Kernel: R (R-Project)
Neural Networks
Part 1: Load all the required libraries
In [3]:
Loading required package: lattice
Loading required package: ggplot2
Part 2: Read and prepare the dataset
In [4]:
radius_mean | texture_mean | perimeter_mean | area_mean | smoothness_mean | compactness_mean | concavity_mean | concave.points_mean | symmetry_mean | fractal_dimension_mean | ⋯ | texture_worst | perimeter_worst | area_worst | smoothness_worst | compactness_worst | concavity_worst | concave.points_worst | symmetry_worst | fractal_dimension_worst | diagnosis |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
17.99 | 10.38 | 122.80 | 1001.0 | 0.11840 | 0.27760 | 0.3001 | 0.14710 | 0.2419 | 0.07871 | ⋯ | 17.33 | 184.60 | 2019.0 | 0.1622 | 0.6656 | 0.7119 | 0.2654 | 0.4601 | 0.11890 | M |
20.57 | 17.77 | 132.90 | 1326.0 | 0.08474 | 0.07864 | 0.0869 | 0.07017 | 0.1812 | 0.05667 | ⋯ | 23.41 | 158.80 | 1956.0 | 0.1238 | 0.1866 | 0.2416 | 0.1860 | 0.2750 | 0.08902 | M |
19.69 | 21.25 | 130.00 | 1203.0 | 0.10960 | 0.15990 | 0.1974 | 0.12790 | 0.2069 | 0.05999 | ⋯ | 25.53 | 152.50 | 1709.0 | 0.1444 | 0.4245 | 0.4504 | 0.2430 | 0.3613 | 0.08758 | M |
11.42 | 20.38 | 77.58 | 386.1 | 0.14250 | 0.28390 | 0.2414 | 0.10520 | 0.2597 | 0.09744 | ⋯ | 26.50 | 98.87 | 567.7 | 0.2098 | 0.8663 | 0.6869 | 0.2575 | 0.6638 | 0.17300 | M |
20.29 | 14.34 | 135.10 | 1297.0 | 0.10030 | 0.13280 | 0.1980 | 0.10430 | 0.1809 | 0.05883 | ⋯ | 16.67 | 152.20 | 1575.0 | 0.1374 | 0.2050 | 0.4000 | 0.1625 | 0.2364 | 0.07678 | M |
12.45 | 15.70 | 82.57 | 477.1 | 0.12780 | 0.17000 | 0.1578 | 0.08089 | 0.2087 | 0.07613 | ⋯ | 23.75 | 103.40 | 741.6 | 0.1791 | 0.5249 | 0.5355 | 0.1741 | 0.3985 | 0.12440 | M |
Part 3: Prepare the train and test data
In [5]:
- 398
- 31
- 171
- 31
radius_mean | texture_mean | perimeter_mean | area_mean | smoothness_mean | compactness_mean | concavity_mean | concave.points_mean | symmetry_mean | fractal_dimension_mean | ⋯ | texture_worst | perimeter_worst | area_worst | smoothness_worst | compactness_worst | concavity_worst | concave.points_worst | symmetry_worst | fractal_dimension_worst | diagnosis | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
65 | 12.68 | 23.84 | 82.69 | 499.0 | 0.11220 | 0.12620 | 0.11280 | 0.06873 | 0.1905 | 0.06590 | ⋯ | 33.47 | 111.80 | 888.3 | 0.1851 | 0.4061 | 0.40240 | 0.17160 | 0.3383 | 0.10310 | M |
354 | 15.08 | 25.74 | 98.00 | 716.6 | 0.10240 | 0.09769 | 0.12350 | 0.06553 | 0.1647 | 0.06464 | ⋯ | 33.22 | 121.20 | 1050.0 | 0.1660 | 0.2356 | 0.40290 | 0.15260 | 0.2654 | 0.09438 | M |
346 | 10.26 | 14.71 | 66.20 | 321.6 | 0.09882 | 0.09159 | 0.03581 | 0.02037 | 0.1633 | 0.07005 | ⋯ | 19.48 | 70.89 | 357.1 | 0.1360 | 0.1636 | 0.07162 | 0.04074 | 0.2434 | 0.08488 | B |
353 | 25.73 | 17.46 | 174.20 | 2010.0 | 0.11490 | 0.23630 | 0.33680 | 0.19130 | 0.1956 | 0.06121 | ⋯ | 23.58 | 229.30 | 3234.0 | 0.1530 | 0.5937 | 0.64510 | 0.27560 | 0.3690 | 0.08815 | M |
487 | 14.64 | 16.85 | 94.21 | 666.0 | 0.08641 | 0.06698 | 0.05192 | 0.02791 | 0.1409 | 0.05355 | ⋯ | 25.44 | 106.00 | 831.0 | 0.1142 | 0.2070 | 0.24370 | 0.07828 | 0.2455 | 0.06596 | B |
362 | 13.30 | 21.57 | 85.24 | 546.1 | 0.08582 | 0.06373 | 0.03344 | 0.02424 | 0.1815 | 0.05696 | ⋯ | 29.20 | 92.94 | 621.2 | 0.1140 | 0.1667 | 0.12120 | 0.05614 | 0.2637 | 0.06658 | B |
radius_mean | texture_mean | perimeter_mean | area_mean | smoothness_mean | compactness_mean | concavity_mean | concave.points_mean | symmetry_mean | fractal_dimension_mean | ⋯ | texture_worst | perimeter_worst | area_worst | smoothness_worst | compactness_worst | concavity_worst | concave.points_worst | symmetry_worst | fractal_dimension_worst | diagnosis | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
65 | -0.3836444 | 1.1363172 | -0.3520389 | -0.42387081 | 1.2386018 | 0.48123664 | 0.3971650 | 0.5818528 | 0.41680306 | 0.4648046 | ⋯ | 1.34090017 | 0.20438984 | 0.08426101 | 2.3700458 | 1.08305535 | 0.72520278 | 0.9362100 | 0.8310058 | 1.1447703 | M |
354 | 0.3387261 | 1.5836671 | 0.3169106 | 0.25425859 | 0.4947992 | -0.07329373 | 0.5431599 | 0.4954039 | -0.55261880 | 0.2815864 | ⋯ | 1.29983700 | 0.50103539 | 0.39700802 | 1.5190796 | -0.06062933 | 0.72777069 | 0.6380515 | -0.3884752 | 0.6465823 | M |
346 | -1.1120346 | -1.0133167 | -1.0725469 | -0.97672078 | 0.2230836 | -0.19194105 | -0.6533159 | -0.7246060 | -0.60522308 | 1.0682615 | ⋯ | -0.95699464 | -1.08664950 | -0.94314293 | 0.1824834 | -0.54359294 | -0.97362211 | -1.1173171 | -0.7564942 | 0.1038317 | B |
353 | 3.5442450 | -0.3658366 | 3.6463651 | 4.28501483 | 1.4435270 | 2.62272361 | 3.4535064 | 3.8931152 | 0.60843296 | -0.2171743 | ⋯ | -0.28355870 | 3.91245929 | 4.62112359 | 0.9398879 | 2.34144388 | 1.97166509 | 2.5682352 | 1.3445595 | 0.2906522 | M |
487 | 0.2062915 | -0.5094595 | 0.1513117 | 0.09656857 | -0.7188134 | -0.67061494 | -0.4335049 | -0.5209108 | -1.44689167 | -1.3310248 | ⋯ | 0.02195125 | 0.02135322 | -0.02656400 | -0.7887764 | -0.25247321 | -0.08985106 | -0.5282188 | -0.7213651 | -0.9770989 | B |
362 | -0.1970320 | 0.6018518 | -0.2406202 | -0.27708820 | -0.7635933 | -0.73382867 | -0.6856531 | -0.6200569 | 0.07863265 | -0.8351723 | ⋯ | 0.63954128 | -0.39079476 | -0.43234214 | -0.7976871 | -0.52279868 | -0.71898840 | -0.8756518 | -0.4169130 | -0.9416773 | B |
radius_mean | texture_mean | perimeter_mean | area_mean | smoothness_mean | compactness_mean | concavity_mean | concave.points_mean | symmetry_mean | fractal_dimension_mean | ⋯ | texture_worst | perimeter_worst | area_worst | smoothness_worst | compactness_worst | concavity_worst | concave.points_worst | symmetry_worst | fractal_dimension_worst | diagnosis | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
3 | 19.69 | 21.25 | 130.00 | 1203.0 | 0.10960 | 0.1599 | 0.19740 | 0.12790 | 0.2069 | 0.05999 | ⋯ | 25.53 | 152.50 | 1709.0 | 0.1444 | 0.4245 | 0.4504 | 0.2430 | 0.3613 | 0.08758 | M |
4 | 11.42 | 20.38 | 77.58 | 386.1 | 0.14250 | 0.2839 | 0.24140 | 0.10520 | 0.2597 | 0.09744 | ⋯ | 26.50 | 98.87 | 567.7 | 0.2098 | 0.8663 | 0.6869 | 0.2575 | 0.6638 | 0.17300 | M |
12 | 15.78 | 17.89 | 103.60 | 781.0 | 0.09710 | 0.1292 | 0.09954 | 0.06606 | 0.1842 | 0.06082 | ⋯ | 27.28 | 136.50 | 1299.0 | 0.1396 | 0.5609 | 0.3965 | 0.1810 | 0.3792 | 0.10480 | M |
14 | 15.85 | 23.95 | 103.70 | 782.7 | 0.08401 | 0.1002 | 0.09938 | 0.05364 | 0.1847 | 0.05338 | ⋯ | 27.66 | 112.00 | 876.5 | 0.1131 | 0.1924 | 0.2322 | 0.1119 | 0.2809 | 0.06287 | M |
16 | 14.54 | 27.54 | 96.73 | 658.8 | 0.11390 | 0.1595 | 0.16390 | 0.07364 | 0.2303 | 0.07077 | ⋯ | 37.13 | 124.10 | 943.2 | 0.1678 | 0.6577 | 0.7026 | 0.1712 | 0.4218 | 0.13410 | M |
19 | 19.81 | 22.15 | 130.00 | 1260.0 | 0.09831 | 0.1027 | 0.14790 | 0.09498 | 0.1582 | 0.05395 | ⋯ | 30.88 | 186.80 | 2398.0 | 0.1512 | 0.3150 | 0.5372 | 0.2388 | 0.2768 | 0.07615 | M |
radius_mean | texture_mean | perimeter_mean | area_mean | smoothness_mean | compactness_mean | concavity_mean | concave.points_mean | symmetry_mean | fractal_dimension_mean | ⋯ | texture_worst | perimeter_worst | area_worst | smoothness_worst | compactness_worst | concavity_worst | concave.points_worst | symmetry_worst | fractal_dimension_worst | diagnosis | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
3 | 1.7262793 | 0.5265087 | 1.7151067 | 1.77007723 | 1.04126642 | 1.13671449 | 1.5514797 | 2.1803467 | 1.0330247 | -0.3945761 | ⋯ | 0.03673399 | 1.4888020 | 1.6715923 | 0.5567304 | 1.2064794 | 0.9717219 | 2.0566580603 | 1.2157529 | 0.2580872 | M |
4 | -0.7628888 | 0.3216695 | -0.5753134 | -0.77571276 | 3.53831796 | 3.54856176 | 2.1518325 | 1.5670999 | 3.0169578 | 5.0510767 | ⋯ | 0.19605908 | -0.2036556 | -0.5358175 | 3.4705100 | 4.1699978 | 2.1863422 | 2.2842000339 | 6.2760136 | 5.1382720 | M |
12 | 0.5494175 | -0.2645943 | 0.5615949 | 0.45495497 | 0.09253862 | 0.53958778 | 0.2162405 | 0.5097220 | 0.1800838 | -0.2738847 | ⋯ | 0.32417616 | 0.9838734 | 0.8786036 | 0.3428750 | 2.1214271 | 0.6949015 | 1.0837199659 | 1.5151865 | 1.2418940 | M |
14 | 0.5704866 | 1.1622164 | 0.5659642 | 0.46025286 | -0.90096912 | -0.02447327 | 0.2140574 | 0.1741923 | 0.1988710 | -1.3557447 | ⋯ | 0.38659217 | 0.2107014 | 0.0614384 | -0.8377850 | -0.3504075 | -0.1489129 | -0.0006352328 | -0.1291891 | -1.1536357 | M |
16 | 0.1761927 | 2.0074723 | 0.2614196 | 0.07413047 | 1.36762878 | 1.12893434 | 1.0943929 | 0.7144978 | 1.9122678 | 1.1729576 | ⋯ | 1.94206492 | 0.5925537 | 0.1904441 | 1.5992754 | 2.7707449 | 2.2669745 | 0.9299329768 | 2.2278050 | 2.9158512 | M |
19 | 1.7623979 | 0.7384113 | 1.7151067 | 1.94771223 | 0.18437547 | 0.02415268 | 0.8760828 | 1.2910038 | -0.7968530 | -1.2728603 | ⋯ | 0.91548576 | 2.5712427 | 3.0042002 | 0.8596922 | 0.4719722 | 1.4175106 | 1.9907493506 | -0.1977745 | -0.3949275 | M |
Part 4a: Neural Network | Model Training
Now that we have created our training and testing datasets, we can start training our model. The rule of thumb is to set the size of the hidden layer to be the square root of the number of features. In our data set that is 5. Let us explore the parameter size, which is the number of nodes in a the hidden layer.
In [14]:
5
In [15]:
# weights: 33
initial value 257.863979
iter 10 value 55.528871
iter 20 value 35.379013
iter 30 value 21.402967
iter 40 value 14.943263
iter 50 value 10.809916
iter 60 value 10.614514
iter 70 value 10.604750
iter 80 value 10.603735
iter 90 value 10.603652
iter 100 value 10.603638
final value 10.603635
converged
# weights: 65
initial value 252.390002
iter 10 value 99.283813
iter 20 value 30.315228
iter 30 value 22.003063
iter 40 value 15.568625
iter 50 value 11.810493
iter 60 value 9.212125
iter 70 value 5.550257
iter 80 value 5.011114
iter 90 value 4.958923
iter 100 value 4.947879
iter 110 value 4.913039
iter 120 value 4.873626
iter 130 value 4.869634
iter 140 value 4.869519
iter 150 value 4.869514
iter 160 value 4.869511
final value 4.869510
converged
# weights: 97
initial value 249.172219
iter 10 value 25.546774
iter 20 value 16.120620
iter 30 value 12.121556
iter 40 value 10.649470
iter 50 value 7.401423
iter 60 value 5.848236
iter 70 value 5.037690
iter 80 value 4.881097
iter 90 value 4.821113
iter 100 value 4.784594
iter 110 value 4.773508
iter 120 value 4.765156
iter 130 value 4.761644
iter 140 value 4.757622
iter 150 value 4.738771
iter 160 value 4.736814
iter 170 value 4.736588
iter 180 value 4.736566
final value 4.736564
converged
# weights: 129
initial value 261.916030
iter 10 value 44.970928
iter 20 value 18.021220
iter 30 value 10.304940
iter 40 value 6.676828
iter 50 value 5.180584
iter 60 value 4.973020
iter 70 value 4.914995
iter 80 value 4.793421
iter 90 value 4.737687
iter 100 value 4.716186
iter 110 value 4.703622
iter 120 value 4.687992
iter 130 value 4.650005
iter 140 value 4.645960
iter 150 value 4.645608
iter 160 value 4.645525
iter 170 value 4.645510
final value 4.645509
converged
# weights: 161
initial value 354.424913
iter 10 value 20.266593
iter 20 value 8.877208
iter 30 value 5.364258
iter 40 value 4.818063
iter 50 value 4.613452
iter 60 value 4.465658
iter 70 value 4.375093
iter 80 value 4.056229
iter 90 value 3.868393
iter 100 value 3.747015
iter 110 value 3.587268
iter 120 value 3.516691
iter 130 value 3.498615
iter 140 value 3.491695
iter 150 value 3.487163
iter 160 value 3.483145
iter 170 value 3.476403
iter 180 value 3.474435
iter 190 value 3.473883
iter 200 value 3.473665
final value 3.473665
stopped after 200 iterations
# weights: 193
initial value 325.391353
iter 10 value 25.655959
iter 20 value 10.524777
iter 30 value 6.875892
iter 40 value 4.392362
iter 50 value 3.931983
iter 60 value 3.832116
iter 70 value 3.760606
iter 80 value 3.678386
iter 90 value 3.572606
iter 100 value 3.541965
iter 110 value 3.525520
iter 120 value 3.510518
iter 130 value 3.488299
iter 140 value 3.481895
iter 150 value 3.472006
iter 160 value 3.466504
iter 170 value 3.465285
iter 180 value 3.464662
iter 190 value 3.464394
iter 200 value 3.464314
final value 3.464314
stopped after 200 iterations
# weights: 225
initial value 258.309694
iter 10 value 12.226687
iter 20 value 6.004129
iter 30 value 4.457358
iter 40 value 4.056669
iter 50 value 3.873897
iter 60 value 3.768283
iter 70 value 3.653021
iter 80 value 3.602031
iter 90 value 3.585194
iter 100 value 3.515852
iter 110 value 3.417382
iter 120 value 3.314688
iter 130 value 3.295375
iter 140 value 3.291969
iter 150 value 3.291438
iter 160 value 3.291270
iter 170 value 3.291022
iter 180 value 3.290869
iter 190 value 3.290848
iter 200 value 3.290843
final value 3.290843
stopped after 200 iterations
# weights: 257
initial value 262.517344
iter 10 value 20.719144
iter 20 value 11.213332
iter 30 value 6.901670
iter 40 value 4.647296
iter 50 value 3.879223
iter 60 value 3.618975
iter 70 value 3.508820
iter 80 value 3.435246
iter 90 value 3.386537
iter 100 value 3.332048
iter 110 value 3.290387
iter 120 value 3.276320
iter 130 value 3.273871
iter 140 value 3.273087
iter 150 value 3.272771
iter 160 value 3.272552
iter 170 value 3.272440
iter 180 value 3.272340
iter 190 value 3.272273
iter 200 value 3.272225
final value 3.272225
stopped after 200 iterations
# weights: 289
initial value 297.456944
iter 10 value 16.558351
iter 20 value 4.495042
iter 30 value 3.658188
iter 40 value 3.500033
iter 50 value 3.423542
iter 60 value 3.381057
iter 70 value 3.360377
iter 80 value 3.349622
iter 90 value 3.338501
iter 100 value 3.322603
iter 110 value 3.308097
iter 120 value 3.296884
iter 130 value 3.287076
iter 140 value 3.277041
iter 150 value 3.270547
iter 160 value 3.266731
iter 170 value 3.264810
iter 180 value 3.263966
iter 190 value 3.263234
iter 200 value 3.262079
final value 3.262079
stopped after 200 iterations
# weights: 321
initial value 274.808672
iter 10 value 19.551491
iter 20 value 5.958951
iter 30 value 4.467927
iter 40 value 3.859546
iter 50 value 3.625411
iter 60 value 3.491668
iter 70 value 3.390900
iter 80 value 3.346708
iter 90 value 3.256310
iter 100 value 3.229063
iter 110 value 3.218689
iter 120 value 3.214570
iter 130 value 3.210556
iter 140 value 3.207747
iter 150 value 3.204027
iter 160 value 3.198930
iter 170 value 3.195641
iter 180 value 3.193463
iter 190 value 3.191616
iter 200 value 3.186874
final value 3.186874
stopped after 200 iterations
# weights: 353
initial value 216.798196
iter 10 value 12.863897
iter 20 value 5.147750
iter 30 value 3.748939
iter 40 value 3.438959
iter 50 value 3.347970
iter 60 value 3.319117
iter 70 value 3.274940
iter 80 value 3.248477
iter 90 value 3.229540
iter 100 value 3.218367
iter 110 value 3.203924
iter 120 value 3.197756
iter 130 value 3.189227
iter 140 value 3.181560
iter 150 value 3.180122
iter 160 value 3.179016
iter 170 value 3.177378
iter 180 value 3.175168
iter 190 value 3.173617
iter 200 value 3.172567
final value 3.172567
stopped after 200 iterations
# weights: 385
initial value 279.597982
iter 10 value 14.530213
iter 20 value 4.291995
iter 30 value 3.426020
iter 40 value 3.306985
iter 50 value 3.269132
iter 60 value 3.249395
iter 70 value 3.223155
iter 80 value 3.194586
iter 90 value 3.182231
iter 100 value 3.177831
iter 110 value 3.173014
iter 120 value 3.162995
iter 130 value 3.152341
iter 140 value 3.145067
iter 150 value 3.139678
iter 160 value 3.132685
iter 170 value 3.130354
iter 180 value 3.129407
iter 190 value 3.128876
iter 200 value 3.128488
final value 3.128488
stopped after 200 iterations
# weights: 417
initial value 386.547550
iter 10 value 10.444153
iter 20 value 3.989170
iter 30 value 3.389091
iter 40 value 3.313958
iter 50 value 3.260114
iter 60 value 3.206295
iter 70 value 3.179305
iter 80 value 3.161373
iter 90 value 3.151782
iter 100 value 3.146699
iter 110 value 3.144128
iter 120 value 3.142953
iter 130 value 3.142618
iter 140 value 3.142420
iter 150 value 3.142210
iter 160 value 3.142031
iter 170 value 3.141883
iter 180 value 3.141473
iter 190 value 3.134430
iter 200 value 3.131296
final value 3.131296
stopped after 200 iterations
# weights: 449
initial value 431.598577
iter 10 value 12.715442
iter 20 value 4.231707
iter 30 value 3.340877
iter 40 value 3.226590
iter 50 value 3.175527
iter 60 value 3.142867
iter 70 value 3.130939
iter 80 value 3.124491
iter 90 value 3.111903
iter 100 value 3.102305
iter 110 value 3.095613
iter 120 value 3.092259
iter 130 value 3.090892
iter 140 value 3.090412
iter 150 value 3.090104
iter 160 value 3.089891
iter 170 value 3.089627
iter 180 value 3.086592
iter 190 value 3.084942
iter 200 value 3.084534
final value 3.084534
stopped after 200 iterations
# weights: 481
initial value 285.277329
iter 10 value 10.780256
iter 20 value 4.080234
iter 30 value 3.414599
iter 40 value 3.263116
iter 50 value 3.203217
iter 60 value 3.178923
iter 70 value 3.151559
iter 80 value 3.138526
iter 90 value 3.128625
iter 100 value 3.122789
iter 110 value 3.120244
iter 120 value 3.117639
iter 130 value 3.114787
iter 140 value 3.112591
iter 150 value 3.111738
iter 160 value 3.111405
iter 170 value 3.111248
iter 180 value 3.111216
iter 190 value 3.111199
iter 200 value 3.111190
final value 3.111190
stopped after 200 iterations
# weights: 513
initial value 494.192086
iter 10 value 12.559779
iter 20 value 4.001673
iter 30 value 3.363932
iter 40 value 3.270504
iter 50 value 3.228051
iter 60 value 3.176728
iter 70 value 3.147232
iter 80 value 3.124421
iter 90 value 3.111151
iter 100 value 3.106053
iter 110 value 3.102501
iter 120 value 3.099274
iter 130 value 3.097141
iter 140 value 3.096004
iter 150 value 3.095389
iter 160 value 3.094963
iter 170 value 3.094781
iter 180 value 3.094535
iter 190 value 3.094217
iter 200 value 3.093990
final value 3.093990
stopped after 200 iterations
# weights: 545
initial value 299.081244
iter 10 value 11.249587
iter 20 value 4.540030
iter 30 value 3.546772
iter 40 value 3.343321
iter 50 value 3.250315
iter 60 value 3.208411
iter 70 value 3.183672
iter 80 value 3.154666
iter 90 value 3.124067
iter 100 value 3.111659
iter 110 value 3.102773
iter 120 value 3.100320
iter 130 value 3.099349
iter 140 value 3.099042
iter 150 value 3.098837
iter 160 value 3.098590
iter 170 value 3.098175
iter 180 value 3.097733
iter 190 value 3.097507
iter 200 value 3.097360
final value 3.097360
stopped after 200 iterations
# weights: 577
initial value 328.579506
iter 10 value 13.776307
iter 20 value 4.078908
iter 30 value 3.327907
iter 40 value 3.196057
iter 50 value 3.148701
iter 60 value 3.133874
iter 70 value 3.125161
iter 80 value 3.117577
iter 90 value 3.110787
iter 100 value 3.105580
iter 110 value 3.101804
iter 120 value 3.099167
iter 130 value 3.094500
iter 140 value 3.091577
iter 150 value 3.089691
iter 160 value 3.088207
iter 170 value 3.087126
iter 180 value 3.086327
iter 190 value 3.086032
iter 200 value 3.085864
final value 3.085864
stopped after 200 iterations
# weights: 609
initial value 325.042803
iter 10 value 14.852799
iter 20 value 4.445404
iter 30 value 3.365770
iter 40 value 3.221212
iter 50 value 3.169312
iter 60 value 3.139500
iter 70 value 3.114018
iter 80 value 3.098575
iter 90 value 3.087093
iter 100 value 3.077279
iter 110 value 3.072672
iter 120 value 3.070042
iter 130 value 3.067592
iter 140 value 3.066163
iter 150 value 3.065136
iter 160 value 3.064571
iter 170 value 3.064143
iter 180 value 3.063739
iter 190 value 3.063132
iter 200 value 3.062671
final value 3.062671
stopped after 200 iterations
# weights: 641
initial value 418.869996
iter 10 value 12.115230
iter 20 value 4.238396
iter 30 value 3.343260
iter 40 value 3.193722
iter 50 value 3.136718
iter 60 value 3.112063
iter 70 value 3.092289
iter 80 value 3.082570
iter 90 value 3.078105
iter 100 value 3.075531
iter 110 value 3.073001
iter 120 value 3.070994
iter 130 value 3.070109
iter 140 value 3.069496
iter 150 value 3.069066
iter 160 value 3.068877
iter 170 value 3.068758
iter 180 value 3.068662
iter 190 value 3.068602
iter 200 value 3.068566
final value 3.068566
stopped after 200 iterations
# weights: 673
initial value 314.637363
iter 10 value 12.243175
iter 20 value 4.675263
iter 30 value 3.648078
iter 40 value 3.372923
iter 50 value 3.249410
iter 60 value 3.187988
iter 70 value 3.153123
iter 80 value 3.130014
iter 90 value 3.117573
iter 100 value 3.113648
iter 110 value 3.110682
iter 120 value 3.108996
iter 130 value 3.107841
iter 140 value 3.106859
iter 150 value 3.103432
iter 160 value 3.099749
iter 170 value 3.097004
iter 180 value 3.096142
iter 190 value 3.095692
iter 200 value 3.095365
final value 3.095365
stopped after 200 iterations
# weights: 705
initial value 361.265149
iter 10 value 13.498529
iter 20 value 4.599951
iter 30 value 3.360746
iter 40 value 3.214219
iter 50 value 3.175039
iter 60 value 3.153169
iter 70 value 3.139097
iter 80 value 3.126699
iter 90 value 3.118049
iter 100 value 3.114376
iter 110 value 3.111453
iter 120 value 3.109224
iter 130 value 3.107955
iter 140 value 3.106545
iter 150 value 3.104856
iter 160 value 3.102469
iter 170 value 3.100844
iter 180 value 3.100009
iter 190 value 3.099635
iter 200 value 3.099389
final value 3.099389
stopped after 200 iterations
# weights: 737
initial value 230.400829
iter 10 value 16.056098
iter 20 value 4.141912
iter 30 value 3.296014
iter 40 value 3.184165
iter 50 value 3.151584
iter 60 value 3.130629
iter 70 value 3.114685
iter 80 value 3.099544
iter 90 value 3.090784
iter 100 value 3.081294
iter 110 value 3.073857
iter 120 value 3.071475
iter 130 value 3.070296
iter 140 value 3.069705
iter 150 value 3.069225
iter 160 value 3.068657
iter 170 value 3.067469
iter 180 value 3.065725
iter 190 value 3.065206
iter 200 value 3.065047
final value 3.065047
stopped after 200 iterations
# weights: 769
initial value 363.131635
iter 10 value 13.532757
iter 20 value 4.253883
iter 30 value 3.400553
iter 40 value 3.204264
iter 50 value 3.142139
iter 60 value 3.117319
iter 70 value 3.099772
iter 80 value 3.085092
iter 90 value 3.072776
iter 100 value 3.068095
iter 110 value 3.064801
iter 120 value 3.063315
iter 130 value 3.062661
iter 140 value 3.062178
iter 150 value 3.061916
iter 160 value 3.061756
iter 170 value 3.061709
iter 180 value 3.061686
iter 190 value 3.061661
iter 200 value 3.061646
final value 3.061646
stopped after 200 iterations
# weights: 801
initial value 301.067817
iter 10 value 11.689812
iter 20 value 4.004337
iter 30 value 3.258485
iter 40 value 3.161594
iter 50 value 3.111821
iter 60 value 3.088506
iter 70 value 3.078017
iter 80 value 3.072778
iter 90 value 3.066961
iter 100 value 3.063273
iter 110 value 3.061409
iter 120 value 3.060268
iter 130 value 3.059403
iter 140 value 3.058726
iter 150 value 3.058338
iter 160 value 3.058037
iter 170 value 3.057891
iter 180 value 3.057829
iter 190 value 3.057785
iter 200 value 3.057758
final value 3.057758
stopped after 200 iterations
Part 4b: Neural Network | Prediction
Now that we have created several model fits, let us see how well each of the above models is at predicting the class in the test dataset.In [11]:
B M
98 73
B M
97 74
B M
101 70
B M
100 71
Part 4c: Neural Network | Accuracy
Lets try to quantify the accuracy of the predictions in the test set.In [12]:
18
Part 4d: Neural Network | Sensitivity Analysis
In [13]:
rel_imp | variable | |
---|---|---|
fractal_dimension_worst | 0.07146494 | fractal_dimension_worst |
compactness_se | 0.06030277 | compactness_se |
texture_worst | 0.05941808 | texture_worst |
radius_se | 0.05479945 | radius_se |
area_se | 0.04921995 | area_se |
concavity_mean | 0.04715165 | concavity_mean |
area_worst | 0.04226448 | area_worst |
radius_worst | 0.04080139 | radius_worst |
perimeter_worst | 0.04008443 | perimeter_worst |
concave.points_se | 0.03627505 | concave.points_se |
symmetry_mean | 0.03368205 | symmetry_mean |
smoothness_worst | 0.03296243 | smoothness_worst |
texture_se | 0.03249893 | texture_se |
symmetry_worst | 0.03091328 | symmetry_worst |
compactness_mean | 0.03043718 | compactness_mean |
texture_mean | 0.02989981 | texture_mean |
smoothness_se | 0.02833369 | smoothness_se |
fractal_dimension_se | 0.02774882 | fractal_dimension_se |
concave.points_mean | 0.02589665 | concave.points_mean |
perimeter_se | 0.02455502 | perimeter_se |
symmetry_se | 0.02423276 | symmetry_se |
compactness_worst | 0.02348785 | compactness_worst |
smoothness_mean | 0.02342914 | smoothness_mean |
fractal_dimension_mean | 0.02271288 | fractal_dimension_mean |
concavity_worst | 0.02215374 | concavity_worst |
radius_mean | 0.01913261 | radius_mean |
perimeter_mean | 0.01881607 | perimeter_mean |
concave.points_worst | 0.01872796 | concave.points_worst |
area_mean | 0.01600735 | area_mean |
concavity_se | 0.01258958 | concavity_se |
In [0]: