Supplementary Material: PN-FAC

This website contains supplementary material to the paper submitted to be taken into account for possible publication in Fuzzy Sets and Systems.

Results obtained by the analyzed methods on each of the datasets are as follows:

  1. Traditional classification methods (Accuracy)
  2. Traditional classification methods (G-mean)
  3. Traditional classification methods (Kappa)
  4. Associative classification methods (Accuracy)
  5. Associative classification methods (G-mean)
  6. Complexity - FURIA
  7. Complexity - FARC-HD
  8. Complexity - PN-FAC
  9. Model obtained by PN-FAC for a real biomedical research problem related to childhood obesity

Traditional classification methods (Accuracy)

Dataset C45Rules 2SLAVE SGERD FURIA PN-FAC
Appendicitis 0.8403 0.8498 0.8779 0.8775 0.8809
Banana 0.8842 0.7596 0.5619 0.8823 0.8708
Bupa 0.6406 0.6 0.5594 0.6725 0.6319
Cleveland 0.4975 0.5319 0.5016 0.5724 0.557
Crx 0.8576 0.8254 0.8636 0.8683 0.8407
Ecoli 0.7649 0.8216 0.7473 0.8037 0.7859
German 0.691 0.657 0.681 0.724 0.696
Heart 0.7852 0.7704 0.7074 0.8148 0.817
Iris 0.94 0.96 0.9133 0.9533 0.94
Magic 0.8138 0.7924 0.7332 0.8475 0.7927
Movement 0.5972 0.8 0.4417 0.6306 0.7958
New-thyroid 0.8977 0.9163 0.8233 0.9395 0.9628
Penbased 0.9481 0.9711 0.6605 0.9792 0.9659
Phoneme 0.8138 0.765 0.7604 0.844 0.8
Pima 0.7383 0.7526 0.7083 0.7486 0.7491
Sonar 0.7747 0.7934 0.7165 0.7649 0.8794
Spectfheart 0.7564 0.794 0.779 0.7981 0.787
Texture 0.9058 0.7938 0.7445 0.9605 0.9555
Twonorm 0.8557 0.9228 0.7035 0.9399 0.9549
Vehicle 0.6631 0.6466 0.5273 0.7057 0.7258
Wine 0.949 0.9552 0.9216 0.9554 0.9607
Vowel 0.6687 0.7343 0.4051 0.8212 0.8556
Wisconsin 0.9502 0.9355 0.937 0.9634 0.9643

Traditional classification methods (G-mean)

Dataset C45Rules 2SLAVE SGERD FURIA PN-FAC
Appendicitis 0.612 0.528 0.7697 0.613 0.704
Banana 0.8807 0.7358 0.2128 0.8747 0.8683
Bupa 0.6267 0.3812 0.2633 0.6337 0.6121
Cleveland 0.3051 0.4257 0.2251 0.2379 0.4122
Crx 0.8608 0.8267 0.8121 0.8688 0.8408
Ecoli 0.6044 0.7697 0.6371 0.7117 0.7593
German 0.5069 0.5433 0.2025 0.5239 0.6618
Heart 0.7819 0.7628 0.4797 0.8042 0.8099
Iris 0.9531 0.9694 0.8922 0.9642 0.954
Magic 0.8097 0.7187 0.627 0.7984 0.7848
Movement 0.7271 0.8715 0.5766 0.7431 0.7821
New-thyroid 0.908 0.8626 0.5525 0.9258 0.949
Penbased 0.9708 0.9838 0.7011 0.9884 0.989
Phoneme 0.7898 0.6267 0.449 0.7942 0.8126
Pima 0.7041 0.6557 0.49 0.6783 0.7446
Sonar 0.7644 0.7921 0.6956 0.7616 0.879
Spectfheart 0.6503 0.53 0.39 0.5075 0.7443
Texture 0.9462 0.8479 0.7912 0.978 0.9781
Twonorm 0.8506 0.9228 0.7022 0.9398 0.9546
Vehicle 0.742 0.7162 0.6434 0.7808 0.7998
Wine 0.9616 0.9673 0.9421 0.9681 0.9765
Vowel 0.7896 0.8279 0.5282 0.8958 0.9161
Wisconsin 0.9448 0.9217 0.6815 0.9591 0.965

Traditional classification methods (Kappa)

Dataset C45Rules 2SLAVE SGERD FURIA PN-FAC
Appendicitis 0.3997 0.3935 0.5849 0.502 0.5072
Banana 0.7652 0.5051 0.1427 0.7601 0.7385
Bupa 0.2674 0.12 0.105 0.3098 0.32
Cleveland 0.2149 0.2697 0.1759 0.1993 0.2772
Crx 0.7161 0.651 0.7297 0.7354 0.7357
Ecoli 0.6674 0.7516 0.6465 0.7221 0.7031
German 0.1802 0.1628 0.1 0.2412 0.3167
Heart 0.5671 0.5331 0.4395 0.6235 0.6257
Iris 0.91 0.94 0.8716 0.93 0.91
Magic 0.603 0.514 0.363 0.6489 0.5545
Movement 0.5691 0.7856 0.403 0.6038 0.7741
New-thyroid 0.7874 0.8056 0.5 0.8697 0.9184
Penbased 0.9424 0.9678 0.6236 0.9768 0.9621
Phoneme 0.5704 0.3741 0.4021 0.6154 0.5652
Pima 0.4239 0.4102 0.2678 0.4199 0.4632
Sonar 0.5476 0.5866 0.4228 0.528 0.8584
Spectfheart 0.3154 0.25 0.19 0.2661 0.4443
Texture 0.8964 0.7732 0.719 0.9566 0.9571
Twonorm 0.7113 0.8457 0.407 0.8797 0.9189
Vehicle 0.5503 0.5296 0.3734 0.608 0.6343
Wine 0.9223 0.9322 0.8815 0.9326 0.9412
Vowel 0.6356 0.7078 0.3463 0.8033 0.8411
Wisconsin 0.8907 0.8565 0.8619 0.9194 0.9208

Associative classification methods (Accuracy)

Dataset CMAR CPAR FARC-HD PN-FAC
Appendicitis 0.8779 0.8498 0.8584 0.8809
Banana 0.7083 0.7498 0.8626 0.8708
Bupa 0.22 0.22 0.6986 0.6319
Cleveland 0.5554 0.5688 0.5333 0.557
Crx 0.8668 0.876 0.8653 0.8407
Ecoli 0.7741 0.768 0.8155 0.7859
German 0.724 0.744 0.715 0.696
Heart 0.8222 0.7963 0.8556 0.817
Iris 0.9333 0.9333 0.9533 0.94
Magic 0.7851 0.8462 0.8458 0.7927
Movement 0.41 0.5889 0.7653 0.7958
New-thyroid 0.9442 0.9023 0.9535 0.9628
Penbased 0.7162 0.9291 0.9584 0.9659
Phoneme 0.7857 0.8144 0.8129 0.8
Pima 0.7461 0.7487 0.7486 0.7491
Sonar 0.7935 0.7837 0.9653 0.8794
Spectfheart 0.7976 0.7865 0.7715 0.787
Texture 0.7553 0.9025 0.9271 0.9555
Twonorm 0.9593 0.8934 0.9534 0.9549
Vehicle 0.6241 0.6939 0.6938 0.7258
Wine 0.9773 0.9663 0.9605 0.9607
Vowel 0.597 0.6333 0.7152 0.8556
Wisconsin 0.9635 0.9475 0.9634 0.9643

Associative classification methods (G-mean)

Dataset CMAR CPAR FARC-HD PN-FAC
Appendicitis 0.7194 0.394 0.6498 0.704
Banana 0.6572 0.7445 0.8495 0.8683
Bupa 0.18 0.19 0.6626 0.6121
Cleveland 0.1194 0.266 0.3157 0.4122
Crx 0.693 0.8749 0.8659 0.8408
Ecoli 0.6695 0.558 0.735 0.7593
German 0.4074 0.5341 0.5875 0.6618
Heart 0.8205 0.789 0.8491 0.8099
Iris 0.948 0.948 0.9639 0.954
Magic 0.6046 0.5361 0.8011 0.7848
Movement 0.35 0.6809 0.7808 0.7821
New-thyroid 0.9107 0.7604 0.9488 0.949
Penbased 0.7724 0.8735 0.9767 0.989
Phoneme 0.7929 0.7123 0.7655 0.8126
Pima 0.6737 0.658 0.6967 0.7446
Sonar 0.79 0.7711 0.9808 0.879
Spectfheart 0.4806 0.4136 0.5533 0.7443
Texture 0.7907 0.867 0.9587 0.9781
Twonorm 0.7042 0.5996 0.9534 0.9546
Vehicle 0.5904 0.7451 0.7777 0.7998
Wine 0.9827 0.8811 0.9719 0.9765
Vowel 0.7064 0.7581 0.8149 0.9161
Wisconsin 0.8984 0.6371 0.9611 0.965

Associative classification methods (Kappa)

Dataset CMAR CPAR FARC-HD PN-FAC
Appendicitis 0.5628 0.312 0.4678 0.5072
Banana 0.3893 0.4928 0.718 0.7385
Bupa 0.14 0.15 0.3655 0.32
Cleveland 0.1178 0.219 0.2553 0.2772
Crx 0.7319 0.7499 0.7292 0.7357
Ecoli 0.673 0.6707 0.742 0.7031
German 0.2608 0.2808 0.2738 0.3167
Heart 0.6408 0.5849 0.7056 0.6257
Iris 0.9 0.9 0.93 0.91
Magic 0.4635 0.6494 0.6472 0.5545
Movement 0.29 0.5597 0.7628 0.7741
New-thyroid 0.8712 0.7737 0.9015 0.9184
Penbased 0.6845 0.9214 0.9538 0.9621
Phoneme 0.5319 0.5484 0.5468 0.5652
Pima 0.4113 0.4058 0.4305 0.4632
Sonar 0.5847 0.5614 0.9783 0.8584
Spectfheart 0.2656 0.1904 0.2519 0.4443
Texture 0.7308 0.893 0.9198 0.9571
Twonorm 0.9187 0.7894 0.9068 0.9189
Vehicle 0.5011 0.5925 0.5916 0.6343
Wine 0.9653 0.9494 0.9402 0.9412
Vowel 0.557 0.5967 0.6867 0.8411
Wisconsin 0.9201 0.8881 0.9198 0.9208

Complexity - FURIA

Dataset #Rules #VarInc
appendicitis 4.4 1.88
banana 19.8 4.79
bupa 9.6 4.38
cleveland 9.6 5.24
crx 8.2 5.3
ecoli 19.2 5.52
german 18.6 5.5
heart 9.4 4.29
iris 4.4 3.52
magic 28 5.48
movement 39 4.62
new-thyroid 5.8 4.46
penbased 125 7.83
phoneme 29.4 5.45
pima 7.6 4.44
sonar 14.2 4.49
spectfheart 14 4.86
texture 88.6 6.39
twonorm 79.4 7.63
vehicle 14.4 4.87
vowel 62.6 5.6
wine 28.2 3.85
wisconsin 12.4 4.62

Complexity - FARC-HD

Dataset #Rules #VarInc
appendicitis 6.8 1.72
banana 23.6 1.46
bupa 12.6 2.98
cleveland 116.2 2.65
crx 22.8 2.52
ecoli 32.2 2.84
german 82.6 2.79
heart 25.6 2.65
iris 4.2 1.16
magic 43 2.47
movement 82.6 2.98
new-thyroid 9.6 2.24
penbased 136.2 2.84
phoneme 16.2 2.2
pima 27 2.48
sonar 17 2.3
spectfheart 13.4 1.74
texture 50.4 2.7
twonorm 58.6 2.57
vehicle 44.2 2.94
vowel 8.4 1.52
wine 71.8 2.89
wisconsin 13.4 1.69

Complexity - PN-FAC

Dataset #Rules #VarInc
appendicitis 5.2 2.2
banana 11.8 1.97
bupa 8.2 2.98
cleveland 77.8 2.97
crx 10.4 2.73
ecoli 38 2.84
german 36.2 2.97
heart 20.4 2.83
iris 4 1.52
magic 9.2 2.1
movement 81.6 2.98
new-thyroid 8.4 2.24
penbased 136.2 2.99
phoneme 10 2.64
pima 6.8 2.67
sonar 16.8 3
spectfheart 8.2 2.14
texture 44.2 2.9
twonorm 17.2 2.95
vehicle 40 2.94
vowel 6 2.04
wine 62.4 2.96
wisconsin 6.8 1.69

Model obtained by PN-FAC for a real biomedical research problem related to childhood obesity

Rule Base

#Rules Support
IF Hip Circumference is not Third_Category [-0.04] THEN Healthy 0.65
IF Origen is not Córdoba and Triglycerides is Top_Category_Pathological [-0.06] and Active Plasminogen Activator Inhibitor 1 is not Top_Category [0.145] THEN Unhealthy 0.01
IF Origen is Santiago and Age is Early childhood [0.02] and Hip Circumference is Third_Category [-0.19] THEN Unhealthy 0.02
IF Origen is Santiago and BMI z-score is not Overweight [-0.16] and Ferritin__ng_ml is Third_Category [0.13] THEN Unhealthy 0.01
IF Origen is Santiago and Aspartate Aminotransferase is not Forth_Category [-0.17] and Soluble Intercellular Adhesion Molecule-1 is Third_Category [0.03] THEN Unhealthy 0.01
IF Origen is Zaragoza and Total Plasminogen Activator Inhibitor 1 is Forth_Category [-0.06] THEN Unhealthy 0.02
IF Origen is Zaragoza and Triglycerides is Third_Category_Normal [0.22] and Total Plasminogen Activator Inhibitor 1 is Second_Category [-0.05] THEN Unhealthy 0.02
IF Origen is Zaragoza and Triglycerides is Third_Category_Normal [-0.08] and Active plasminogen activator inhibitor 1 is not Second_Category [0.05] THEN Unhealthy 0.01
IF Origen is not Zaragoza and Apolipoprotein A is not Second_Category_Normal [0.17] and Aspartate aminotransferase is Second_Category [0.11] THEN Unhealthy 0.03
IF Origen is not Zaragoza and Apolipoprotein A is Third_Category_Normal [0.15] and Aspartate aminotransferase is Second_Category [-0.11] THEN Unhealthy 0.03
IF Age is Late childhood [0.19] and BMI z-score is Severe Overweight [0.01] and Total Plasminogen Activator Inhibitor 1 is Third_Category [0.03] THEN Unhealthy 0.01
IF BMI z-score is not Normal-weight [0.18] and Glucose is Top_Category_Pathological [-0.21] and HOMA-IR is Third_Category_Pathological [0.11] THEN Unhealthy 0.01
IF BMI z-score is Overweight [0.09] and HOMA-IR is Third_Category_Pathological [0.06] and Uric acid is Second_Category [0.24] THEN Unhealthy 0.02
IF BMI z-score is Severe Overweight [-0.07] and Uric acid is not Forth_Category [-0.15] and Total Plasminogen Activator Inhibitor 1 is Third_Category [0.08] THEN Unhealthy 0.01
IF Uric acid is not Second_Category [-0.06] and Adiponectin is Third_Category [0.03] and Tumor necrosis factor is Third_Category [0.02] THEN Unhealthy 0.01

Data Base

Fuzzy Partitions

This figure can be downloaded in pdf format here.