Aprendizaje no supervisado

María Paula Bravo
Elian Hernández Morales
Maria Renata Schuppel
Thomas Santiago Lopez

Introducción

El aprendizaje No-Supervisado es la tarea encargada de encontrar patrones de estructuras en un conjunto de datos, que a priori son desconocidos. La idea principal consiste en generar agrupaciones por clusters, que representen homogeneidad.

Existen diversos métodos de aplicar aprendizaje no supervisado, los más populares son los siguientes:

  • KNN (vecinos más cercanos)

  • Agrupación jerárquica

  • Redes neuronales

  • Análisis de Componentes Principales (APC)

  • Analisis de Componentes Independientes (ACI)

  • Detección de anomalías

  • Clusterización

Metodología

Para el desarrollo del estudio fue necesario utilizar las siguientes técnicas:

  • Análisis de Componenetes Principales (ACP): Se basa en transformar un conjunto de variables, a las que se denominan variables originales, en un nuevo conjunto de variables denominadas componentes principales. Estas últimas se caracterizan por estar no correlacionadas entre sí.

  • Clusterización: Tiene como fin clasificar determinada cantidad de observaciones con ciertos caracteristicas, como que exista homogeneidad entre los datos en cada grupo y que la relación entre los grupos sea lo menor posible.

Datos

A.ELEC A.ELEC.RUR A.CL.TEC AIR.TR EL.PO.CO EM EX EXP FE.RA FO.AR GDP INF LIFE.EXP MOR.RA.M MOR.RA.H PO
Albania 100.00000 100.000000 73.15 865848.0 2533.25283 1.7386210 24.160773 28.916315 1.697 28.6985584 1.0020175 1.9376208 78.12300 49.424 93.142 2895092
Armenia 99.42000 99.437149 97.50 45000.0 1928.73404 0.4622048 22.637182 28.353485 1.600 11.5889006 3.3000000 5.7896678 73.67600 72.570 194.234 2901385
Australia 100.00000 100.000000 100.00 68197955.0 10220.88730 6.3144580 25.893428 19.985708 1.855 17.1400674 2.5787543 2.4498886 82.14878 45.018 75.516 23128129
Austria 100.00000 100.000000 100.00 15037454.0 8509.61158 4.4855900 46.621622 53.441293 1.440 46.9461222 0.0255047 2.0001562 81.13659 45.326 89.369 8479823
Azerbaijan 100.00000 100.000000 95.20 1651710.0 2092.53652 10.0780200 20.925544 48.415833 1.980 12.8205035 5.8098008 2.4157175 70.88100 95.575 198.338 9416801
Bangladesh 61.50000 48.587765 15.80 2781708.0 299.48035 0.7874798 9.507120 19.537874 2.184 14.4839579 6.0136057 7.5304064 69.56500 112.607 193.102 154030139
Belarus 100.00000 100.000000 99.10 1159500.0 3657.12468 0.8015825 28.254697 58.333578 1.668 42.5419402 1.0034708 18.3122610 72.47073 95.272 273.671 9443211
Belgium 100.00000 100.000000 100.00 9521421.0 7989.67185 4.2991340 45.542074 79.324348 1.760 22.7717305 0.4592422 1.1130959 80.58780 57.509 94.410 11159407
Bosnia and Herzegovina 99.50000 100.000000 44.20 15000.0 3402.29420 4.9467770 37.365558 33.743047 1.276 41.7453906 2.3498567 -0.0930457 76.33000 58.445 117.110 3617559
Botswana 57.99192 25.996208 60.80 270996.0 1978.10108 2.4486210 29.485975 61.379762 2.964 28.3782401 11.1028238 5.8846071 61.99600 276.868 389.904 2217278
Brazil 99.57515 97.502037 95.00 95591641.0 2560.09556 4.1203680 30.836338 11.742231 1.748 60.6550213 3.0048227 6.2043107 73.91800 89.138 184.185 201721767
Bulgaria 100.00000 100.000000 87.71 1013220.0 4639.70632 3.9201340 32.955537 64.581696 1.480 34.9539425 -0.5604940 0.8900935 74.86098 82.085 184.811 7265115
Cambodia 57.57370 47.412548 16.20 615123.3 221.93802 0.1621311 11.861371 62.387936 2.620 54.0663041 7.3566651 2.9416251 69.30400 142.717 211.913 14999683
Cameroon 56.20781 19.195698 21.40 287208.0 257.38634 2.9864490 12.935409 23.639109 4.914 43.8587718 4.9955292 2.0503472 58.47600 295.688 339.178 21632850
Canada 100.00000 100.000000 100.00 71526725.9 15750.81163 4.7293450 17.084882 30.331939 1.610 38.7256511 2.3291225 0.9382919 81.74488 50.975 81.208 35082954
Chile 99.60000 100.000000 100.00 13806283.0 3893.50611 4.2738600 20.196301 32.087464 1.786 23.1970541 3.3085082 1.7895555 79.33900 62.354 112.222 17509925
Colombia 97.77942 90.073769 88.45 26929238.0 1317.96557 4.6761330 33.285193 18.086440 1.905 54.4424624 5.1339935 2.0169922 75.82700 74.943 151.666 46237930
Congo, Rep. 42.54397 10.660739 21.80 652452.0 204.01544 1.0963820 10.876954 52.934341 4.691 64.5358712 -0.7124345 4.6316162 62.69500 269.144 306.870 4828066
Costa Rica 99.56351 98.436027 93.60 1498996.0 1919.84406 3.2624070 26.517740 30.591649 1.838 57.1934587 2.4947661 5.2313361 79.40300 55.171 107.356 4791535
Cote d'Ivoire 61.36259 34.323063 20.60 234996.0 229.20195 0.8713149 9.930602 29.160403 4.920 11.4054151 10.7602131 2.5811704 56.74800 362.679 376.871 22469268
Croatia 100.00000 100.000000 100.00 1716702.0 3754.26870 4.3870210 41.465264 39.759333 1.460 34.3292116 -0.3978277 2.2165821 77.12683 50.612 125.021 4255689
Cyprus 100.00000 100.000000 100.00 1211208.0 3516.80595 4.0395980 42.331228 61.296590 1.305 18.6971861 -6.5874823 -0.3993577 80.40200 47.827 80.092 1166968
Czechia 100.00000 100.000000 100.00 5186676.0 6284.79081 3.3626310 34.734025 76.058382 1.460 34.4986532 -0.0459037 1.4382979 78.17561 56.750 120.745 10514272
Dominican Republic 98.38586 93.441986 88.20 20004.0 1535.09124 4.0844650 15.453339 25.167159 2.466 43.2920306 4.8752051 4.8309510 72.71300 104.449 198.442 10157051
Egypt, Arab Rep. 99.85039 99.826103 99.70 10593780.2 1595.17419 12.5586900 32.201731 17.017846 3.419 0.0555608 2.1854661 9.4697198 70.05200 119.806 215.247 93377890
El Salvador 95.04311 89.257606 82.10 2509003.0 971.44322 4.2887920 22.995813 29.724896 2.154 29.6998069 2.2356244 0.7576692 71.77100 114.784 276.703 6185642
Estonia 100.00000 100.000000 100.00 627588.0 6664.65857 3.7693270 34.225445 84.568170 1.520 54.9117552 1.4584286 2.7805666 77.14146 67.015 169.327 1317997
Ethiopia 30.67167 17.626913 3.20 5671501.0 62.93495 0.5011358 10.211914 12.484074 4.724 15.5767636 10.5822700 7.4640219 62.37300 212.412 286.512 97084366
Finland 100.00000 100.000000 100.00 10467321.0 15510.83550 4.0158280 40.089859 38.017629 1.750 73.5206818 -0.9016963 1.4782862 80.97561 48.344 104.868 5438972
France 100.00000 100.000000 100.00 63925151.0 7367.44145 4.2992330 48.119370 29.364738 1.990 30.4428580 0.5763267 0.8637155 82.21951 50.507 105.322 66002289
Gabon 86.40000 32.792557 83.60 0.0 1031.42319 2.6161740 16.330782 57.357406 4.019 91.6434354 5.6386990 0.5054411 64.77600 208.763 287.784 1902226
Georgia 100.00000 100.000000 74.10 189316.0 2498.34036 1.3679350 25.070734 41.721954 2.017 40.6159160 3.6213054 -0.5120584 72.62800 78.977 236.467 3717668
Germany 100.00000 100.000000 100.00 109062321.5 7217.52909 4.7214380 28.546001 45.418678 1.420 32.7189865 0.4375913 1.5047233 80.49024 51.743 94.684 80645605
Ghana 70.70000 50.829639 19.60 396372.0 363.40720 5.3719940 19.281135 25.440783 4.136 34.7430606 7.3125250 11.6661923 62.42000 234.312 285.680 27525597
Greece 100.00000 100.000000 100.00 8761116.0 5028.99579 6.6541870 60.297064 30.207207 1.290 30.2700000 -2.5159972 -0.9212695 81.28537 38.036 95.259 10965211
Guatemala 87.96929 80.204193 40.20 78264.0 578.90262 2.7420290 13.033096 21.998155 3.151 33.9727510 3.6948192 4.3433713 71.72800 129.959 232.777 15043981
Honduras 87.18488 73.406059 44.50 372972.0 631.53851 12.7809500 23.893840 47.941490 2.699 58.1686120 2.7915598 5.1618990 71.96300 114.729 176.103 8960657
Hungary 100.00000 100.000000 100.00 13926540.0 3892.11370 5.2181380 46.932291 85.410822 1.350 22.7001878 1.8025221 1.7331998 75.56585 85.688 182.243 9893082
Iceland 100.00000 100.000000 100.00 2602714.0 54799.17471 4.1338140 34.659804 53.247751 1.930 0.4664738 4.5524603 3.8722792 82.06098 38.876 67.441 323764
India 81.99933 75.219864 41.60 75589071.0 758.11068 1.5880430 16.638683 25.430861 2.406 23.6430232 6.3861064 10.0178785 68.46000 142.920 214.491 1291132063
Indonesia 96.46426 92.994202 58.00 81721356.0 769.49677 3.4946860 15.375020 23.923576 2.427 51.6002341 5.5572637 6.4125133 69.26400 152.461 206.261 253275918
Ireland 100.00000 100.000000 100.00 93408036.0 5698.75618 4.6527840 38.353088 104.008518 1.930 10.7556104 1.1256896 0.5087149 80.94878 48.066 81.065 4623816
Israel 100.00000 100.000000 100.00 5565864.0 6710.09368 3.8630970 36.190993 33.236775 3.030 7.4214418 4.4155016 1.5762120 82.05610 41.393 75.007 8059500
Italy 100.00000 100.000000 100.00 27846220.0 5159.18365 6.9137680 43.710645 28.633243 1.390 31.0750918 -1.8410655 1.2199934 82.69024 38.636 67.898 60233948
Jamaica 93.90000 90.685432 86.00 46272.0 1044.30771 3.2499910 25.015986 30.575883 1.636 52.6182825 0.5176860 9.3415008 73.41200 116.674 143.705 2773129
Japan 100.00000 100.000000 100.00 107573000.0 7988.58331 2.2039810 18.140651 15.784157 1.430 68.4576132 2.0051002 0.3350379 83.33195 39.211 75.083 127445000
Jordan 99.70144 97.577934 99.90 3294911.0 2052.94111 5.3611040 26.240000 41.295603 3.436 1.0982203 2.6099474 4.8246231 74.56200 82.045 123.750 7694814
Kazakhstan 100.00000 100.000000 92.60 4785588.0 5345.46843 1.8504650 14.608982 38.617038 2.640 1.1919641 6.0000000 5.8464092 70.62000 120.979 285.972 17035551
Korea, Rep. 100.00000 100.000000 100.00 54530105.0 10384.62216 6.0606270 24.032610 51.292071 1.187 65.2495227 3.1647086 1.3013475 81.27073 29.503 80.300 50428893
Latvia 100.00000 100.000000 100.00 2754720.0 3472.54138 4.2002240 43.901878 60.395173 1.520 54.3769103 2.0079669 -0.0294548 73.98293 93.690 242.150 2012647
Lithuania 100.00000 100.000000 100.00 1009728.0 3663.67120 2.2010860 33.067322 78.668573 1.590 34.7857998 3.5500728 1.0474794 73.91463 91.556 265.849 2957689
Luxembourg 100.00000 100.000000 100.00 1555788.0 14193.16843 2.6745050 38.551525 176.383331 1.550 34.4538272 3.1717905 1.7340396 81.80000 52.429 80.788 543360
Malaysia 99.60445 98.751060 97.20 47995842.0 4420.46966 3.8677070 20.602120 75.629041 2.089 58.6138853 4.6937225 2.1050123 75.03500 83.541 161.236 30134807
Malta 100.00000 100.000000 100.00 1603404.0 4915.87376 4.3778250 39.611797 155.973465 1.360 1.0937500 5.4730579 1.1802844 81.74634 33.370 62.594 425967
Mauritius 99.48051 99.264267 97.10 1318052.0 2148.32841 3.6887980 21.585500 52.571070 1.440 18.8847291 3.3604061 3.5432957 74.01707 82.448 182.597 1258653
Moldova 100.00000 100.000000 93.80 557653.0 1683.47696 0.7281489 27.128270 32.092613 1.654 11.6070560 9.0438656 4.5978790 69.09900 124.700 303.294 2859558
Mongolia 81.20000 45.767261 40.80 585864.0 1918.35026 1.1479870 23.668820 38.890237 2.897 9.1061359 11.6489162 10.4906568 68.58500 136.525 305.241 2845153
Morocco 97.20000 94.977913 97.30 6507408.0 879.13903 2.6426620 27.843056 32.777644 2.594 12.7283038 4.5354242 1.8806547 72.12200 108.787 151.140 33803527
Myanmar 56.34927 42.515839 15.10 1572120.0 189.77919 2.8899020 14.902148 15.818134 2.256 46.8118209 7.8986695 5.6430388 64.81500 174.112 276.409 50648334
Namibia 47.40000 27.308245 43.00 510000.0 1714.66675 3.1744210 35.448430 37.501985 3.653 8.6676214 5.6147196 5.6009250 58.69400 363.641 505.335 2204510
Nepal 77.46619 73.552338 26.10 643140.0 134.32400 0.9959893 12.690435 9.294659 2.334 41.5907220 3.5251532 9.0401631 67.96500 158.705 213.731 27381555
Netherlands 100.00000 100.000000 100.00 33455251.0 6833.91143 3.8663660 41.733451 79.880478 1.680 10.9317305 -0.1301753 2.5068985 81.30488 51.226 70.412 16804432
New Zealand 100.00000 100.000000 100.00 14434056.0 9089.61977 4.6803110 33.092112 28.813581 2.010 37.3977973 2.6954166 1.1344227 81.40488 52.498 80.470 4442100
Paraguay 99.01588 97.873222 63.10 711548.5 1585.83947 6.3405900 14.361881 38.713666 2.636 46.1299975 8.2930765 2.6838574 72.75700 120.675 192.331 6005652
Peru 92.13537 69.905014 71.70 12255937.8 1289.83143 4.7451030 18.958351 24.808299 2.432 57.4504984 5.8525182 2.7678967 74.96700 96.736 146.978 30038809
Philippines 87.50000 81.899696 40.90 25540880.0 677.28112 3.3373750 13.207152 26.177420 3.096 23.2899956 6.7505313 2.5826877 70.83500 124.722 165.874 99700107
Poland 100.00000 100.000000 100.00 5002975.7 3938.25521 4.1972310 36.075739 45.980924 1.290 30.6443291 0.8565571 0.9919826 77.00000 66.784 172.362 38040196
Portugal 100.00000 100.000000 100.00 11860998.0 4685.05479 5.2333430 45.373802 39.606505 1.210 35.8931589 -0.9226447 0.2744167 80.72195 45.643 112.016 10457295
Romania 100.00000 100.000000 85.30 3087143.0 2494.53392 1.2678990 32.027291 40.247345 1.460 29.3291136 0.2699639 3.9847124 75.06341 77.344 186.459 19983693
Russian Federation 100.00000 100.000000 94.40 64072322.0 6539.20737 1.2837400 24.606190 25.845337 1.707 49.7660735 1.7554221 6.7537103 70.57878 120.120 321.874 143506995
Saudi Arabia 100.00000 100.000000 100.00 28252104.0 8385.61159 1.8894480 26.139005 51.917958 2.737 0.4544841 2.6992811 3.5325247 76.62600 78.763 98.106 31482498
Serbia 99.92000 100.000000 70.45 1241352.0 4444.22297 3.7777740 40.794312 39.851505 1.430 31.0646924 2.8926367 7.6942636 75.18537 72.468 148.746 7164132
Singapore 100.00000 100.000000 100.00 31729241.0 8680.60636 6.2591220 12.375338 195.077796 1.190 24.0155587 4.8176310 2.3586042 82.24634 37.955 66.841 5399162
Slovak Republic 100.00000 100.000000 100.00 64008.0 5202.46729 3.1245540 40.104788 93.442006 1.340 39.9312510 0.6327400 1.4004737 76.41220 65.973 156.215 5413393
Slovenia 100.00000 100.000000 100.00 857000.0 6779.28089 3.2632500 53.734400 74.216475 1.550 61.9463754 -1.0292828 1.7692009 80.32195 48.585 106.140 2059953
South Africa 85.20000 80.737785 81.50 16311250.0 4270.81041 5.3357000 31.259191 28.379280 2.428 14.2651328 2.4854680 5.7844691 62.53300 304.887 419.532 53873616
Spain 100.00000 100.000000 100.00 48056735.8 5409.41134 5.0880700 35.758717 32.951952 1.270 37.0821135 -1.4033419 1.4085811 83.07805 39.350 79.558 46620045
Sudan 43.34352 27.057098 40.95 541644.0 220.27910 4.9695720 11.519020 11.686020 4.903 10.4702495 1.9551446 36.5223449 63.67800 184.077 275.049 35990704
Sweden 100.00000 100.000000 100.00 51925707.0 13870.38991 3.8089280 33.596352 42.526809 1.890 68.7809217 1.1877757 -0.0442930 81.95610 43.703 67.302 9600379
Switzerland 100.00000 100.000000 100.00 27503416.0 7807.05882 6.0916780 16.788762 72.068214 1.520 31.5070857 1.7921441 -0.2173232 82.79756 38.848 66.885 8089346
Tanzania 16.40000 1.735447 2.20 1173942.8 98.67290 2.2967140 14.831074 19.012204 5.122 55.1298307 6.7815856 7.8707236 62.96000 241.458 318.490 49253643
Thailand 99.44057 99.026161 77.10 43029150.6 2462.92675 2.6527070 19.093726 67.171141 1.547 39.2761651 2.6874956 2.1848862 77.08300 86.192 198.905 69578602
Togo 40.83137 16.907938 5.30 840948.0 141.28450 1.5111210 17.877512 46.476024 4.723 22.6142673 6.1123431 1.8253948 58.68400 286.269 299.149 7106229
Turkiye 100.00000 100.000000 94.70 74413804.6 2732.20957 4.6311870 29.121362 23.793010 2.165 27.8203968 8.4858170 7.4930903 76.29700 56.695 129.115 76576117
Ukraine 100.00000 100.000000 94.80 5218814.6 3600.22570 1.0184220 38.681594 42.897383 1.506 16.5942830 0.0454391 -0.2389486 71.15951 111.279 292.069 45489648
Acceso a la electricidad (% de la población)
Acceso a la electricidad, zona rural (% de la población)
Acceso a combustibles limpios para cocinar (% de la población)
Tasa de fertilidad (Nacimientos por mujeres en edad fertil)
Tasa de mortalidad en Hombres (por cada mil hombres adultos)
Tasa de mortalidad en Mujeres (por cada mil mujeres adultos)
Esperanza de vida (Años)
Transporte aéreo (personas transportados)
Población total (cantidad de personas)

Análisis de Componentes Principales (ACP)

Variable Sigla Dim. 1 Dim. 2
Acceso a la electricidad A.ELEC 10.97 0.26
Acceso a la electricidad, rural A.ELEC.RU 11.52 0.46
Acceso a tecnologías para cocinar A.CL.TEC 10.70 0.24
Transporte aéreo AIR.TR 1.30 36.93
Consumo de energía EL.PO.CO 3.06 0.28
Empleados totales EM 1.71 0.10
Gastos EX 5.88 6.66
Exportaciones de bienes y servicios EXP 1.91 10.53
Tasa de fertilidad FE.RA 10.31 0.16
Área forestal FO.AR 0.02 3.05
Crecimiento del PIB GDP 5.73 0.72
Inflación INF 3.226 1.92
Esperanza de vida LIFE.EXP 12.42 0.34
Tasa de mortalidad en mujeres MOR.RA.M 11.51 0.89
Tasa de mortalidad en hombres MOR.RA.H 9.42 1.27
Población PO 0.24 36.21
A.ELEC A.ELEC.RUR A.CL.TEC AIR.TR EL.PO.CO EM EX EXP FE.RA FO.AR GDP INF LIFE.EXP MOR.RA.M MOR.RA.H PO
Togo 40.83137 16.907938 5.3 840948 141.28450 1.5111210 17.87751 46.47602 4.723 22.614267 6.1123431 1.8253948 58.68400 286.269 299.149 7106229
Ethiopia 30.67167 17.626913 3.2 5671501 62.93495 0.5011358 10.21191 12.48407 4.724 15.576764 10.5822700 7.4640219 62.37300 212.412 286.512 97084366
Tanzania 16.40000 1.735447 2.2 1173943 98.67290 2.2967140 14.83107 19.01220 5.122 55.129831 6.7815856 7.8707236 62.96000 241.458 318.490 49253643
Namibia 47.40000 27.308245 43.0 510000 1714.66675 3.1744210 35.44843 37.50198 3.653 8.667621 5.6147196 5.6009250 58.69400 363.641 505.335 2204510
Ghana 70.70000 50.829639 19.6 396372 363.40720 5.3719940 19.28113 25.44078 4.136 34.743061 7.3125250 11.6661923 62.42000 234.312 285.680 27525597
India 81.99933 75.219864 41.6 75589071 758.11068 1.5880430 16.63868 25.43086 2.406 23.643023 6.3861064 10.0178785 68.46000 142.920 214.491 1291132063
Indonesia 96.46426 92.994202 58.0 81721356 769.49677 3.4946860 15.37502 23.92358 2.427 51.600234 5.5572637 6.4125133 69.26400 152.461 206.261 253275918
Brazil 99.57515 97.502037 95.0 95591641 2560.09556 4.1203680 30.83634 11.74223 1.748 60.655021 3.0048227 6.2043107 73.91800 89.138 184.185 201721767
Spain 100.00000 100.000000 100.0 48056736 5409.41134 5.0880700 35.75872 32.95195 1.270 37.082113 -1.4033419 1.4085811 83.07805 39.350 79.558 46620045
Poland 100.00000 100.000000 100.0 5002976 3938.25521 4.1972310 36.07574 45.98092 1.290 30.644329 0.8565571 0.9919826 77.00000 66.784 172.362 38040196
Croatia 100.00000 100.000000 100.0 1716702 3754.26870 4.3870210 41.46526 39.75933 1.460 34.329212 -0.3978277 2.2165821 77.12683 50.612 125.021 4255689
A.ELEC A.ELEC.RUR A.CL.TEC AIR.TR EL.PO.CO EM EX EXP FE.RA FO.AR GDP INF LIFE.EXP MOR.RA.M MOR.RA.H PO
90.39 84.97 78.55 18489122 4628.18 3.76 27.83 46.58 2.23 33.39 3.21 3.84 74.11 106.06 181.07 45420729

Análisis de Componentes Principales (ACP)

Dendograma

Clusterización

Caracterización de los clusters 

class: 1
           Test.Value   Class.Mean Frequency  Global.Mean
A.ELEC.RUR      6.739       98.168        59       84.974
A.CL.TEC        6.645       93.116        59       78.548
A.ELEC          6.504       99.267        59       90.393
LIFE.EXP        6.339       77.254        59       74.108
EX              4.881       31.916        59       27.825
EXP             3.186       54.034        59       46.582
EM              3.183        4.281        59        3.763
EL.PO.CO        2.753     5936.236        59     4628.181
PO             -2.753 16876630.712        59 45420729.200
INF            -3.566        2.584        59        3.837
GDP            -4.563        2.135        59        3.213
MOR.RA.H       -5.393      143.652        59      181.065
FE.RA          -5.728        1.804        59        2.229
MOR.RA.M       -6.438       70.219        59      106.056
------------------------------------------------------------ 
class: 2
       Test.Value Class.Mean Frequency Global.Mean
AIR.TR      6.332   79195550         8    18489122
PO          4.929  284250447         8    45420729
------------------------------------------------------------ 
class: 3
           Test.Value  Class.Mean Frequency  Global.Mean
MOR.RA.M        7.507     227.490        18      106.056
FE.RA           6.830       3.702        18        2.229
MOR.RA.H        6.239     306.863        18      181.065
GDP             4.444       6.265        18        3.213
INF             3.445       7.354        18        3.837
EXP            -2.167      31.854        18       46.582
AIR.TR         -2.792 1842640.508        18 18489122.322
EL.PO.CO       -2.792     773.053        18     4628.181
EM             -3.035       2.328        18        3.763
EX             -4.453      16.981        18       27.825
LIFE.EXP       -7.162      63.777        18       74.108
A.CL.TEC       -7.462      31.008        18       78.548
A.ELEC         -7.930      58.951        18       90.393
A.ELEC.RUR     -8.263      37.956        18       84.974

Predicción

Al inicio del procedimiento se realizó una selección de 85 países que estarían en el modelo y otros 5 por aparte que se guardaron para poder realizar una prueba a este. Es decir, la prueba de este modelo consiste en la predicción de los valores y agrupación que se le da a cada país. Estos se adicionan y se verifica si el modelo los agrupa de manera adecuada.

En este gráfico se puede identificar donde el modelo posiciona los nuevos países anexados, siendo Zambia y Estados Unidos los más representados por las dimensiones.

Este último gráfico permite la clasificación que le ha dado el modelo a cada uno de los 5 países anexados. Introduciendo dos al primer grupo, de los países desarrollados y en vía de desarrollo, uno al grupo de países más poblados y uno al grupo de países poco desarrollados.

Conclusiones

  • Error en el modelo

  • Representatividad de las variables

  • Precisión inexacta

  • Complejidad

  • Efectiva capacidad de predicción