112832 110.6607005 58.88494802 0.487939752 9.4271 12.5462 9.74172 -33.848051 9.4194 Abnormal
60.62621697 20.5959577 64.53526221 40.03025927 117.2255542 104.8592474 0.386903046 17.0217 8.8097 16.82108 -30.591567 35.4529 Abnormal
60.04417717 14.30965614 58.03886519 45.73452103 105.1316639 30.40913315 0.41469298 17.6829 16.5256 10.35218 1.270053 10.4207 Abnormal
85.64378664 42.68919513 78.7506635 42.95459151 105.1440758 42.88742577 0.844294085 16.9272 8.0109 15.0803 -1.056403 11.4148 Abnormal
85.58171024 30.45703858 78.23137949 55.12467166 114.8660487 68.37612182 0.624974835 26.5001 11.2204 12.33663 -15.774389 40.4629 Abnormal
55.08076562 -3.759929872 55.99999999 58.84069549 109.9153669 31.77358318 0.651920192 36.7439 9.0278 14.69484 -4.850453 18.1958 Abnormal
65.75567895 9.832874231 50.82289501 55.92280472 104.3949585 39.30721246 0.081033285 35.6242 7.4483 12.13128 -5.163605 43.2649 Abnormal
79.24967118 23.94482471 40.79669829 55.30484647 98.62251165 36.7063954 0.672569597 29.0324 14.5804 16.56784 -0.26959 31.7726 Abnormal
81.11260488 20.69044356 60.68700588 60.42216132 94.01878339 40.51098228 0.530804498 11.4265 8.3428 7.26048 -15.985527 29.5574 Abnormal
48.0306238 3.969814743 58.34451924 44.06080905 125.3509625 35.00007784 0.820727828 22.6313 14.8226 8.35383 -32.826775 38.8071 Abnormal
63.40448058 14.11532726 48.13680562 49.28915333 111.9160075 31.78449499 0.113089671 20.9044 13.1978 13.33661 -24.275516 9.173 Abnormal
57.28694488 15.1493501 63.99999999 42.13759477 116.7353868 30.34120327 0.431125462 22.253 17.6755 12.20726 -21.986137 23.1484 Abnormal
41.18776972 5.792973871 42.86739151 35.39479584 103.3488802 27.66027669 0.044130317 21.0757 10.5374 9.66748 -9.571667 30.5253 Abnormal
66.80479632 14.55160171 72.08491177 52.25319461 82.45603817 41.6854736 0.738028916 24.6372 12.5023 11.90802 -7.585607 39.7443 Abnormal
79.4769781 26.73226755 70.65098189 52.74471055 118.5886691 61.70059824 0.642084751 8.2975 8.384 11.96108 5.237386 10.8006 Abnormal
44.21646446 1.507074501 46.11033909 42.70938996 108.6295666 42.81048066 0.480821979 20.0603 14.7325 11.98973 5.365967 13.7113 Abnormal
57.03509717 0.34572799 49.19800263 56.68936918 103.0486975 52.16514503 0.561323329 35.4921 14.1033 7.99506 -26.223143 40.1564 Abnormal
64.27481758 12.50864276 68.70237672 51.76617482 95.25245421 39.40982612 0.352038125 36.3579 7.0378 13.83023 -27.923626 7.0698 Abnormal
92.02630795 35.39267395 77.41696348 56.633634 115.72353 58.05754155 0.302441921 30.0162 9.8318 11.21248 -19.264777 19.9972 Abnormal
67.26314926 7.194661096 51.69688681 60.06848816 97.8010854 42.13694325 0.936622832 17.7459 9.6738 7.23554 -32.43783 33.0292 Abnormal
118.1446548 38.44950127 50.83851954 79.69515353 81.0245406 74.04376736 0.599392845 35.8563 10.9266 13.11354 -17.52081 21.2408 Abnormal
115.9232606 37.51543601 76.79999999 78.40782459 104.6986033 81.19892712 0.542816002 22.3317 8.8519 11.4896 -6.754004 32.5082 Abnormal
53.94165809 9.306594428 43.10049819 44.63506366 124.3978211 25.0821266 0.871551213 17.5525 17.5404 16.73581 -17.874616 19.5841 Abnormal
83.7031774 20.26822858 77.1105979 63.43494882 125.4801739 69.279571 0.73595883 33.8124 15.1125 14.38085 -20.214168 11.7348 Abnormal
56.99140382 6.87408897 57.00900516 50.11731485 109.978045 36.81011057 0.555518055 33.3025 18.5683 16.03569 -0.718491 34.6601 Abnormal
72.34359434 16.42078962 59.86901238 55.92280472 70.08257486 12.07264427 0.056944145 31.823 15.7134 9.36778 -33.489059 28.9479 Abnormal
95.38259648 24.82263131 95.15763273 70.55996517 89.3075466 57.66084135 0.268276345 28.6901 7.2124 13.13055 -6.412477 19.9792 Abnormal
44.25347645 1.101086714 38 43.15238973 98.27410705 23.9106354 0.180863626 9.971 12.4275 9.73836 -6.195062 25.57 Abnormal
64.80954139 15.17407796 58.83999352 49.63546343 111.679961 21.40719845 0.303206157 25.2382 7.175 10.20296 -33.025711 17.1654 Abnormal
78.40125389 14.04225971 79.69426258 64.35899418 104.7312342 12.39285327 0.842278621 29.9807 7.1135 13.21647 -29.71579 19.1168 Abnormal
56.66829282 13.45820343 43.76970978 43.21008939 93.69220863 21.10812135 0.524781111 8.0015 18.1719 15.03453 -16.408583 33.2835 Abnormal
50.82502875 9.064729049 56.29999999 41.7602997 78.99945411 23.04152435 0.051929588 29.3962 16.3725 11.35215 -26.496342 33.9151 Abnormal
61.41173702 25.38436364 39.09686927 36.02737339 103.4045971 21.84340688 0.697750246 8.4084 15.698 12.90325 -27.124475 22.9564 Abnormal
56.56382381 8.961261611 52.57784639 47.6025622 98.77711506 50.70187326 0.588947646 18.1451 13.9634 12.46567 0.74424 32.4471 Abnormal
67.02766447 13.28150221 66.15040334 53.74616226 100.7154129 33.98913551 0.053300996 8.5072 13.34 12.63134 -21.818611 40.6229 Abnormal
80.81777144 19.23898066 61.64245116 61.57879078 89.47183446 44.167602 0.080967648 23.0765 12.6822 11.71401 -32.340192 27.1091 Abnormal
80.65431956 26.34437939 60.89811835 54.30994017 120.1034928 52.46755185 0.93160362 20.0845 18.4914 8.98429 -19.329173 31.0862 Abnormal
68.72190982 49.4318636 68.0560124 19.29004622 125.0185168 54.69128928 0.3798954 17.4281 16.0009 14.48126 -31.852569 30.533 Abnormal
37.90391014 4.47909896 24.71027447 33.42481118 157.848799 33.60702661 0.473130085 24.8271 17.5433 10.87176 -11.190833 29.909 Abnormal
64.62400798 15.22530262 67.63216653 49.39870535 90.298468 31.32641123 0.781685896 24.7626 18.5975 13.0176 -20.526277 17.3548 Abnormal
75.43774787 31.53945399 89.59999999 43.89829388 106.8295898 54.96578902 0.030341261 8.763 11.0399 16.74065 -22.735586 43.1209 Abnormal
71.00194076 37.51577195 84.53709256 33.48616882 125.1642324 67.77118983 0.60269836 10.1025 14.5544 10.61123 -23.883075 38.7949 Abnormal
81.05661087 20.80149217 91.78449512 60.2551187 125.430176 38.18178176 0.849081982 11.0201 10.3301 12.1325 -4.893491 29.244 Abnormal
91.46874146 24.50817744 84.62027202 66.96056402 117.3078968 52.62304673 0.560009753 13.9263 12.1023 15.45998 -11.179414 30.316 Abnormal
81.08232025 21.25584028 78.76675639 59.82647997 90.07187999 49.159426 0.817563954 16.7111 13.4438 13.7822 -23.922201 29.5953 Abnormal
60.419932 5.265665422 59.8142356 55.15426658 109.0330745 30.26578534 0.916504638 35.031 18.2437 11.9537 -1.30467 34.2437 Abnormal
85.68094951 38.65003527 82.68097744 47.03091424 120.8407069 61.95903428 0.807918832 24.8883 13.238 10.73285 0.627326 11.2469 Abnormal
82.4065243 29.27642195 77.05456489 53.13010235 117.0422439 62.76534831 0.418463519 29.7716 16.189 8.58139 -31.511149 32.6221 Abnormal
43.7182623 9.811985315 51.99999999 33.90627699 88.43424213 40.88092253 0.81109806 10.6583 16.9317 9.51271 -8.828259 12.1023 Abnormal
86.472905 40.30376567 61.14101155 46.16913933 97.4041888 55.75222146 0.273687068 10.1834 10.416 16.38788 -11.786587 10.0888 Abnormal
74.46908181 33.28315665 66.94210105 41.18592517 146.4660009 124.9844057 0.059381409 33.708 12.3988 10.01481 -27.349859 14.9309 Abnormal
70.25043628 10.34012252 76.37007032 59.91031376 119.2370072 32.66650243 0.163594906 9.0344 11.9015 7.54207 -5.95662 43.8608 Abnormal
72.64385013 18.92911726 67.99999999 53.71473287 116.9634162 25.38424676 0.438382061 13.0121 14.5781 13.75328 -21.282686 41.2131 Abnormal
71.24176388 5.268270454 85.99958417 65.97349342 110.703107 38.2598637 0.506379066 23.0527 15.243 14.14875 -19.895641 8.6239 Abnormal
63.7723908 12.76338484 65.36052425 51.00900596 89.82274067 55.99545386 0.276928366 24.5529 10.4232 14.9747 -22.28622 21.7822 Abnormal
58.82837872 37.57787321 125.7423855 21.25050551 135.6294176 117.3146829 0.751482204 12.6576 15.9381 15.2392 -15.444826 7.2157 Abnormal
74.85448008 13.90908417 62.69325884 60.9453959 115.2087008 33.17225512 0.82191484 20.4667 9.351 14.37763 4.230442 39.2266 Abnormal
75.29847847 16.67148361 61.29620362 58.62699486 118.8833881 31.57582292 0.677506366 10.1345 12.2607 11.22559 -12.196755 31.7385 Abnormal
63.36433898 20.02462134 67.49870507 43.33971763 130.9992576 37.55670552 0.659016993 34.2436 10.1943 15.12032 1.278801 39.9331 Abnormal
67.51305267 33.2755899 96.28306169 34.23746278 145.6010328 88.30148594 0.575212433 9.1217 19.324 11.30614 -3.519343 28.2238 Abnormal
76.31402766 41.93368293 93.2848628 34.38034472 132.2672855 101.2187828 0.218938743 31.5204 13.6555 12.22936 4.894807 16.5217 Abnormal
73.63596236 9.711317947 62.99999999 63.92464442 98.72792982 26.97578722 0.198909407 30.8752 9.4553 11.84325 -34.729173 26.674 Abnormal
56.53505139 14.37718927 44.99154663 42.15786212 101.7233343 25.77317356 0.052601671 31.0079 14.4887 14.17105 -31.121553 32.2469 Abnormal
80.11157156 33.94243223 85.10160773 46.16913933 125.5936237 100.2921068 0.088561249 11.6503 16.1451 9.6995 4.44648 36.0749 Abnormal
95.48022873 46.55005318 58.99999999 48.93017555 96.68390337 77.28307195 0.778847512 29.838 14.5939 12.2245 -21.695815 38.7849 Abnormal
74.09473084 18.82372712 76.03215571 55.27100372 128.4057314 73.38821617 0.910885747 13.1813 10.1368 8.49572 -0.33713 11.6844 Abnormal
87.67908663 20.36561331 93.82241589 67.31347333 120.9448288 76.73062904 0.57477539 23.8665 13.0473 9.41012 5.212541 28.6308 Abnormal
48.25991962 16.41746236 36.32913708 31.84245726 94.88233607 28.34379914 0.388444626 16.1775 15.0636 13.79474 -8.044644 21.6135 Abnormal
38.50527283 16.96429691 35.11281407 21.54097592 127.6328747 7.986683227 0.396363819 34.8106 12.7802 15.24996 -28.833891 18.0442 normal
54.92085752 18.96842952 51.60145541 35.952428 125.8466462 2.001642472 0.106174649 7.3907 11.3014 8.37076 -17.723457 9.8711 normal
44.36249017 8.945434892 46.90209626 35.41705528 129.220682 4.994195288 0.537574087 33.0601 7.808 11.3766 -5.202362 33.2503 normal
48.3189305 17.45212105 47.99999999 30.86680945 128.9803079 -0.910940567 0.744321935 36.6194 14.635 11.6271 -28.598802 10.3379 normal
45.70178875 10.65985935 42.5778464 35.0419294 130.1783144 -3.38890999 0.990034481 26.6333 18.3694 16.44832 -13.438814 34.2846 normal
30.74193812 13.35496594 35.90352597 17.38697218 142.4101072 -2.005372903 0.326835429 16.5218 18.0205 7.55792 2.00213 30.1215 normal
50.91310144 6.6769999 30.89652243 44.23610154 118.151531 -1.057985526 0.038359424 35.6096 13.0974 12.04558 -9.237245 31.722 normal
38.12658854 6.557617408 50.44507473 31.56897113 132.114805 6.338199339 0.023094566 19.7932 11.3293 14.17628 -30.312742 38.1538 normal
51.62467183 15.96934373 35 35.6553281 129.385308 1.00922834 0.00504538 32.42 13.8149 11.2849 -25.770956 35.6191 normal
64.31186727 26.32836901 50.95896417 37.98349826 106.1777511 3.118221289 0.379709586 7.9787 11.4337 13.81463 -30.220853 17.9129 normal
44.48927476 21.78643263 31.47415392 22.70284212 113.7784936 -0.284129366 0.547080375 23.9247 13.4464 9.27506 -8.230224 15.5635 normal
54.9509702 5.865353416 52.99999999 49.08561678 126.9703283 -0.631602951 0.777717236 16.7774 10.5263 16.4625 -31.937038 22.1518 normal
56.10377352 13.10630665 62.63701952 42.99746687 116.2285032 31.17276727 0.713860571 9.1686 16.5844 16.49071 -8.594772 7.7532 normal
69.3988184 18.89840693 75.96636144 50.50041147 103.5825398 -0.44366081 0.647608649 29.0187 13.1408 9.58711 -22.403652 12.5917 normal
89.83467631 22.63921678 90.56346144 67.19545953 100.5011917 3.040973261 0.379932692 9.4868 17.7556 10.98189 -16.891891 28.09 normal
59.72614016 7.724872599 55.34348527 52.00126756 125.1742214 3.235159224 0.08021879 26.2021 8.7872 7.46821 3.916838 43.4384 normal
63.95952166 16.06094486 63.12373633 47.8985768 142.3601245 6.298970934 0.134954068 31.7659 10.957 13.32169 -9.939014 31.3141 normal
61.54059876 19.67695713 52.89222856 41.86364163 118.6862678 4.815031084 0.212129265 14.4911 7.5117 12.11463 -19.934103 41.7304 normal
38.04655072 8.30166942 26.23683004 29.7448813 123.8034132 3.885773488 0.933377696 14.7528 11.1235 11.05746 5.412408 38.2581 normal
43.43645061 10.09574326 36.03222439 33.34070735 137.4396942 -3.114450861 0.283588696 36.0097 11.0132 8.51675 -23.90419 35.0749 normal
65.61180231 23.13791922 62.58217893 42.47388309 124.1280012 -4.083298414 0.997247491 30.0422 17.6222 13.39076 -16.36997 21.4495 normal
53.91105429 12.93931796 38.99999999 40.97173633 118.1930354 5.074353176 0.146745173 17.7116 17.7521 16.43174 0.138844 30.7846 normal
43.11795103 13.81574355 40.34738779 29.30220748 128.5177217 0.970926407 0.110795865 8.9802 15.1873 10.59114 -17.943314 33.0483 normal
40.6832291 9.148437195 31.02159252 31.53479191 139.1184721 -2.511618596 0.775688024 31.2682 13.6632 13.015 -4.591917 19.9869 normal
37.7319919 9.386298276 41.99999999 28.34569362 135.740926 13.68304672 0.465169721 28.9703 10.2016 11.24951 -19.160909 34.0011 normal
63.92947003 19.97109671 40.17704963 43.95837332 113.0659387 -11.05817866 0.412296214 19.7733 11.1443 7.97351 -7.809627 29.5091 normal
61.82162717 13.59710457 63.99999999 48.22452261 121.779803 1.296191194 0.629660667 17.9906 13.6082 8.34518 -10.939434 20.7594 normal
62.14080535 13.96097523 57.99999999 48.17983012 133.2818339 4.955105669 0.122419736 33.8766 16.3819 9.66244 -16.783645 43.8402 normal
69.00491277 13.29178975 55.5701429 55.71312302 126.6116215 10.83201105 0.385073208 35.4534 7.4752 7.76405 -11.716465 13.0886 normal
56.44702568 19.44449915 43.5778464 37.00252653 139.1896903 -1.859688529 0.076818991 11.2853 16.1623 14.93052 -12.656406 40.5705 normal
41.6469159 8.835549101 36.03197484 32.8113668 116.5551679 -6.054537956 0.098119047 10.0549 8.7771 8.64451 -5.079724 29.4263 normal
51.52935759 13.51784732 35 38.01151027 126.7185156 13.92833085 0.863545131 33.2628 11.087 12.42093 -15.259539 18.2936 normal
39.08726449 5.536602477 26.93203835 33.55066201 131.5844199 -0.75946135 0.252511739 26.2684 12.6508 12.36056 -34.071611 43.7183 normal
34.64992241 7.514782784 42.99999999 27.13513962 123.9877408 -4.082937601 0.419743489 29.72 15.279 16.49241 -3.437709 21.8868 normal
63.02630005 27.33624023 51.60501665 35.69005983 114.5066078 7.439869802 0.577847158 11.2203 14.0752 7.38995 6.635051 13.4565 normal
47.80555887 10.68869819 53.99999999 37.11686068 125.3911378 -0.402523218 0.750423593 32.8112 12.0502 15.65862 -4.137017 39.6199 normal
46.63786363 15.85371711 39.99999999 30.78414653 119.3776026 9.06458168 0.478970567 23.5284 11.0671 7.58202 5.157255 17.469 normal
49.82813487 16.73643493 28 33.09169994 121.4355585 1.91330704 0.487833677 30.4187 15.5507 15.89565 -28.277945 22.042 normal
47.31964755 8.573680295 35.56025198 38.74596726 120.5769719 1.630663508 0.634019655 27.8268 15.313 13.47998 -1.889282 37.7836 normal
50.75329025 20.23505957 37 30.51823068 122.343516 2.288487746 0.147745134 28.9054 14.5673 11.98326 -26.881964 10.3342 normal
36.15782981 -0.810514093 33.62731353 36.96834391 135.9369096 -2.092506504 0.332027235 10.4752 17.1414 13.60366 -12.162522 28.3449 normal
40.74699612 1.835524271 49.99999999 38.91147185 139.2471502 0.668556793 0.277170683 11.196 16.527 15.75651 -28.284145 7.4324 normal
42.91804052 -5.845994341 57.99999999 48.76403486 121.6068586 -3.362044654 0.542970928 12.4697 8.5981 9.07771 -27.62739 12.7281 normal
63.79242525 21.34532339 65.99999999 42.44710185 119.5503909 12.38260373 0.607879237 21.5605 8.0233 8.72676 -8.842283 34.5721 normal
72.95564397 19.57697146 61.00707117 53.37867251 111.2340468 0.813491154 0.409585847 25.4781 12.4063 7.05411 -9.04664 16.8122 normal
67.53818154 14.65504222 58.00142908 52.88313932 123.6322597 25.9702063 0.330438834 8.351 9.9145 16.25839 -27.302888 25.0493 normal
54.75251965 9.752519649 47.99999999 45 123.0379985 8.235294118 0.385732443 28.1386 14.9326 13.57371 -18.445718 13.8497 normal
50.16007802 -2.970024337 41.99999999 53.13010235 131.8024914 -8.290203373 0.308798826 17.9008 16.4723 8.02315 -34.615429 9.9615 normal
40.34929637 10.19474845 37.96774659 30.15454792 128.0099272 0.458901373 0.170983426 12.8223 13.9897 10.31438 -30.255112 18.7992 normal
63.61919213 16.93450781 49.34926218 46.68468432 117.0897469 -0.357811974 0.9539319 15.5713 9.9518 15.09867 -26.758834 40.4129 normal
54.14240778 11.93511014 42.99999999 42.20729763 122.2090834 0.153549242 0.354894839 22.1191 9.3492 14.34981 -19.444964 40.8512 normal
74.97602148 14.92170492 53.73007172 60.05431656 105.6453997 1.594747729 0.318966687 13.2564 11.3042 13.47166 -20.789258 41.2149 normal
42.51727249 14.37567126 25.32356538 28.14160123 128.9056892 0.75702014 0.625180876 35.6342 18.7123 8.97822 -14.510574 22.6375 normal
33.78884314 3.675109986 25.5 30.11373315 128.3253556 -1.776111234 0.389858261 9.673 11.3129 13.23731 -2.244119 10.2925 normal
54.5036853 6.819910138 46.99999999 47.68377516 111.7911722 -4.406769011 0.509022104 28.2247 18.7158 12.21306 5.672553 43.6689 normal
48.17074627 9.594216702 39.71092029 38.57652956 135.6233101 5.360050572 0.859959636 21.7568 14.418 12.55075 -24.517621 18.4675 normal
46.37408781 10.21590237 42.69999999 36.15818544 121.2476572 -0.54202201 0.95599665 34.9209 8.8496 12.75813 3.332207 9.3333 normal
52.86221391 9.410371613 46.98805181 43.4518423 123.0912395 1.856659161 0.226819134 21.8843 15.3118 13.91499 -32.013803 17.6135 normal
57.1458515 16.48909145 42.84214764 40.65676005 113.8061775 5.0151857 0.223549676 25.7485 9.5092 7.06295 -31.862036 24.3522 normal
37.14014978 16.48123972 24 20.65891006 125.0143609 7.366425398 0.851140631 10.7294 18.2159 9.4178 -31.427534 35.7839 normal
51.31177106 8.875541276 56.99999999 42.43622979 126.4722584 -2.144043911 0.46741327 22.7101 10.5134 10.13608 5.738583 36.7874 normal
42.51561014 16.54121618 41.99999999 25.97439396 120.631941 7.876730692 0.040763821 16.7193 15.9657 8.1948 -33.380627 30.2644 normal
39.35870531 7.011261806 37 32.3474435 117.8187599 1.904048199 0.58775384 29.1291 9.8168 15.93402 -8.871793 12.5514 normal
35.8775708 1.112373561 43.45725694 34.76519724 126.9239062 -1.632238263 0.793121083 10.7594 11.0116 7.92836 -5.852864 22.7358 normal
43.1919153 9.976663803 28.93814927 33.21525149 123.4674001 1.741017579 0.300086307 12.799 17.7684 7.77773 -35.077537 27.5972 normal
67.28971201 16.7175142 50.99999999 50.5721978 137.5917777 4.960343813 0.233195482 23.3207 13.7148 10.46265 -9.187554 27.8587 normal
51.32546366 13.63122319 33.25857782 37.69424047 131.3061224 1.78886965 0.417720656 29.8852 12.3509 11.99547 -34.927709 19.3766 normal
65.7563482 13.20692644 43.99999999 52.54942177 129.3935728 -1.982120038 0.72753665 33.264 17.5228 8.31382 6.972071 31.7892 normal
40.41336566 -1.329412398 30.98276809 41.74277806 119.3356546 -6.173674823 0.456246663 27.1984 16.4107 7.95631 -11.376063 23.331 normal
48.80190855 18.01776202 51.99999999 30.78414653 139.1504066 10.44286169 0.10501352 26.1245 19.2659 8.31303 -22.690688 39.6096 normal
50.08615264 13.43004422 34.45754051 36.65610842 119.1346221 3.089484465 0.744332895 31.9991 15.1042 14.46625 -7.052293 15.9536 normal
64.26150724 14.49786554 43.90250363 49.76364169 115.3882683 5.951454368 0.033702747 32.2615 15.3692 16.31794 -4.179409 32.9659 normal
53.68337998 13.44702168 41.58429713 40.23635831 113.9137026 2.737035292 0.702208022 24.7795 11.4937 10.80051 -30.625194 41.901 normal
48.99595771 13.11382047 51.87351997 35.88213725 126.3981876 0.535471617 0.732730192 33.7477 7.5426 15.7409 -6.421289 11.9857 normal
59.16761171 14.56274875 43.19915768 44.60486296 121.0356423 2.830504124 0.693905676 24.8746 14.7433 8.02792 -33.650471 16.7094 normal
67.80469442 16.55066167 43.25680184 51.25403274 119.6856451 4.867539941 0.03615827 18.4894 15.4016 13.86568 -17.473008 39.3526 normal
61.73487533 17.11431203 46.89999999 44.6205633 120.9201997 3.087725997 0.455056082 8.866 14.9831 8.27541 -0.48876 24.9564 normal
33.04168754 -0.324678459 19.0710746 33.366366 120.3886112 9.354364925 0.167308823 17.196 11.2466 9.14463 -29.11456 40.9249 normal
74.56501543 15.72431994 58.61858244 58.84069549 105.417304 0.599247113 0.117780016 18.0547 15.6236 10.54562 -32.494544 16.6229 normal
44.43070103 14.17426387 32.2434952 30.25643716 131.7176127 -3.604255336 0.126792054 15.1269 7.9912 12.23055 -26.340144 32.3929 normal
36.42248549 13.87942449 20.24256187 22.543061 126.0768612 0.179717077 0.686409465 8.3909 10.87 7.27404 -26.195988 21.8465 normal
51.07983294 14.20993529 35.95122893 36.86989765 115.8037111 6.905089963 0.705725568 24.1378 12.6652 13.92353 -3.478546 28.7425 normal
34.75673809 2.631739646 29.50438112 32.12499844 127.1398495 -0.460894198 0.281611979 24.1257 11.2762 11.54866 -12.02522 44.3412 normal
48.90290434 5.587588658 55.49999999 43.31531568 137.1082886 19.85475919 0.215175297 29.8825 9.9608 10.86798 1.956131 23.7274 normal
46.23639915 10.0627701 37 36.17362905 128.0636203 -5.100053328 0.860783838 9.5912 15.1769 16.49989 -22.420021 40.2061 normal
46.42636614 6.620795049 48.09999999 39.80557109 130.3500956 2.449382401 0.515439224 9.1955 10.6369 15.11344 2.963625 23.0719 normal
39.65690201 16.20883944 36.67485694 23.44806258 131.922009 -4.968979881 0.794716755 31.3737 18.3533 13.16102 -6.652617 26.3297 normal
45.57548229 18.75913544 33.77414297 26.81634684 116.7970069 3.131909921 0.514212483 24.2526 12.9572 12.40401 -12.363109 31.9668 normal
66.50717865 20.89767207 31.72747138 45.60950658 128.9029049 1.517203356 0.787252431 12.8877 11.8978 9.2322 -14.824364 43.8409 normal
82.90535054 29.89411893 58.25054221 53.01123161 110.7089577 6.079337831 0.827146263 12.5622 12.3646 16.61754 -15.758791 35.9458 normal
50.67667667 6.461501271 35 44.2151754 116.5879699 -0.214710615 0.021178285 18.7846 8.007 9.74352 -1.228604 14.2547 normal
89.01487529 26.07598143 69.02125897 62.93889386 111.4810746 6.061508401 0.544504889 27.0219 13.3731 11.04819 -3.5053 33.4196 normal
54.60031622 21.48897426 29.36021618 33.11134196 118.3433212 -1.471067262 0.962907494 30.8554 11.4198 13.82322 -5.606449 18.5514 normal
34.38229939 2.062682882 32.39081996 32.31961651 128.3001991 -3.365515555 0.581168695 12.0774 16.6255 7.20496 -31.374823 29.5748 normal
45.07545026 12.30695118 44.58317718 32.76849908 147.8946372 -8.941709421 0.932921843 32.1169 14.3037 10.64326 -31.198847 11.2307 normal
47.90356517 13.61668819 36 34.28687698 117.4490622 -4.245395422 0.129744031 7.8433 14.7484 8.51707 -15.728927 11.5472 normal
53.93674778 20.72149628 29.22053381 33.21525149 114.365845 -0.421010392 0.047913469 19.1986 18.1972 7.08745 6.013843 43.8693 normal
61.44659663 22.6949683 46.17034732 38.75162833 125.6707246 -2.707879517 0.081070436 16.2059 13.5565 8.89572 3.564463 18.4151 normal
45.25279209 8.693157364 41.5831264 36.55963472 118.5458418 0.214750167 0.159250601 14.7334 16.0928 9.75922 5.767308 33.7192 normal
33.84164075 5.073991409 36.64123294 28.76764934 123.9452436 -0.199249089 0.674504089 19.3825 17.6963 13.72929 1.783007 40.6049 normal
A partir desses dados a coluna do paciente era classificada como normal ou anormal. O dataset não especifica as enfermidades de coluna que foram consideradas mas aqui foi feito um resumo das prováveis condições que foram consideradas baseando-se nos dados informados.

Hiperlordoses / Hipercifoses
ou
Hipolordoses / Hipocifoses

As hiperlordoses e hipercifoses são caracterizadas por um aumento de uma ou mais lordose ou cifose da coluna. As hipolordoses e hipocifoses são caracterizadas por uma diminuição de uma ou mais lordose ou cifose da coluna.



Escoliose

A escoliose é uma curvatura anormal da coluna para um dos lados do tronco, podendo causar assimetria e dor.



Espondilolistese

Distúrbio da coluna em que um osso (vértebra) desliza para frente sobre o osso abaixo dele.

Sobre os Algoritmos



O dataset processado foi submetido a algoritmos de árvore de decisão.
Foram utilizados os algoritmos J48 do Weka e o Simple CART do Weka.
O dataset foi processado de diferentes formas para a verificação das
melhores condições para a criação da melhor árvore de decisão.
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Weka J48

O algoritmo J48, desenvolvido por Ross Quinlan, constrói árvores de decisão a partir de um conjunto de dados de treinamento. As árvores de decisão geradas pelo algoritmo podem ser utilizadas para classificação, logo são conhecidas como classificadores estatísticos. A direita é mostrado o output do algoritmo quando este é rodado sobre todos os dados, com os parâmetros tal, tal e tal. A esquerda estão sendo usados os mesmos parâmetros, só que alguma coisa foi alterada.

J48 pruned tree com todos os atributos photo_size_select_actualVer

=== Run information === Scheme: weka.classifiers.trees.J48 -C 0.25 -M 2 Relation: dataset-coluna Instances: 310 Attributes: 13 pelvic_incidence pelvic_tilt lumbar_lordosis_angle sacral_slope pelvic_radius degree_spondylolisthesis pelvic_slope direct_tilt thoracic_slope cervical_tilt sacrum_angle scoliosis_slope class_att Test mode: 10-fold cross-validation === Classifier model (full training set) === J48 pruned tree ------------------ degree_spondylolisthesis <= 19.854759 | pelvic_radius <= 125.212716 | | sacral_slope <= 40.475232 | | | sacrum_angle <= 4.894807: Abnormal (71.0/20.0) | | | sacrum_angle > 4.894807: Normal (5.0) | | sacral_slope > 40.475232 | | | degree_spondylolisthesis <= 9.064582 | | | | pelvic_tilt <= 18.898407: Normal (20.0) | | | | pelvic_tilt > 18.898407 | | | | | lumbar_lordosis_angle <= 56.3 | | | | | | scoliosis_slope <= 28.3449: Abnormal (4.0) | | | | | | scoliosis_slope > 28.3449: Normal (2.0) | | | | | lumbar_lordosis_angle > 56.3: Normal (5.0) | | | degree_spondylolisthesis > 9.064582: Abnormal (6.0/1.0) | pelvic_radius > 125.212716: Normal (52.0/7.0) degree_spondylolisthesis > 19.854759: Abnormal (145.0/2.0) Number of Leaves : 9 Size of the tree : 17 Time taken to build model: 0.01 seconds === Stratified cross-validation === === Summary === Correctly Classified Instances 253 81.6129 % Incorrectly Classified Instances 57 18.3871 % Kappa statistic 0.5597 Mean absolute error 0.2071 Root mean squared error 0.3912 Relative absolute error 47.331 % Root relative squared error 83.6934 % Total Number of Instances 310 === Detailed Accuracy By Class === TP Rate FP Rate Precision Recall F-Measure MCC ROC Area PRC Area Class 0.905 0.370 0.837 0.905 0.870 0.565 0.816 0.844 Abnormal 0.630 0.095 0.759 0.630 0.689 0.565 0.816 0.690 Normal Weighted Avg. 0.816 0.281 0.812 0.816 0.811 0.565 0.816 0.794 === Confusion Matrix === a b <-- classified as 190 20 | a = Abnormal 37 63 | b = Normal

J48 unpruned tree com todos os atributos photo_size_select_actualVer

=== Run information === Scheme: weka.classifiers.trees.J48 -U -M 2 Relation: dataset-coluna Instances: 310 Attributes: 13 pelvic_incidence pelvic_tilt lumbar_lordosis_angle sacral_slope pelvic_radius degree_spondylolisthesis pelvic_slope direct_tilt thoracic_slope cervical_tilt sacrum_angle scoliosis_slope class_att Test mode: 10-fold cross-validation === Classifier model (full training set) === J48 unpruned tree ------------------ degree_spondylolisthesis <= 19.854759 | pelvic_radius <= 125.212716 | | sacral_slope <= 40.475232 | | | sacrum_angle <= 4.894807: Abnormal (71.0/20.0) | | | sacrum_angle > 4.894807: Normal (5.0) | | sacral_slope > 40.475232 | | | degree_spondylolisthesis <= 9.064582 | | | | pelvic_tilt <= 18.898407: Normal (20.0) | | | | pelvic_tilt > 18.898407 | | | | | lumbar_lordosis_angle <= 56.3 | | | | | | scoliosis_slope <= 28.3449: Abnormal (4.0) | | | | | | scoliosis_slope > 28.3449: Normal (2.0) | | | | | lumbar_lordosis_angle > 56.3: Normal (5.0) | | | degree_spondylolisthesis > 9.064582: Abnormal (6.0/1.0) | pelvic_radius > 125.212716: Normal (52.0/7.0) degree_spondylolisthesis > 19.854759: Abnormal (145.0/2.0) Number of Leaves : 9 Size of the tree : 17 Time taken to build model: 0 seconds === Stratified cross-validation === === Summary === Correctly Classified Instances 252 81.2903 % Incorrectly Classified Instances 58 18.7097 % Kappa statistic 0.5532 Mean absolute error 0.2061 Root mean squared error 0.3891 Relative absolute error 47.0987 % Root relative squared error 83.2325 % Total Number of Instances 310 === Detailed Accuracy By Class === TP Rate FP Rate Precision Recall F-Measure MCC ROC Area PRC Area Class 0.900 0.370 0.836 0.900 0.867 0.557 0.816 0.843 Abnormal 0.630 0.100 0.750 0.630 0.685 0.557 0.816 0.690 Normal Weighted Avg. 0.813 0.283 0.808 0.813 0.808 0.557 0.816 0.794 === Confusion Matrix === a b <-- classified as 189 21 | a = Abnormal 37 63 | b = Normal











J48 pruned tree com atributos selecionados photo_size_select_actualVer

=== Run information === Scheme: weka.classifiers.trees.J48 -C 0.25 -M 2 Relation: dataset-coluna-weka.filters.unsupervised.attribute.Remove-R1-3-weka.filters.unsupervised.attribute.Remove-R4-9 Instances: 310 Attributes: 4 sacral_slope pelvic_radius degree_spondylolisthesis class_att Test mode: 10-fold cross-validation === Classifier model (full training set) === J48 pruned tree ------------------ degree_spondylolisthesis <= 19.854759 | pelvic_radius <= 125.212716 | | sacral_slope <= 40.475232: Abnormal (76.0/25.0) | | sacral_slope > 40.475232 | | | degree_spondylolisthesis <= 9.064582: Normal (31.0/4.0) | | | degree_spondylolisthesis > 9.064582: Abnormal (6.0/1.0) | pelvic_radius > 125.212716: Normal (52.0/7.0) degree_spondylolisthesis > 19.854759: Abnormal (145.0/2.0) Number of Leaves : 5 Size of the tree : 9 Time taken to build model: 0 seconds === Stratified cross-validation === === Summary === Correctly Classified Instances 257 82.9032 % Incorrectly Classified Instances 53 17.0968 % Kappa statistic 0.595 Mean absolute error 0.2083 Root mean squared error 0.3495 Relative absolute error 47.607 % Root relative squared error 74.7756 % Total Number of Instances 310 === Detailed Accuracy By Class === TP Rate FP Rate Precision Recall F-Measure MCC ROC Area PRC Area Class 0.905 0.330 0.852 0.905 0.878 0.598 0.878 0.928 Abnormal 0.670 0.095 0.770 0.670 0.717 0.598 0.878 0.721 Normal Weighted Avg. 0.829 0.254 0.826 0.829 0.826 0.598 0.878 0.861 === Confusion Matrix === a b <-- classified as 190 20 | a = Abnormal 33 67 | b = Normal

J48 unpruned tree com atributos selecionados photo_size_select_actualVer

=== Run information === Scheme: weka.classifiers.trees.J48 -U -M 2 Relation: dataset-coluna-weka.filters.unsupervised.attribute.Remove-R1-3-weka.filters.unsupervised.attribute.Remove-R4-9 Instances: 310 Attributes: 4 sacral_slope pelvic_radius degree_spondylolisthesis class_att Test mode: 10-fold cross-validation === Classifier model (full training set) === J48 unpruned tree ------------------ degree_spondylolisthesis <= 19.854759 | pelvic_radius <= 125.212716 | | sacral_slope <= 40.475232: Abnormal (76.0/25.0) | | sacral_slope > 40.475232 | | | degree_spondylolisthesis <= 9.064582: Normal (31.0/4.0) | | | degree_spondylolisthesis > 9.064582: Abnormal (6.0/1.0) | pelvic_radius > 125.212716: Normal (52.0/7.0) degree_spondylolisthesis > 19.854759: Abnormal (145.0/2.0) Number of Leaves : 5 Size of the tree : 9 Time taken to build model: 0 seconds === Stratified cross-validation === === Summary === Correctly Classified Instances 257 82.9032 % Incorrectly Classified Instances 53 17.0968 % Kappa statistic 0.595 Mean absolute error 0.2089 Root mean squared error 0.35 Relative absolute error 47.7606 % Root relative squared error 74.8698 % Total Number of Instances 310 === Detailed Accuracy By Class === TP Rate FP Rate Precision Recall F-Measure MCC ROC Area PRC Area Class 0.905 0.330 0.852 0.905 0.878 0.598 0.878 0.928 Abnormal 0.670 0.095 0.770 0.670 0.717 0.598 0.878 0.721 Normal Weighted Avg. 0.829 0.254 0.826 0.829 0.826 0.598 0.878 0.861 === Confusion Matrix === a b <-- classified as 190 20 | a = Abnormal 33 67 | b = Normal

Como é possível visualizar, o maior valor médio de precisão foi o encontrado nas árvores com atributos selecinados (as duas últimas) É provavel que isso se dê pois quando os atributos excedentes são excluídos a árvore de decisão é menor e o problema de overfitting é menor. Nas duas últimas árvores tanto pruned quanto unpruned obtiveram o mesmo valor, provavelmente por possuírem um número de ramificações limitados a "poda" não chegou a ser necessária.

Gini

O algoritmo CART utiliza a medida Gini, um índice de dispersão estatístico proposto em 1912 pelo estatístico italiano Corrado Gini. Este índice é muito utilizado em análises econômicas e sociais, por exemplo, para quantificar a distribuição de renda em um certo país.
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Weka Simple Cart

CART ou Classification And Regression Tree (árvore de classificação e regressão) é um algoritmo usado na mineração de dados que usa dois conceitos principais: A análise da árvore de classificação é feita quando o resultado previsto é a classe à qual os dados pertencem. A análise de árvore de regressão é quando o resultado previsto pode ser considerado um número real (por exemplo, o preço de uma casa ou o tempo de permanência de um paciente em um hospital). Esse algoritmo usa a métrica de Gini para dividir as categorias em grupos separados.

Simple Cart pruned tree com todos os atributos

=== Run information === Scheme: weka.classifiers.trees.SimpleCart -M 2.0 -N 5 -C 1.0 -S 1 Relation: dataset-coluna Instances: 310 Attributes: 13 pelvic_incidence pelvic_tilt lumbar_lordosis_angle sacral_slope pelvic_radius degree_spondylolisthesis pelvic_slope direct_tilt thoracic_slope cervical_tilt sacrum_angle scoliosis_slope class_att Test mode: 10-fold cross-validation === Classifier model (full training set) === CART Decision Tree degree_spondylolisthesis < 14.85401384 | pelvic_radius < 125.30192704999999 | | sacral_slope < 40.56599579 | | | sacrum_angle < 4.968382: Abnormal(50.0/20.0) | | | sacrum_angle >= 4.968382: Normal(5.0/0.0) | | sacral_slope >= 40.56599579: Normal(28.0/8.0) | pelvic_radius >= 125.30192704999999: Normal(44.0/6.0) degree_spondylolisthesis >= 14.85401384: Abnormal(146.0/3.0) Number of Leaf Nodes: 5 Size of the Tree: 9 Time taken to build model: 0.03 seconds === Stratified cross-validation === === Summary === Correctly Classified Instances 258 83.2258 % Incorrectly Classified Instances 52 16.7742 % Kappa statistic 0.6121 Mean absolute error 0.2176 Root mean squared error 0.3561 Relative absolute error 49.7267 % Root relative squared error 76.1705 % Total Number of Instances 310 === Detailed Accuracy By Class === TP Rate FP Rate Precision Recall F-Measure MCC ROC Area PRC Area Class 0.886 0.280 0.869 0.886 0.877 0.612 0.877 0.930 Abnormal 0.720 0.114 0.750 0.720 0.735 0.612 0.877 0.684 Normal Weighted Avg. 0.832 0.227 0.831 0.832 0.831 0.612 0.877 0.850 === Confusion Matrix === a b <-- classified as 186 24 | a = Abnormal 28 72 | b = Normal

Simple Cart unpruned tree com todos os atributos

=== Run information === Scheme: weka.classifiers.trees.SimpleCart -M 2.0 -N 5 -U -C 1.0 -S 1 Relation: dataset-coluna Instances: 310 Attributes: 13 pelvic_incidence pelvic_tilt lumbar_lordosis_angle sacral_slope pelvic_radius degree_spondylolisthesis pelvic_slope direct_tilt thoracic_slope cervical_tilt sacrum_angle scoliosis_slope class_att Test mode: 10-fold cross-validation === Classifier model (full training set) === CART Decision Tree degree_spondylolisthesis < 14.85401384 | pelvic_radius < 125.30192704999999 | | sacral_slope < 40.56599579 | | | sacrum_angle < 4.968382 | | | | sacrum_angle < -26.7661665 | | | | | degree_spondylolisthesis < 0.7433087965: Abnormal(2.0/0.0) | | | | | degree_spondylolisthesis >= 0.7433087965 | | | | | | thoracic_slope < 18.41905: Normal(8.0/1.0) | | | | | | thoracic_slope >= 18.41905: Abnormal(2.0/0.0) | | | | sacrum_angle >= -26.7661665 | | | | | sacrum_angle < -16.0536515: Abnormal(23.0/0.0) | | | | | sacrum_angle >= -16.0536515 | | | | | | pelvic_tilt < 10.958787335 | | | | | | | pelvic_radius < 114.66567725: Abnormal(2.0/0.0) | | | | | | | pelvic_radius >= 114.66567725: Normal(6.0/0.0) | | | | | | pelvic_tilt >= 10.958787335 | | | | | | | sacrum_angle < -5.1851815 | | | | | | | | pelvic_incidence < 43.128503245000005: Abnormal(3.0/0.0) | | | | | | | | pelvic_incidence >= 43.128503245000005: Normal(5.0/1.0) | | | | | | | sacrum_angle >= -5.1851815 | | | | | | | | sacral_slope < 36.767766565: Abnormal(15.0/0.0) | | | | | | | | sacral_slope >= 36.767766565: Abnormal(1.0/1.0) | | | sacrum_angle >= 4.968382: Normal(5.0/0.0) | | sacral_slope >= 40.56599579 | | | degree_spondylolisthesis < 9.333633029000001 | | | | pelvic_tilt < 18.922291485000002: Normal(20.0/0.0) | | | | pelvic_tilt >= 18.922291485000002 | | | | | lumbar_lordosis_angle < 56.401487939999996 | | | | | | scoliosis_slope < 28.4339: Abnormal(4.0/0.0) | | | | | | scoliosis_slope >= 28.4339: Normal(2.0/0.0) | | | | | lumbar_lordosis_angle >= 56.401487939999996: Normal(5.0/0.0) | | | degree_spondylolisthesis >= 9.333633029000001: Abnormal(4.0/1.0) | pelvic_radius >= 125.30192704999999 | | sacral_slope < 28.136471795 | | | sacral_slope < 24.274835645 | | | | pelvic_tilt < 18.20377501: Normal(4.0/0.0) | | | | pelvic_tilt >= 18.20377501: Abnormal(2.0/0.0) | | | sacral_slope >= 24.274835645: Abnormal(3.0/0.0) | | sacral_slope >= 28.136471795 | | | sacral_slope < 29.929307225000002: Normal(3.0/1.0) | | | sacral_slope >= 29.929307225000002: Normal(37.0/0.0) degree_spondylolisthesis >= 14.85401384 | degree_spondylolisthesis < 20.085037255: Abnormal(3.0/1.0) | degree_spondylolisthesis >= 20.085037255 | | cervical_tilt < 16.24324: Abnormal(129.0/0.0) | | cervical_tilt >= 16.24324: Abnormal(14.0/2.0) Number of Leaf Nodes: 24 Size of the Tree: 47 Time taken to build model: 0.01 seconds === Stratified cross-validation === === Summary === Correctly Classified Instances 248 80 % Incorrectly Classified Instances 62 20 % Kappa statistic 0.5471 Mean absolute error 0.2088 Root mean squared error 0.4251 Relative absolute error 47.7207 % Root relative squared error 90.9431 % Total Number of Instances 310 === Detailed Accuracy By Class === TP Rate FP Rate Precision Recall F-Measure MCC ROC Area PRC Area Class 0.843 0.290 0.859 0.843 0.851 0.547 0.798 0.858 Abnormal 0.710 0.157 0.683 0.710 0.696 0.547 0.798 0.600 Normal Weighted Avg. 0.800 0.247 0.802 0.800 0.801 0.547 0.798 0.774 === Confusion Matrix === a b <-- classified as 177 33 | a = Abnormal 29 71 | b = Normal











Simple Cart pruned tree com atributos selecionados

=== Run information === Scheme: weka.classifiers.trees.SimpleCart -M 2.0 -N 5 -C 1.0 -S 1 Relation: dataset-coluna-weka.filters.unsupervised.attribute.Remove-R1-3-weka.filters.unsupervised.attribute.Remove-R4-9 Instances: 310 Attributes: 4 sacral_slope pelvic_radius degree_spondylolisthesis class_att Test mode: 10-fold cross-validation === Classifier model (full training set) === CART Decision Tree degree_spondylolisthesis < 14.85401384 | pelvic_radius < 125.30192704999999 | | sacral_slope < 40.56599579: Abnormal(50.0/25.0) | | sacral_slope >= 40.56599579 | | | degree_spondylolisthesis < 9.333633029000001: Normal(27.0/4.0) | | | degree_spondylolisthesis >= 9.333633029000001: Abnormal(4.0/1.0) | pelvic_radius >= 125.30192704999999: Normal(44.0/6.0) degree_spondylolisthesis >= 14.85401384: Abnormal(146.0/3.0) Number of Leaf Nodes: 5 Size of the Tree: 9 Time taken to build model: 0.01 seconds === Stratified cross-validation === === Summary === Correctly Classified Instances 256 82.5806 % Incorrectly Classified Instances 54 17.4194 % Kappa statistic 0.5929 Mean absolute error 0.2056 Root mean squared error 0.3712 Relative absolute error 46.9934 % Root relative squared error 79.4114 % Total Number of Instances 310 === Detailed Accuracy By Class === TP Rate FP Rate Precision Recall F-Measure MCC ROC Area PRC Area Class 0.890 0.310 0.858 0.890 0.874 0.594 0.846 0.871 Abnormal 0.690 0.110 0.750 0.690 0.719 0.594 0.846 0.711 Normal Weighted Avg. 0.826 0.245 0.823 0.826 0.824 0.594 0.846 0.820 === Confusion Matrix === a b <-- classified as 187 23 | a = Abnormal 31 69 | b = Normal

Simple Cart unpruned tree com atributos selecionados

=== Run information === Scheme: weka.classifiers.trees.SimpleCart -M 2.0 -N 5 -U -C 1.0 -S 1 Relation: dataset-coluna-weka.filters.unsupervised.attribute.Remove-R1-3-weka.filters.unsupervised.attribute.Remove-R4-9 Instances: 310 Attributes: 4 sacral_slope pelvic_radius degree_spondylolisthesis class_att Test mode: 10-fold cross-validation === Classifier model (full training set) === CART Decision Tree degree_spondylolisthesis < 14.85401384 | pelvic_radius < 125.30192704999999 | | sacral_slope < 40.56599579 | | | pelvic_radius < 113.5225841 | | | | sacral_slope < 37.32456687: Abnormal(13.0/0.0) | | | | sacral_slope >= 37.32456687: Abnormal(2.0/1.0) | | | pelvic_radius >= 113.5225841 | | | | sacral_slope < 29.61038515 | | | | | degree_spondylolisthesis < 6.924067247: Abnormal(18.0/4.0) | | | | | degree_spondylolisthesis >= 6.924067247: Normal(2.0/1.0) | | | | sacral_slope >= 29.61038515 | | | | | pelvic_radius < 123.9299325 | | | | | | pelvic_radius < 117.35956485 | | | | | | | pelvic_radius < 115.84036425 | | | | | | | | sacral_slope < 37.45847009: Normal(3.0/0.0) | | | | | | | | sacral_slope >= 37.45847009: Abnormal(2.0/1.0) | | | | | | | pelvic_radius >= 115.84036425 | | | | | | | | sacral_slope < 32.96135438: Abnormal(1.0/1.0) | | | | | | | | sacral_slope >= 32.96135438: Abnormal(5.0/0.0) | | | | | | pelvic_radius >= 117.35956485 | | | | | | | sacral_slope < 37.112350225: Normal(12.0/2.0) | | | | | | | sacral_slope >= 37.112350225: Abnormal(2.0/1.0) | | | | | pelvic_radius >= 123.9299325: Abnormal(4.0/0.0) | | sacral_slope >= 40.56599579 | | | degree_spondylolisthesis < 9.333633029000001 | | | | pelvic_radius < 114.80064045 | | | | | sacral_slope < 47.148657045 | | | | | | pelvic_radius < 112.68771509999999: Abnormal(2.0/0.0) | | | | | | pelvic_radius >= 112.68771509999999: Normal(2.0/1.0) | | | | | sacral_slope >= 47.148657045: Normal(8.0/1.0) | | | | pelvic_radius >= 114.80064045: Normal(17.0/0.0) | | | degree_spondylolisthesis >= 9.333633029000001: Abnormal(4.0/1.0) | pelvic_radius >= 125.30192704999999 | | sacral_slope < 28.136471795 | | | sacral_slope < 24.274835645 | | | | sacral_slope < 20.995261765000002: Abnormal(2.0/1.0) | | | | sacral_slope >= 20.995261765000002: Normal(3.0/0.0) | | | sacral_slope >= 24.274835645: Abnormal(3.0/0.0) | | sacral_slope >= 28.136471795 | | | sacral_slope < 29.929307225000002: Normal(3.0/1.0) | | | sacral_slope >= 29.929307225000002: Normal(37.0/0.0) degree_spondylolisthesis >= 14.85401384 | degree_spondylolisthesis < 20.085037255: Abnormal(3.0/1.0) | degree_spondylolisthesis >= 20.085037255 | | degree_spondylolisthesis < 31.24958925: Abnormal(33.0/2.0) | | degree_spondylolisthesis >= 31.24958925: Abnormal(110.0/0.0) Number of Leaf Nodes: 24 Size of the Tree: 47 Time taken to build model: 0 seconds === Stratified cross-validation === === Summary === Correctly Classified Instances 260 83.871 % Incorrectly Classified Instances 50 16.129 % Kappa statistic 0.621 Mean absolute error 0.1755 Root mean squared error 0.3744 Relative absolute error 40.1157 % Root relative squared error 80.0936 % Total Number of Instances 310 === Detailed Accuracy By Class === TP Rate FP Rate Precision Recall F-Measure MCC ROC Area PRC Area Class 0.905 0.300 0.864 0.905 0.884 0.623 0.850 0.888 Abnormal 0.700 0.095 0.778 0.700 0.737 0.623 0.850 0.710 Normal Weighted Avg. 0.839 0.234 0.836 0.839 0.836 0.623 0.850 0.831 === Confusion Matrix === a b <-- classified as 190 20 | a = Abnormal 30 70 | b = Normal

Como é possível visualizar, o maior valor médio de precisão foi o encontrado na árvore unpruned com atributos selecinados seguido de perto pela árvore pruned com todos os atributos. A justificativa continua sendo parecida com a apresentada para o J48 já que árvores menores sofrem menos com o overfitting, então tanto a podada com todas as variáveis quanto a que não tinha tantas variáveis e não foi podada eram compostas por árvores bem enxutas, o que explica por que a precisão ficou um pouco maior.

Discussão

Comparando os resultados obtidos pelo J48 e pelo Simple Cart
é possível visualizar que a diferença na precisão é muito pequena.
Os dois maiores valores de precisão (836 e 831) foram obtidos com
o simple cart indicando que esse algoritmo seja teve um desempenho
levemente melhor para esse conjunto de dados.
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