Complete results and additional material for the article “UnPART: PART without the 'partial' condition of it”

2018-11-05

 

This page contains the full tables related to the work presented in the article:

Igor Ibarguren, Jesús M. Pérez, Javier Muguerza, Ibai Gurrutxaga and Olatz Arbelaitz.  
"UnPART: PART without the 'partial' condition of it". Information Sciences (2018). Vol. 465, pp 505-522.

doi:10.1016/j.ins.2018.07.022

 First, we present the table with the characteristics for the 96 datasets used in this study, divided into three contexts.

Then, for each of the evaluation measures, we include the full tables of the results related to the different proposed PART-like algorithm and their base decision trees, companion figures for the statistical significance, and pair-wise p-value tables.

 

All the tables of results can be downloaded as an Excel document or as a CSV file.

 

Content

1. Datasets characteristics. 2

2. Results for the C4.5-based and CHAID*-based algorithms for all 6 metrics over each dataset context. 5

 

Index of Tables

Table 1. Description of standard datasets. 3

Table 2. Description of imbalanced datasets. 3

Table 3. Kappa values for the C4.5-based and CHAID*-based algorithms for each of the 30 standard datasets  5

Table 4. GM values for the C4.5-based and CHAID*-based algorithms for each of the 33 imbalanced datasets  6

Table 5. GM values for the C4.5-based and CHAID*-based algorithms for each of the 33 SMOTE-preprocessed imbalanced datasets  6

Table 6. p-values adjusted with the Bergman-Hommel post-hoc procedure for the C4.5-based and CHAID*-based algorithms for the Kappa and GM measures. 7

Table 7. AUC values for the C4.5-based and CHAID*-based algorithms for each of the 30 standard datasets  8

Table 8. AUC values for the C4.5-based and CHAID*-based algorithms for each of the 33 imbalanced datasets  9

Table 9. AUC values for the C4.5-based and CHAID*-based algorithms for each of the 33 SMOTE-preprocessed imbalanced datasets  10

Table 10. p-values adjusted with the Bergman-Hommel post-hoc procedure for the C4.5-based and CHAID*-based algorithms for the AUC measure. 11

Table 15. Length values for the C4.5-based and CHAID*-based algorithms for each of the 30 standard datasets  12

Table 16. Length values for the C4.5-based and CHAID*-based algorithms for each of the 33 imbalanced datasets  13

Table 17. Length values for the C4.5-based and CHAID*-based algorithms for each of the 33 SMOTE-preprocessed imbalanced datasets. 14

Table 18. p-values adjusted with the Bergman-Hommel post-hoc procedure for the C4.5-based and CHAID*-based algorithms for the Length measure. 15

Table 11. Number of Rules multiplied by Length values for the C4.5-based and CHAID*-based algorithms for each of the 30 standard datasets. 15

Table 12. Number of Rules multiplied by Length values for the C4.5-based and CHAID*-based algorithms for each of the 33 imbalanced datasets. 16

Table 13. Number of Rules values multiplied by Length for the C4.5-based and CHAID*-based algorithms for each of the 33 SMOTE-preprocessed imbalanced datasets. 17

Table 14. p-values adjusted with the Bergman-Hommel post-hoc procedure for the C4.5-based and CHAID*-based algorithms for the Number of Rules multiplied by Length. 18

Table 19. Time values for the C4.5-based and CHAID*-based algorithms for each of the 30 standard datasets  19

Table 20. Time values for the C4.5-based and CHAID*-based algorithms for each of the 33 imbalanced datasets  20

Table 21. Time values for the C4.5-based and CHAID*-based algorithms for each of the 33 SMOTE-preprocessed imbalanced datasets. 21

Table 22. p-values adjusted with the Bergman-Hommel post-hoc procedure for the C4.5-based and CHAID*-based algorithms for the Time measure. 22

 

Index of Figures

Figure 1. Friedman Aligned Ranks for the C4.5-based and CHAID*-based algorithms for the Kappa and GM measures  8

Figure 2. Friedman Aligned Ranks for the C4.5-based and CHAID*-based algorithms for the AUC measure  12

Figure 4. Friedman Aligned Ranks for the C4.5-based and CHAID*-based algorithms for the Length measure  15

Figure 3. Friedman Aligned Ranks for the C4.5-based and CHAID*-based algorithms for the Number of Rules multiplied by Length  19

Figure 5. Friedman Aligned Ranks for the C4.5-based and CHAID*-based algorithms for the Time measure  22

 

1. Datasets characteristics

This section contains the tables with the characteristics for the 96 datasets from the KEEL repository used in this study. First we present the datasets from the first (Standard) context and then from the second (Imbalanced) context. SMOTE-preprocessed datasets have have the same characteristics as the datasets from Table 2, but the minority class oversampled until it has the majority class’ size.

 

Table 1. Description of standard datasets.¡Error! Marcador no definido.

Data set

#Ants

#Examples

#Classes

%min

%maj

Size Of Min. Class

Size of Maj. Class

lymphography

18

148

4

1.36%

54.73%

2

81

ecoli

7

336

8

0.6%

42.56%

2

143

car

6

1728

4

3.77%

70.03%

65

1210

nursery

8

1296

5

0.08%

33.34%

1

432

cleveland

13

297

5

4.38%

53.88%

13

160

zoo

17

101

7

3.97%

40.6%

4

41

glass

9

214

6

4.21%

35.52%

9

76

flare

10

1066

6

4.04%

31.06%

43

331

abalone

8

418

22

0.24%

16.51%

1

69

balance

4

625

3

7.84%

46.08%

49

288

dermatology

33

358

6

5.59%

31.01%

20

111

hepatitis

19

80

2

16.25%

83.75%

13

67

newthyroid

5

215

3

13.96%

69.77%

30

150

haberman

3

306

2

26.48%

73.53%

81

225

breast

9

277

2

29.25%

70.76%

81

196

german

20

1000

2

30%

70%

300

700

wisconsin

9

630

2

34.61%

65.4%

218

412

contraceptive

9

1473

3

22.61%

42.71%

333

629

 

tictactoe

9

958

2

34.66%

65.35%

332

626

pima

8

768

2

34.9%

65.11%

268

500

magic

10

1902

2

35.13%

64.88%

668

1234

wine

13

178

3

26.97%

39.89%

48

71

bupa

6

345

2

42.03%

57.98%

145

200

heart

13

270

2

44.45%

55.56%

120

150

australian

14

690

2

44.5%

55.51%

307

383

crx

15

653

2

45.33%

54.68%

296

357

vehicle

18

846

4

23.53%

25.77%

199

218

penbased

16

1100

10

9.55%

10.46%

105

115

ring

20

740

2

49.6%

50.41%

367

373

iris

4

150

3

33.34%

33.34%

50

50

Mean

11.77

638.93

4.27

21%

50%

139

319.93

Median

9.5

521.5

3

23%

54%

73

209

 

 

Table 2. Description of imbalanced datasets.

Data set

#Atts.

#Examples

Imbalance

Size Of Min. Class

Size of Maj. Class

Abalone19

8

4174

0.77%

32

4142

Yeast6

8

1484

2.49%

37

1447

Yeast5

8

1484

2.96%

44

1440

Yeast4

8

1484

3.43%

51

1433

Yeast2vs8

8

482

4.15%

20

462

Glass5

9

214

4.2%

9

205

Abalone9vs18

8

731

5.65%

41

690

Glass4

9

214

6.07%

13

201

Ecoli4

7

336

6.74%

23

313

Glass2

9

214

8.78%

19

195

Vowel0

13

988

9.01%

89

899

Page-blocks0

10

5472

10.23%

560

4912

Ecoli3

7

336

10.88%

37

299

Yeast3

8

1484

10.98%

163

1321

Glass6

9

214

13.55%

29

185

Segment0

19

2308

14.26%

329

1979

Ecoli2

7

336

15.48%

52

284

New-thyroid1

5

215

16.28%

35

180

New-thyroid2

5

215

16.89%

36

179

Ecoli1

7

336

22.92%

77

259

Vehicle0

18

846

23.64%

200

646

Glass0123vs456

9

214

23.83%

51

163

Haberman

3

306

27.42%

84

222

Vehicle1

18

846

28.37%

240

606

Vehicle2

18

846

28.37%

240

606

Vehicle3

18

846

28.37%

240

606

Yeast1

8

1484

28.91%

429

1055

Glass0

9

214

32.71%

70

144

Iris0

4

150

33.33%

50

100

Pima

8

768

34.84%

268

500

Ecoli0vs1

7

220

35%

77

143

Wisconsin

9

683

35%

239

444

Glass1

9

214

35.51%

76

138

Mean

9.39

919.94

17.61%

120

799.94

Median

8

482

15.48%

52

444

 

 

2. Results for the C4.5-based and CHAID*-based algorithms for all 6 metrics over each dataset context.

This section includes the full tables of the results related to the C4.5-based and CHAID*-based algorithms (UnPART, BFPART, PART, and C4.5/CHAID*) for the six performance metrics used in the study: Kappa, GM, AUC, Number of Rules, Length, and Time. For Length the unit of measurement is the number of decisions per rule or tree branch. Computational cost is measured in milliseconds. Numbers in bold indicate the best value for that particular dataset.     In these tables we have treated C4.5 as reference for all algorithms, as it is the base for UnPART_C45, BFPART_C45, PART_C45, and the CHAID* algorithm also takes elements from C4.5. Cells with gray background indicate algorithms performing better than C4.5.

The figures used in the article to show the results of the statistical significance only show if the differences are significant at the .05 level, but do not show the actual p-values. In order to complement those figures, we include a table with all the pair-wise p-values for the Bergman-Hommel test. In these tables, the algorithms are ordered according to their Friedman Aligned Rank, from lowest to highest.

We also include a Figure for each global analysis for statistical significance performed in the article. Unlike the figures in the article, these graphically represent the differences between the Friedman Aligned Ranks for each algorithm.

2.1 Results for Kappa and GM measures

 

Table 3. Kappa values for the C4.5-based and CHAID*-based algorithms for each of the 30 standard datasets

 

C4.5-based

CHAID*-based

UnPART

BFPART

PART

C4.5

UnPART

BFPART

PART

CHAID*

lymphography

.5593

.5758

.4688

.5367

.5354

.5764

.6374

.5304

ecoli

.7359

.6986

.7289

.7030

.6981

.7065

.6814

.6805

car

.9033

.9068

.8894

.7986

.8924

.8900

.8971

.9076

nursery

.8424

.8482

.8753

.8341

.8478

.8477

.8947

.8684

cleveland

.2789

.2187

.2444

.2257

.2738

.2390

.2366

.2256

zoo

.9215

.9215

.9215

.9215

.9218

.9218

.9218

.9398

glass

.5394

.5526

.6076

.5494

.5085

.5085

.5124

.5391

flare

.6668

.6751

.6470

.6676

.6707

.6559

.6613

.6893

abalone

.1035

.0918

.0683

.0962

.1314

.1326

.1497

.1533

balance

.6447

.6447

.6494

.5922

.6175

.6209

.6262

.5996

dermatology

.9226

.9226

.9226

.9045

.9335

.9335

.9300

.9383

hepatitis

.2520

.2520

.5485

.1115

.1330

.0899

.2285

.1908

newthyroid

.8795

.8795

.8525

.8519

.8618

.8618

.8618

.8686

haberman

.1186

.1186

.0924

.1521

.0265

.0265

.0265

.0265

breast

.2418

.2418

.2300

.2330

.2970

.2970

.2663

.2970

german

.3124

.3243

.3333

.3049

.3158

.3150

.2705

.2714

wisconsin

.8474

.8474

.8236

.8515

.8699

.8556

.8907

.8410

contraceptive

.2816

.2641

.2356

.2845

.2815

.2896

.2778

.2909

tictactoe

.7803

.7573

.8430

.6770

.6817

.6789

.7847

.7605

pima

.3814

.3814

.4078

.4175

.4051

.4051

.3893

.4043

magic

.5186

.5190

.4806

.5183

.5034

.4979

.4871

.5266

wine

.8969

.8969

.8971

.9222

.8795

.8795

.8966

.8797

bupa

.2867

.2701

.2594

.3124

.2613

.2613

.2424

.2444

heart

.5703

.5384

.5239

.5636

.6225

.6537

.6537

.5489

australian

.7156

.7063

.6742

.6886

.6845

.6851

.6681

.6837

crx

.7371

.7184

.6651

.7194

.7354

.7194

.7116

.7172

vehicle

.6421

.6248

.6452

.6185

.5789

.5707

.5969

.5902

penbased

.8818

.8889

.8737

.8838

.8331

.8311

.8355

.8373

ring

.7702

.7702

.7623

.7135

.7482

.7420

.7420

.7482

iris

.9100

.9100

.9000

.9000

.9200

.9200

.9200

.9200

Mean

.6047

.5989

.6024

.5851

.5890

.5871

.5966

.5906

Median

.6557

.6599

.6482

.6431

.6466

.6548

.6575

.6400

This table can be downloaded as an Excel document or as a CSV file by clicking on the following links xls and csv.

 

 

Table 4. GM values for the C4.5-based and CHAID*-based algorithms for each of the 33 imbalanced datasets

 

C4.5-based

CHAID*-based

UnPART

BFPART

PART

C4.5

UnPART

BFPART

PART

CHAID*

abalone19

.0000

.0000

.0000

.0000

.0000

.0000

.0000

.0000

yeast6

.5660

.5660

.7333

.5660

.1302

.1302

.2359

.1302

yeast5

.8846

.8742

.8850

.8612

.7967

.7957

.8601

.7715

yeast4

.4731

.4731

.4239

.4208

.3844

.3844

.2326

.3844

yeast-2_vs_8

.3137

.1704

.1704

.1723

.7274

.7274

.7264

.7274

glass5

.8787

.8787

.8787

.8804

.9876

.9876

.9876

.9876

abalone9-18

.4173

.3897

.4157

.3882

.2983

.2983

.2930

.2975

glass4

.5836

.5836

.5836

.5769

.3397

.3397

.3397

.3030

ecoli4

.7791

.7791

.7786

.7777

.7821

.7821

.8405

.8123

glass2

.4597

.4597

.4597

.4427

.0000

.0000

.0000

.0000

vowel0

.9149

.9149

.9207

.9683

.8552

.9112

.9194

.8722

page-blocks0

.9136

.8944

.8932

.9225

.8879

.9001

.9096

.9002

ecoli3

.7227

.7227

.7290

.6773

.7003

.7003

.7003

.6749

yeast3

.8567

.8567

.8097

.8479

.8537

.8537

.8552

.8670

glass6

.7940

.7940

.7874

.7940

.7946

.7946

.7946

.7920

segment0

.9858

.9858

.9893

.9814

.9794

.9796

.9867

.9829

ecoli2

.8041

.8041

.7963

.8497

.7564

.7564

.7564

.7564

new-thyroid1

.9394

.9394

.9394

.9460

.9529

.9529

.9529

.9503

new-thyroid2

.9206

.9206

.9206

.9327

.9328

.9328

.9328

.9355

ecoli1

.8590

.8590

.8411

.8538

.8062

.8062

.8062

.8221

vehicle0

.9029

.9242

.9267

.9378

.9209

.9213

.8902

.9023

glass-0-1-2-3_vs_4-5-6

.8711

.8711

.8682

.9210

.8638

.8660

.8576

.8766

haberman

.3252

.3252

.2876

.3563

.0931

.0931

.0931

.0931

vehicle1

.6362

.6112

.3773

.6512

.5063

.4975

.5113

.5033

vehicle2

.9421

.9514

.9499

.9453

.9234

.9284

.9394

.9221

vehicle3

.6581

.6489

.5071

.6728

.5250

.4651

.4939

.5542

yeast1

.6093

.6093

.5333

.6276

.6048

.6068

.5996

.5889

glass0

.7703

.7742

.7967

.7845

.7726

.7726

.7752

.7726

iris0

.9897

.9897

.9897

.9897

.9897

.9897

.9897

.9897

pima

.6724

.6795

.6973

.7023

.6879

.6879

.6709

.6953

ecoli-0_vs_1

.9831

.9831

.9723

.9831

.9831

.9831

.9831

.9831

wisconsin

.9365

.9345

.9347

.9315

.9445

.9561

.9521

.9411

glass1

.7065

.6974

.6503

.7198

.6493

.6732

.6732

.6278

Mean

.7294

.7232

.7105

.7298

.6797

.6810

.6836

.6793

Median

.7940

.7940

.7963

.7940

.7821

.7821

.7946

.7726

This table can be downloaded as an Excel document or as a CSV file by clicking on the following links xls and csv.

 

 

 

Table 5. GM values for the C4.5-based and CHAID*-based algorithms for each of the 33 SMOTE-preprocessed imbalanced datasets

 

C4.5-based

CHAID*-based

UnPART

BFPART

PART

C4.5

UnPART

BFPART

PART

CHAID*

abalone19

.0806

.0811

.1560

.1558

.0809

.1624

.1625

.1600

yeast6

.8042

.8042

.7855

.8048

.6794

.6122

.6283

.5637

yeast5

.9210

.9210

.9198

.9445

.8428

.8571

.7098

.7987

yeast4

.6952

.6782

.6954

.6521

.6151

.6814

.6043

.5417

yeast-2_vs_8

.7313

.7323

.7171

.7402

.7047

.6653

.6607

.6509

glass5

.9274

.9274

.9249

.8720

.9242

.6687

.8688

.9266

abalone9-18

.5534

.5845

.5773

.5319

.6157

.6260

.6714

.5169

glass4

.8406

.8406

.8406

.8443

.6714

.7097

.7097

.6673

ecoli4

.8184

.8184

.8468

.7410

.8123

.7712

.9060

.8142

glass2

.6600

.6600

.6754

.6500

.6053

.4813

.4993

.6873

vowel0

.9367

.9311

.8956

.9357

.8831

.8639

.8343

.8452

page-blocks0

.9435

.9439

.9438

.9428

.9291

.9374

.9317

.9174

ecoli3

.8338

.8338

.8387

.7442

.8108

.7867

.8200

.8365

yeast3

.8783

.8790

.8939

.8843

.8994

.8867

.9034

.8996

glass6

.8868

.8868

.8255

.8662

.8596

.8596

.8454

.8019

segment0

.9891

.9891

.9878

.9944

.9919

.9924

.9880

.9921

ecoli2

.8452

.8577

.8797

.8809

.8599

.9024

.8949

.8785

new-thyroid1

.9741

.9741

.9713

.9741

.9624

.9624

.9651

.9624

new-thyroid2

.9473

.9445

.9449

.9677

.9888

.9888

.9647

.9916

ecoli1

.9222

.9031

.8923

.9125

.8837

.8837

.8838

.9111

vehicle0

.9294

.9302

.9247

.9139

.9243

.9163

.9102

.9018

glass-0-1-2-3_vs_4-5-6

.8898

.8898

.8688

.8668

.9085

.8825

.8887

.8922

haberman

.6189

.6085

.6381

.6074

.5368

.5368

.5368

.5368

vehicle1

.7227

.7033

.7367

.6838

.7526

.7501

.7239

.7156

vehicle2

.9649

.9649

.9695

.9486

.9508

.9464

.9262

.9398

vehicle3

.7297

.7292

.7183

.7085

.7454

.7542

.7514

.7477

yeast1

.7012

.6972

.6881

.7135

.6988

.6983

.7086

.7199

glass0

.7617

.7617

.7617

.7726

.7913

.7913

.7906

.7916

iris0

.9897

.9897

.9897

.9897

.9897

.9897

.9897

.9897

pima

.7174

.7145

.6840

.7128

.7025

.7028

.7268

.6980

ecoli-0_vs_1

.9760

.9760

.9760

.9725

.9831

.9831

.9831

.9831

wisconsin

.9436

.9436

.9434

.9454

.9362

.9662

.9552

.9393

glass1

.7002

.7002

.7158

.7480

.6885

.6885

.6811

.6902

Mean

.8132

.8121

.8129

.8068

.7948

.7850

.7886

.7851

Median

.8452

.8577

.8468

.8662

.8428

.7913

.8343

.8142

This table can be downloaded as an Excel document or as a CSV file by clicking on the following links xls and csv.

 

 

 

 

Table 6. p-values adjusted with the Bergman-Hommel post-hoc procedure for the C4.5-based and CHAID*-based algorithms for the Kappa and GM measures

 

BFPART_C45

C4.5

PART_C45

PART_CHD

BFPART_CHD

UnPART_CHD

CHAID*

UnPART_C45

1

1

.7081598

.0007771

.0001318

.0001198

.0000982

BFPART_C45

1

1

.0043687

.0007936

.0007771

.0007018

C4.5

1

.0773584

.0173961

.0173961

.0173961

PART_C45

.2244410

.0773584

.0773584

.0773584

PART_CHD

1

1

1

BFPART_CHD

1

1

UnPART_CHD

 

 

 

 

 

 

1

 

 

 

 

Figure 1. Friedman Aligned Ranks for the C4.5-based and CHAID*-based algorithms for the Kappa and GM measures

 

 

 

2.2 Results for the AUC measure

 

Table 7. AUC values for the C4.5-based and CHAID*-based algorithms for each of the 30 standard datasets

 

C4.5-based

CHAID*-based

UnPART

BFPART

PART

C4.5

UnPART

BFPART

PART

CHAID*

lymphography

.8402

.8192

.7544

.8193

.8369

.8363

.8459

.8163

ecoli

.9048

.8818

.8980

.8780

.9099

.9132

.9036

.9125

car

.9870

.9870

.9858

.9681

.9843

.9844

.9898

.9914

nursery

.9678

.9709

.9723

.9610

.9736

.9741

.9828

.9781

cleveland

.7082

.6549

.6695

.6604

.7346

.7225

.7614

.7161

zoo

.9804

.9804

.9804

.9814

.9860

.9860

.9860

.9869

glass

.7832

.7922

.8201

.8230

.8009

.8009

.7992

.7777

flare

.9177

.9243

.9096

.9154

.9225

.9212

.9213

.9251

abalone

.5820

.5878

.5525

.5668

.6824

.6823

.6878

.6847

balance

.8616

.8616

.8953

.8359

.8466

.8606

.8604

.8328

dermatology

.9667

.9667

.9667

.9572

.9839

.9762

.9751

.9707

hepatitis

.6860

.6860

.7744

.4690

.6001

.5858

.6735

.6103

newthyroid

.9318

.9318

.9300

.9331

.9177

.9177

.9177

.9290

haberman

.5700

.5700

.5883

.5714

.5117

.5117

.5390

.5171

breast

.6299

.6299

.6096

.6016

.6709

.6709

.6487

.6712

german

.7028

.7149

.6961

.6643

.7094

.7091

.7179

.6815

wisconsin

.9540

.9540

.9587

.9323

.9381

.9614

.9623

.9370

contraceptive

.6896

.6894

.6485

.6683

.6896

.6878

.7100

.6935

tictactoe

.9397

.9313

.9722

.9002

.8952

.8991

.9352

.9275

pima

.7574

.7574

.7688

.7529

.7444

.7501

.7751

.7550

magic

.8165

.8149

.8113

.7655

.8003

.7974

.7956

.7999

wine

.9469

.9469

.9522

.9609

.9473

.9473

.9442

.9381

bupa

.6709

.6418

.6536

.6897

.6502

.6502

.6345

.6567

heart

.7651

.7706

.7894

.8021

.8166

.8381

.8395

.8019

australian

.8762

.8548

.8400

.8578

.8646

.8925

.9033

.8745

crx

.9059

.8964

.8772

.8664

.8739

.8821

.8969

.8781

vehicle

.8833

.8751

.8789

.8462

.8752

.8704

.8798

.8761

penbased

.9448

.9487

.9458

.9523

.9476

.9426

.9481

.9436

ring

.8990

.8990

.8739

.8489

.8742

.8714

.8714

.8776

iris

.9640

.9640

.9687

.9538

.9683

.9683

.9683

.9577

Mean

.8345

.8301

.8314

.8134

.8319

.8337

.8425

.8306

Median

.8797

.8684

.8755

.8475

.8693

.8709

.8756

.8753

This table can be downloaded as an Excel document or as a CSV file by clicking on the following links xls and csv.

 

 

Table 8. AUC values for the C4.5-based and CHAID*-based algorithms for each of the 33 imbalanced datasets

 

C4.5-based

CHAID*-based

UnPART

BFPART

PART

C4.5

UnPART

BFPART

PART

CHAID*

abalone19

.5000

.5000

.5000

.5000

.5000

.5000

.5001

.5000

yeast6

.7846

.7846

.8542

.7855

.5798

.5798

.6040

.5798

yeast5

.9692

.9694

.9469

.9584

.8248

.8237

.8782

.8242

yeast4

.7583

.7583

.8651

.7799

.7381

.7381

.8107

.7381

yeast-2_vs_8

.6239

.5818

.6057

.5718

.7728

.7728

.7704

.7720

glass5

.9927

.9927

.9927

.9951

.9878

.9878

.9878

.9878

abalone9-18

.6831

.7312

.7218

.6547

.6384

.6384

.6847

.6371

glass4

.6517

.6517

.6517

.6925

.6046

.6046

.6046

.5988

ecoli4

.7659

.7659

.8401

.7643

.8187

.8187

.8866

.8655

glass2

.7724

.7724

.7780

.7535

.4975

.4975

.4975

.4975

vowel0

.9449

.9405

.9393

.9706

.8970

.9464

.9320

.8865

page-blocks0

.9765

.9764

.9604

.9595

.9624

.9647

.9654

.9552

ecoli3

.7726

.7726

.8412

.7638

.9071

.9071

.9071

.9014

yeast3

.9132

.9132

.9388

.9054

.9144

.9144

.9081

.9088

glass6

.7914

.7914

.8171

.7914

.7895

.7895

.7895

.7873

segment0

.9860

.9860

.9901

.9844

.9774

.9776

.9904

.9832

ecoli2

.8296

.8296

.8296

.8459

.8288

.8288

.7824

.7966

new-thyroid1

.9548

.9548

.9548

.9655

.9544

.9544

.9544

.9516

new-thyroid2

.9349

.9349

.9349

.9472

.9345

.9345

.9345

.9373

ecoli1

.9131

.9159

.9347

.8807

.9356

.9356

.9356

.9223

vehicle0

.9297

.9544

.9477

.9468

.9460

.9483

.9352

.9490

glass-0-1-2-3_vs_4-5-6

.9005

.9005

.8894

.9209

.9564

.9564

.9583

.9284

haberman

.5700

.5700

.5883

.5714

.5117

.5117

.5390

.5117

vehicle1

.6864

.7123

.7383

.7099

.6718

.6786

.7085

.6751

vehicle2

.9448

.9489

.9448

.9398

.9632

.9584

.9530

.9564

vehicle3

.7628

.7666

.8012

.7357

.7455

.7516

.7857

.7788

yeast1

.7083

.7134

.7425

.7017

.6768

.6746

.7036

.7007

glass0

.7780

.7834

.8231

.8119

.7992

.7992

.7789

.8004

iris0

.9900

.9900

.9900

.9900

.9900

.9900

.9900

.9900

pima

.7604

.7574

.7688

.7529

.7462

.7501

.7751

.7550

ecoli-0_vs_1

.9832

.9832

.9726

.9832

.9832

.9832

.9832

.9832

wisconsin

.9647

.9651

.9666

.9700

.9593

.9606

.9571

.9632

glass1

.7112

.7170

.6984

.7192

.6977

.6831

.6831

.6882

Mean

.8245

.8268

.8415

.8250

.8094

.8109

.8205

.8094

Median

.7914

.7914

.8542

.8119

.8248

.8237

.8782

.8242

This table can be downloaded as an Excel document or as a CSV file by clicking on the following links xls and csv.

 

 

Table 9. AUC values for the C4.5-based and CHAID*-based algorithms for each of the 33 SMOTE-preprocessed imbalanced datasets

 

C4.5-based

CHAID*-based

UnPART

BFPART

PART

C4.5

UnPART

BFPART

PART

CHAID*

abalone19

.5640

.6000

.5299

.5363

.5778

.6585

.5965

.6054

yeast6

.8677

.8677

.8561

.8490

.8023

.7879

.8001

.7078

yeast5

.9633

.9633

.9312

.9646

.9043

.8819

.7965

.8122

yeast4

.8557

.8426

.8494

.8107

.8293

.8253

.7932

.7136

yeast-2_vs_8

.7756

.7761

.8423

.7259

.7326

.7249

.7454

.6726

glass5

.9415

.9415

.9415

.8890

.9220

.8646

.8829

.9402

abalone9-18

.7274

.7436

.6611

.6579

.6308

.6973

.7252

.5543

glass4

.8583

.8583

.8583

.8621

.7173

.7490

.7490

.6848

ecoli4

.8485

.8485

.8874

.7783

.8425

.8270

.9111

.8021

glass2

.7360

.7360

.7703

.7325

.6801

.6288

.6349

.7195

vowel0

.9395

.9439

.9046

.9523

.8859

.8751

.8830

.8582

page-blocks0

.9727

.9759

.9697

.9582

.9678

.9731

.9682

.9549

ecoli3

.8929

.8929

.8793

.7989

.8874

.8696

.8722

.8635

yeast3

.9345

.9348

.9340

.9158

.9387

.9277

.9478

.9290

glass6

.8323

.8323

.8073

.8908

.8386

.8386

.8759

.7245

segment0

.9883

.9883

.9895

.9941

.9917

.9916

.9892

.9954

ecoli2

.8906

.8834

.8957

.8768

.8447

.8855

.8979

.8909

new-thyroid1

.9802

.9802

.9718

.9802

.9603

.9603

.9659

.9615

new-thyroid2

.9516

.9536

.9460

.9714

.9865

.9865

.9794

.9921

ecoli1

.9235

.9028

.9133

.9261

.9160

.9129

.9258

.9282

vehicle0

.9459

.9448

.9355

.9320

.9469

.9329

.9363

.9303

glass-0-1-2-3_vs_4-5-6

.8971

.8971

.8714

.8953

.9261

.8766

.9027

.9223

haberman

.6243

.6510

.6518

.6262

.6031

.6031

.5992

.6081

vehicle1

.7638

.7335

.7814

.6967

.7836

.7826

.7650

.7536

vehicle2

.9623

.9666

.9708

.9600

.9608

.9524

.9556

.9525

vehicle3

.7807

.7858

.7708

.7378

.7720

.7820

.7924

.7837

yeast1

.7507

.7550

.7523

.7362

.7160

.7210

.7487

.7607

glass0

.7673

.7686

.7686

.7716

.7802

.7802

.7858

.8134

iris0

.9900

.9900

.9900

.9900

.9900

.9900

.9900

.9900

pima

.7686

.7618

.7511

.7374

.7431

.7464

.7760

.7514

ecoli-0_vs_1

.9762

.9762

.9762

.9728

.9832

.9832

.9832

.9832

wisconsin

.9725

.9725

.9738

.9706

.9527

.9760

.9682

.9488

glass1

.7175

.7175

.7490

.7717

.7005

.7005

.7058

.7170

Mean

.8594

.8602

.8570

.8445

.8398

.8392

.8439

.8250

Median

.8906

.8834

.8793

.8768

.8447

.8646

.8759

.8134

This table can be downloaded as an Excel document or as a CSV file by clicking on the following links xls and csv.

 

 

 

 

Table 10. p-values adjusted with the Bergman-Hommel post-hoc procedure for the C4.5-based and CHAID*-based algorithms for the AUC measure

 

UnPART_C45

BFPART_C45

PART_CHD

BFPART_CHD

UnPART_CHD

C4.5

CHAID*

PART_C45

1

1

1

.0275614

.0150307

.0147886

.0046853

UnPART_C45

1

1

.0349476

.0150307

.0150307

.0051593

BFPART_C45

1

.0349476

.0173031

.0173031

.0064811

PART_CHD

.1460833

.0778909

.0778909

.0349476

BFPART_CHD

1

1

1

UnPART_CHD

1

1

C4.5

 

 

 

 

 

 

1

 

 

 

 

Figure 2. Friedman Aligned Ranks for the C4.5-based and CHAID*-based algorithms for the AUC measure

 

 

2.3 Results for the Length measure

 

Table 11. Length values for the C4.5-based and CHAID*-based algorithms for each of the 30 standard datasets

 

C4.5-based

CHAID*-based

UnPART

BFPART

PART

C4.5

UnPART

BFPART

PART

CHAID*

lymphography

2.10

2.05

2.34

3.68

2.30

2.52

2.46

2.99

ecoli

2.84

2.57

2.46

5.36

4.02

4.11

4.56

4.69

car

2.36

2.38

2.30

4.62

2.31

2.35

2.98

5.17

nursery

1.93

2.04

2.27

4.10

2.19

2.18

3.23

4.35

cleveland

4.03

3.94

3.77

6.61

2.06

2.00

2.75

3.50

zoo

1.55

1.55

1.25

3.76

1.77

1.76

1.76

2.51

glass

2.97

3.02

2.78

5.55

2.93

2.93

3.10

3.88

flare

1.64

1.57

2.68

3.33

1.36

2.61

3.06

1.77

abalone

4.83

5.03

3.98

7.67

3.62

4.03

4.30

5.02

balance

2.18

2.18

2.98

6.06

1.89

2.04

2.69

4.00

dermatology

2.38

2.38

2.38

3.90

2.59

3.09

3.43

4.71

hepatitis

1.28

1.28

1.45

2.48

.99

1.09

1.25

1.88

newthyroid

1.58

1.62

1.69

3.42

2.00

2.16

2.16

3.17

haberman

.63

.63

1.23

1.26

.20

.20

.30

.43

breast

.80

.80

1.94

2.11

.79

.79

1.25

2.24

german

2.48

2.30

2.68

5.27

1.41

1.39

2.46

3.56

wisconsin

.93

.93

.98

1.78

.99

1.30

2.00

1.93

contraceptive

6.06

4.88

5.14

10.14

2.80

2.98

3.63

4.57

tictactoe

2.31

2.30

2.70

4.49

2.13

2.13

2.82

4.94

pima

1.90

1.90

1.93

5.55

1.65

1.63

2.05

3.15

magic

2.32

2.31

2.68

6.94

2.32

2.48

3.61

3.60

wine

1.29

1.29

1.14

2.45

2.05

2.05

2.25

3.13

bupa

2.00

2.18

2.22

5.74

.93

.93

1.42

2.16

heart

1.56

1.59

2.48

3.74

1.26

1.34

2.02

3.17

australian

2.09

2.24

3.47

6.27

1.05

1.89

2.65

2.20

crx

1.58

1.53

2.41

4.54

1.07

1.61

2.71

2.36

vehicle

4.45

4.42

3.47

7.62

3.88

4.02

4.61

6.19

penbased

3.82

3.84

3.31

6.86

6.44

6.50

6.90

7.39

ring

3.58

3.58

2.61

8.64

7.02

8.14

8.14

7.95

iris

.95

.95

.92

2.35

1.02

1.20

1.20

2.36

Mean

2.35

2.31

2.46

4.88

2.23

2.45

2.93

3.63

Median

2.10

2.18

2.44

4.58

2.03

2.09

2.70

3.34

This table can be downloaded as an Excel document or as a CSV file by clicking on the following links xls and csv.

 

 

Table 12. Length values for the C4.5-based and CHAID*-based algorithms for each of the 33 imbalanced datasets

 

C4.5-based

CHAID*-based

UnPART

BFPART

PART

C4.5

UnPART

BFPART

PART

CHAID*

abalone19

.00

.00

.00

.00

.00

.00

.30

.00

yeast6

.89

.89

1.17

2.77

.15

.15

.28

.45

yeast5

1.17

1.25

1.39

4.65

.95

1.00

1.20

2.50

yeast4

1.13

1.13

1.71

3.81

.68

.68

1.14

1.90

yeast-2_vs_8

.20

.60

.73

.65

.90

.90

1.17

1.53

glass5

.75

.75

.75

2.25

.67

.67

.67

1.67

abalone9-18

1.09

1.07

1.62

3.06

.83

.83

1.17

1.50

glass4

1.17

1.17

1.17

2.73

.80

.80

.80

1.69

ecoli4

.87

.87

1.17

1.93

.97

1.02

1.73

2.11

glass2

1.18

1.18

1.34

3.51

.10

.10

.10

.20

vowel0

1.48

1.59

1.39

3.20

2.50

2.75

2.71

4.29

page-blocks0

3.49

3.58

3.40

6.68

3.61

4.17

5.60

5.86

ecoli3

1.00

1.00

1.05

2.96

.73

.73

.73

1.73

yeast3

1.50

1.50

2.04

4.39

.93

1.00

1.48

2.12

glass6

.80

.80

1.07

1.81

.87

.87

.87

1.92

segment0

1.72

1.72

1.72

3.70

1.55

1.59

2.40

4.06

ecoli2

1.35

1.35

1.36

3.56

1.20

1.20

1.90

2.69

new-thyroid1

1.27

1.27

1.27

2.80

1.02

1.02

1.02

2.37

new-thyroid2

.97

1.04

1.04

2.23

.93

.93

.93

2.25

ecoli1

1.06

1.09

1.37

3.31

1.33

1.33

1.47

2.32

vehicle0

2.21

2.39

2.31

6.83

2.33

2.33

2.76

4.87

glass-0-1-2-3_vs_4-5-6

1.23

1.23

1.52

2.80

1.36

1.35

1.47

2.37

haberman

.63

.63

1.23

1.26

.20

.20

.30

.40

vehicle1

3.20

4.01

3.05

6.93

1.16

1.24

2.06

2.64

vehicle2

2.05

2.26

2.22

5.00

2.49

2.49

2.99

4.45

vehicle3

4.05

4.06

2.64

8.34

1.76

1.92

2.76

3.22

yeast1

2.18

2.09

2.52

6.29

1.52

1.60

2.50

2.90

glass0

1.75

1.85

1.74

4.06

1.01

1.01

1.31

2.03

iris0

.50

.50

.50

1.00

.50

.50

.50

1.00

pima

1.95

1.90

1.93

5.55

1.66

1.63

2.05

3.15

ecoli-0_vs_1

.50

.50

.70

1.00

.50

.50

1.00

1.00

wisconsin

1.03

1.05

1.07

1.62

1.28

1.40

1.97

2.79

glass1

1.90

1.91

2.10

4.26

1.13

1.20

1.20

2.37

Mean

1.40

1.46

1.52

3.48

1.14

1.19

1.53

2.31

Median

1.17

1.18

1.37

3.20

.97

1.01

1.20

2.25

This table can be downloaded as an Excel document or as a CSV file by clicking on the following links xls and csv.

 

 

Table 13. Length values for the C4.5-based and CHAID*-based algorithms for each of the 33 SMOTE-preprocessed imbalanced datasets

 

C4.5-based

CHAID*-based

UnPART

BFPART

PART

C4.5

UnPART

BFPART

PART

CHAID*

abalone19

4.92

4.29

3.63

9.73

5.40

6.40

7.52

9.78

yeast6

2.80

2.89

2.55

5.69

4.34

4.71

6.25

6.98

yeast5

1.93

1.95

1.97

4.77

2.99

4.22

4.30

4.99

yeast4

3.97

4.20

3.21

7.42

4.83

4.92

5.04

7.58

yeast-2_vs_8

2.09

2.17

2.09

5.80

2.76

2.81

3.24

5.45

glass5

1.90

1.90

1.70

3.40

2.24

2.34

2.64

3.79

abalone9-18

3.54

3.84

2.88

7.48

2.97

3.05

3.52

5.71

glass4

1.83

1.83

1.83

3.99

2.08

2.75

2.80

3.26

ecoli4

1.61

1.61

1.65

4.10

1.85

2.18

2.17

3.58

glass2

2.29

2.29

2.46

6.68

2.54

2.60

2.93

4.53

vowel0

2.10

2.23

2.16

4.00

3.34

3.63

3.93

4.45

page-blocks0

5.08

5.04

3.76

9.40

5.03

5.36

6.25

8.01

ecoli3

1.80

1.80

1.86

5.04

2.20

2.33

2.05

3.86

yeast3

3.09

3.07

2.74

6.44

2.94

3.23

3.67

5.55

glass6

1.65

1.65

1.85

3.33

1.94

1.94

1.74

2.95

segment0

2.07

2.04

2.01

4.32

2.19

2.40

3.19

5.20

ecoli2

1.90

1.76

1.84

5.22

1.99

2.43

2.80

3.76

new-thyroid1

1.16

1.16

1.16

2.41

1.13

1.13

1.43

2.03

new-thyroid2

1.40

1.40

1.20

2.73

1.27

1.33

1.43

2.24

ecoli1

1.33

1.31

1.45

3.69

1.27

1.17

1.68

2.60

vehicle0

2.81

2.88

2.55

7.21

3.13

3.26

3.92

6.14

glass-0-1-2-3_vs_4-5-6

1.47

1.47

1.55

3.57

1.94

2.02

2.05

3.61

haberman

1.75

2.02

2.18

4.06

.68

.68

.87

1.52

vehicle1

5.38

5.75

3.69

8.56

2.63

2.76

3.88

5.41

vehicle2

2.49

2.49

2.71

5.11

2.83

3.10

3.85

4.81

vehicle3

4.79

5.11

3.02

10.30

2.89

3.05

4.05

5.48

yeast1

3.27

2.97

2.79

7.70

1.98

1.85

3.08

3.90

glass0

1.96

2.11

2.11

4.59

1.60

1.60

1.90

2.72

iris0

.50

.50

.50

1.00

.50

.50

.50

1.00

pima

2.60

2.37

2.67

6.16

1.70

1.72

1.94

3.39

ecoli-0_vs_1

.76

.76

.76

2.33

.60

.60

1.00

1.13

wisconsin

.98

.98

1.05

1.82

1.48

1.59

2.12

2.68

glass1

2.02

2.05

2.05

4.91

1.58

1.58

1.75

2.93

Mean

2.40

2.42

2.17

5.24

2.39

2.58

3.02

4.27

Median

2.02

2.05

2.09

4.91

2.19

2.40

2.80

3.86

This table can be downloaded as an Excel document or as a CSV file by clicking on the following links xls and csv.

 

 

 

 

Table 14. p-values adjusted with the Bergman-Hommel post-hoc procedure for the C4.5-based and CHAID*-based algorithms for the Length measure

 

UnPART_C45

BFPART_C45

BFPART_CHD

PART_C45

PART_CHD

CHAID*

C4.5

UnPART_CHD

.7961195

.7928757

.7928757

.3944330

4.65E-07

0

0

UnPART_C45

1

1

1

.0002222

0

0

BFPART_C45

1

1

.0003191

0

0

BFPART_CHD

1

.0004252

0

0

PART_C45

.0039008

0

0

PART_CHD

5.19E-08

0

CHAID*

 

 

 

 

 

 

.0467747

 

 

 

 

Figure 3. Friedman Aligned Ranks for the C4.5-based and CHAID*-based algorithms for the Length measure

 

 

2.4 Results for the Number of Rules by the Length of rules

 

Table 15. Number of Rules multiplied by Length values for the C4.5-based and CHAID*-based algorithms for each of the 30 standard datasets

 

C4.5-based

CHAID*-based

UnPART

BFPART

PART

C4.5

UnPART

BFPART

PART

CHAID*

lymphography

13.40

14.40

21.80

53.20

12.88

17.20

17.40

34.00

ecoli

34.80

27.00

35.20

104.20

26.40

27.80

31.00

62.08

car

90.20

92.60

121.80

527.80

54.88

56.40

83.60

249.60

nursery

52.00

58.00

113.80

268.80

39.60

39.80

70.20

163.80

cleveland

77.36

75.80

129.60

244.40

7.72

8.00

14.40

33.20

zoo

11.20

11.20

9.00

32.80

14.84

14.80

14.40

26.60

glass

36.40

36.40

44.80

123.00

16.80

16.80

18.20

39.32

flare

16.00

13.60

91.00

152.60

9.92

31.40

47.40

13.80

abalone

225.20

235.40

322.20

776.00

17.44

18.92

18.72

56.28

balance

26.80

26.80

97.60

224.40

13.00

12.60

19.60

58.00

dermatology

18.00

18.00

18.00

91.40

20.96

29.00

31.60

71.80

hepatitis

4.40

4.40

6.20

12.00

2.36

2.56

3.16

10.08

newthyroid

7.00

7.20

7.40

23.40

10.00

10.80

10.80

24.80

haberman

2.40

2.40

4.00

5.20

0.40

0.40

0.60

0.92

breast

3.20

3.20

28.60

28.60

3.00

3.00

4.00

9.40

german

44.40

34.60

161.00

343.80

6.80

7.80

17.00

54.00

wisconsin

4.80

4.80

8.40

57.40

4.80

6.80

8.40

13.00

contraceptive

203.00

149.80

737.60

1126.40

16.40

16.20

34.00

72.80

tictactoe

48.40

52.40

107.20

348.20

18.80

18.20

38.40

157.44

pima

12.20

12.20

14.40

125.20

6.92

7.20

9.20

24.60

magic

18.40

18.00

27.00

273.80

9.40

10.80

21.32

33.20

wine

5.40

5.40

4.80

12.80

8.60

8.60

9.00

24.40

bupa

17.20

18.20

15.40

148.80

3.20

3.20

4.20

9.60

heart

11.60

13.00

41.80

81.00

5.12

5.64

10.68

29.20

australian

25.00

26.00

93.40

130.00

5.00

10.40

14.20

13.52

crx

11.60

11.60

79.00

91.60

4.04

7.24

15.20

14.16

vehicle

91.40

98.60

109.20

477.80

44.44

45.88

65.60

231.84

penbased

91.20

90.80

96.20

343.20

145.64

145.68

163.88

453.04

ring

25.80

25.80

29.00

217.00

14.04

16.28

16.28

121.04

iris

3.00

3.00

4.00

10.20

3.20

3.60

3.60

10.00

Mean

41.06

39.69

85.98

215.17

18.22

20.10

27.20

70.52

Median

18.20

18.10

38.50

127.60

9.96

11.70

16.64

33.20

 

This table can be downloaded as an Excel document or as a CSV file by clicking on the following links xls and csv.

 

 

Table 16. Number of Rules multiplied by Length values for the C4.5-based and CHAID*-based algorithms for each of the 33 imbalanced datasets

 

C4.5-based

CHAID*-based

UnPART

BFPART

PART

C4.5

UnPART

BFPART

PART

CHAID*

abalone19

0.00

0.00

0.00

0.00

0.00

0.00

1.20

0.00

yeast6

4.20

4.20

5.60

17.40

0.60

0.60

1.00

1.80

yeast5

8.40

9.20

10.20

43.00

3.80

4.00

4.80

12.80

yeast4

6.00

6.00

12.40

35.40

2.80

2.80

4.00

9.00

yeast-2_vs_8

0.40

2.20

2.60

2.20

1.80

1.80

2.80

4.40

glass5

3.00

3.00

3.00

9.00

2.00

2.00

2.00

5.00

abalone9-18

5.40

5.60

13.60

27.40

2.20

2.20

3.60

4.80

glass4

4.60

4.60

4.60

15.40

2.20

2.20

2.20

6.20

ecoli4

2.60

2.60

4.40

7.20

3.00

3.20

5.60

9.80

glass2

6.40

6.40

7.40

25.60

0.20

0.20

0.20

0.40

vowel0

7.60

8.80

8.60

25.00

10.80

11.96

13.60

56.04

page-blocks0

40.40

39.00

58.60

242.80

25.84

35.60

57.76

198.36

ecoli3

4.60

4.60

4.20

20.20

2.20

2.20

2.20

5.60

yeast3

9.00

9.00

18.60

60.20

3.00

3.20

5.20

8.80

glass6

2.40

2.40

3.60

6.40

2.60

2.60

2.60

7.00

segment0

10.00

10.00

10.80

36.00

8.00

8.60

16.40

33.60

ecoli2

6.00

6.00

6.60

27.00

3.80

3.80

3.80

13.00

new-thyroid1

3.80

3.80

3.80

15.20

3.80

3.80

3.80

11.40

new-thyroid2

3.40

3.60

3.60

10.40

3.60

3.60

3.60

10.60

ecoli1

5.00

5.40

7.20

23.80

4.00

4.00

4.40

11.20

vehicle0

22.00

24.00

28.20

137.00

16.64

17.16

23.48

84.04

glass-0-1-2-3_vs_4-5-6

5.00

5.00

7.00

16.40

4.08

4.04

4.40

12.00

haberman

2.40

2.40

4.00

5.20

0.40

0.40

0.60

0.80

vehicle1

37.80

51.80

35.40

254.60

4.60

5.20

10.40

15.60

vehicle2

15.00

20.20

19.60

79.00

16.00

17.40

23.40

68.60

vehicle3

43.80

39.80

29.80

354.20

8.40

9.20

19.00

27.80

yeast1

19.40

20.20

22.00

142.80

5.88

6.16

13.60

17.60

glass0

9.80

9.80

12.80

41.40

2.68

2.68

2.76

7.80

iris0

1.00

1.00

1.00

2.00

1.00

1.00

1.00

2.00

pima

11.80

12.20

14.40

125.20

6.96

7.20

9.20

24.60

ecoli-0_vs_1

1.00

1.00

2.20

2.00

1.00

1.00

2.00

2.00

wisconsin

7.20

7.80

9.60

55.60

7.20

8.80

9.60

32.20

glass1

10.80

9.80

12.60

47.60

3.40

3.00

3.00

12.00

Mean

9.70

10.35

11.76

57.96

4.98

5.50

7.98

21.72

Median

6.00

6.00

7.40

25.60

3.40

3.20

3.80

10.60

 

This table can be downloaded as an Excel document or as a CSV file by clicking on the following links xls and csv.

 

 

Table 17. Number of Rules values multiplied by Length for the C4.5-based and CHAID*-based algorithms for each of the 33 SMOTE-preprocessed imbalanced datasets

 

C4.5-based

CHAID*-based

UnPART

BFPART

PART

C4.5

UnPART

BFPART

PART

CHAID*

abalone19

112.20

103.20

125.20

658.20

101.44

127.20

154.00

737.00

yeast6

28.40

29.20

27.20

125.20

43.80

51.60

75.40

256.00

yeast5

13.20

13.40

15.20

55.20

28.00

40.00

53.60

59.20

yeast4

61.00

61.60

58.40

307.00

66.48

69.80

74.80

345.00

yeast-2_vs_8

15.20

15.80

16.60

75.00

20.20

21.20

28.80

81.00

glass5

5.80

5.80

7.20

21.20

8.40

9.80

10.00

34.00

abalone9-18

72.80

74.80

75.00

367.00

32.40

34.16

42.32

167.80

glass4

8.80

8.80

8.80

35.20

7.00

9.40

9.60

26.20

ecoli4

8.20

8.20

9.00

40.60

7.60

9.00

11.60

34.00

glass2

17.40

17.40

20.00

108.80

8.60

9.40

13.60

45.40

vowel0

13.80

15.20

13.60

49.00

29.44

34.08

42.64

58.80

page-blocks0

151.40

143.60

157.40

1097.00

96.60

110.60

210.40

710.40

ecoli3

12.80

12.80

14.60

66.20

9.20

10.20

8.20

35.80

yeast3

41.00

41.40

41.60

203.80

21.20

25.80

30.40

135.60

glass6

7.80

7.80

7.40

29.60

6.80

6.80

7.00

19.80

segment0

14.80

16.00

15.40

59.80

13.20

15.20

26.00

72.40

ecoli2

14.80

14.40

16.00

83.40

10.00

12.60

11.40

32.60

new-thyroid1

4.00

4.00

4.00

11.00

3.20

3.20

4.40

8.40

new-thyroid2

5.20

5.20

4.40

17.80

3.80

4.00

5.20

10.40

ecoli1

6.80

9.00

10.00

33.40

5.40

4.80

5.80

15.60

vehicle0

38.60

39.60

45.40

213.60

26.36

29.60

44.40

162.40

glass-0-1-2-3_vs_4-5-6

6.40

6.40

9.00

31.20

8.80

9.64

9.80

37.20

haberman

9.60

11.40

11.20

44.80

1.80

1.80

2.00

4.60

vehicle1

90.00

103.80

76.40

612.20

20.28

18.68

35.40

154.88

vehicle2

23.80

23.80

32.00

95.20

25.44

29.00

41.24

80.60

vehicle3

85.80

88.80

83.60

788.40

23.80

26.60

46.28

146.20

yeast1

45.20

42.20

49.00

440.00

7.32

8.80

21.20

46.00

glass0

11.40

11.80

11.80

60.60

4.40

4.40

4.20

13.80

iris0

1.00

1.00

1.00

2.00

1.00

1.00

1.00

2.00

pima

25.60

20.80

27.20

185.00

7.84

7.64

9.32

30.20

ecoli-0_vs_1

3.20

3.20

3.20

10.80

1.20

1.20

2.00

2.60

wisconsin

9.40

9.40

13.20

65.00

9.40

11.60

13.40

39.00

glass1

13.00

13.20

15.00

70.00

5.72

5.72

6.60

20.00

Mean

29.65

29.79

31.06

183.73

20.19

23.17

32.18

109.84

Median

13.80

14.40

15.20

66.20

9.20

10.20

13.40

39.00

 

This table can be downloaded as an Excel document or as a CSV file by clicking on the following links xls and csv.

 

 

 

 

Table 18. p-values adjusted with the Bergman-Hommel post-hoc procedure for the C4.5-based and CHAID*-based algorithms for the Number of Rules multiplied by Length

 

BFPART_CHD

PART_CHD

UnPART_C45

BFPART_C45

PART_C45

CHAID*

C4.5

UnPART_CHD

1

0.806812

0.806812

0.806812

0.000198

0

0

BFPART_CHD

1

1

1

0.000929

0

0

PART_CHD

1

1

0.026575

0.000000

0

UnPART_C45

1

0.030899

0.000000

0

BFPART_C45

0.063328

0.000000

0

PART_C45

0.000065

0

CHAID*

 

 

 

 

 

 

0.000049

 

 

 

 

Figure 4. Friedman Aligned Ranks for the C4.5-based and CHAID*-based algorithms for the Number of Rules multiplied by Length

 

2.5 Results for the Time Measure

 

Table 19. Time values for the C4.5-based and CHAID*-based algorithms for each of the 30 standard datasets

 

C4.5-based

CHAID*-based

UnPART

BFPART

PART

C4.5

UnPART

BFPART

PART

CHAID*

lymphography

14

19

16

8

94

99

59

46

ecoli

50

40

34

19

208

204

174

91

car

145

198

47

18

708

703

330

114

nursery

107

110

55

14

633

576

226

94

cleveland

107

99

82

26

128

143

122

89

zoo

9

8

8

7

60

99

31

24

glass

70

64

52

21

321

299

265

148

flare

56

51

47

20

175

306

184

84

abalone

1867

1623

1858

139

794

871

849

575

balance

47

47

27

13

57

58

39

27

dermatology

23

18

18

13

381

578

243

117

hepatitis

8

2

7

7

22

18

16

24

newthyroid

11

6

7

7

69

55

47

44

haberman

4

7

6

5

6

7

7

11

breast

11

9

22

9

42

41

41

25

german

204

193

284

51

1071

1157

1173

462

wisconsin

18

14

16

7

160

179

177

77

contraceptive

657

710

314

71

254

249

228

106

tictactoe

89

90

54

15

319

267

129

94

pima

67

59

53

33

555

596

515

338

magic

1661

1432

1914

886

21053

21710

25879

12293

wine

16

17

16

11

243

175

146

123

bupa

26

31

16

13

45

47

44

33

heart

21

24

28

13

106

106

137

81

australian

79

74

97

33

417

499

443

260

crx

50

48

128

27

357

432

529

257

vehicle

390

370

227

68

3567

3162

1930

847

penbased

779

693

371

106

13565

11505

5144

1420

ring

965

821

1294

586

8835

8842

8526

8329

iris

10

5

5

6

22

22

17

16

Mean

252

229

237

75

1809

1767

1588

875

Median

53

49

47

16

248

258

180

94

This table can be downloaded as an Excel document or as a CSV file by clicking on the following links xls and csv.

 

 

 

Table 20. Time values for the C4.5-based and CHAID*-based algorithms for each of the 33 imbalanced datasets

 

C4.5-based

CHAID*-based

UnPART

BFPART

PART

C4.5

UnPART

BFPART

PART

CHAID*

abalone19

343

293

295

287

6623

6210

7475

6270

yeast6

18

17

16

11

213

198

194

206

yeast5

21

19

15

12

273

202

205

212

yeast4

19

21

20

14

303

277

248

250

yeast-2_vs_8

5

6

7

7

57

50

59

52

glass5

8

8

8

8

66

42

52

57

abalone9-18

51

46

54

40

731

693

734

608

glass4

11

9

8

11

104

73

73

93

ecoli4

8

6

7

8

71

50

62

63

glass2

19

15

15

13

29

26

24

29

vowel0

179

154

151

139

7295

5876

5529

5664

page-blocks0

1058

914

934

596

33853

33153

42501

22628

ecoli3

9

9

9

8

58

45

42

40

yeast3

28

23

27

16

303

272

301

246

glass6

10

10

10

9

108

87

83

90

segment0

781

663

789

551

19787

14595

24362

12074

ecoli2

10

11

10

7

66

67

54

46

new-thyroid1

8

7

11

7

35

31

27

26

new-thyroid2

6

6

6

6

34

20

17

25

ecoli1

11

11

10

10

79

84

82

62

vehicle0

81

74

51

31

1201

1046

900

456

glass-0-1-2-3_vs_4-5-6

13

12

13

10

125

110

120

90

haberman

14

6

6

8

11

27

28

11

vehicle1

189

223

129

49

709

714

718

420

vehicle2

69

76

51

29

1287

1040

950

506

vehicle3

222

178

108

56

903

828

912

438

yeast1

63

61

44

30

373

381

508

256

glass0

21

22

18

14

104

120

97

75

iris0

4

3

3

3

9

4

4

11

pima

68

65

55

35

556

575

532

336

ecoli-0_vs_1

5

4

5

5

30

24

19

27

wisconsin

18

14

16

8

200

193

173

91

glass1

21

21

18

13

118

100

89

88

Mean

103

91

88

62

2294

2037

2642

1562

Median

19

17

16

12

125

120

120

91

This table can be downloaded as an Excel document or as a CSV file by clicking on the following links xls and csv.

 

 

 

Table 21. Time values for the C4.5-based and CHAID*-based algorithms for each of the 33 SMOTE-preprocessed imbalanced datasets

 

C4.5-based

CHAID*-based

UnPART

BFPART

PART

C4.5

UnPART

BFPART

PART

CHAID*

abalone19

50138

38491

29208

7766

1411243

1415336

1086926

252893

yeast6

691

587

647

403

45184

38775

44531

13834

yeast5

854

731

724

467

41557

36696

28528

12344

yeast4

1473

1298

782

334

62353

57358

49315

15453

yeast-2_vs_8

120

101

77

50

3902

3155

3113

1296

glass5

33

27

28

34

674

492

556

462

abalone9-18

1505

1327

985

220

18950

17504

15040

4769

glass4

40

33

48

32

756

595

470

419

ecoli4

54

45

52

33

924

704

900

552

glass2

93

79

81

50

698

592

910

484

vowel0

1210

1024

907

622

68271

54730

44627

19085

page-blocks0

13534

11673

7944

2798

776982

741953

763009

145189

ecoli3

60

48

39

32

676

575

535

422

yeast3

565

491

587

320

25298

22970

21088

11619

glass6

32

30

21

28

489

378

304

325

segment0

4480

3765

4726

3269

148637

115337

170759

96426

ecoli2

45

41

39

33

674

597

562

423

new-thyroid1

10

10

9

15

140

107

110

119

new-thyroid2

13

10

12

15

172

120

112

121

ecoli1

25

30

26

25

361

332

308

254

vehicle0

164

164

99

54

2694

2300

1818

991

glass-0-1-2-3_vs_4-5-6

22

22

21

23

475

389

354

292

haberman

12

19

7

17

15

13

18

23

vehicle1

551

535

256

93

2301

2113

2155

957

vehicle2

116

105

84

52

2772

2258

1823

853

vehicle3

557

547

264

102

2538

2513

2525

956

yeast1

402

367

446

158

5653

6328

7564

3550

glass0

33

30

25

28

250

222

201

192

iris0

4

2

4

11

17

9

9

21

pima

152

135

121

63

1303

1269

1048

654

ecoli-0_vs_1

8

5

7

12

67

31

31

52

wisconsin

22

27

23

15

313

636

258

109

glass1

32

28

32

24

327

260

230

176

Mean

2335

1873

1465

521

79596

76565

68174

17737

Median

93

79

77

50

924

704

910

552

This table can be downloaded as an Excel document or as a CSV file by clicking on the following links xls and csv.

 

 

Table 22. p-values adjusted with the Bergman-Hommel post-hoc procedure for the C4.5-based and CHAID*-based algorithms for the Time measure

 

PART_C45

BFPART_C45

UnPART_C45

CHAID*

PART_CHD

BFPART_CHD

UnPART_CHD

C4.5

1

1

1

4.12E-12

0

0

0

PART_C45

1

1

8.23E-11

0

0

0

BFPART_C45

1

3.06E-10

0

0

0

UnPART_C45

4.47E-10

0

0

0

CHAID*

.0000318

.0000032

.0000014

PART_CHD

1

1

BFPART_CHD

 

 

 

 

 

 

1

 

 

 

 

Figure 5. Friedman Aligned Ranks for the C4.5-based and CHAID*-based algorithms for the Time measure