Benchmarks

Introduction

A benchmark is supplied for select algorithms to provide an overview of the implemented models. In total, 17 benchmark datasets are used for comparison, which can be downloaded at ODDS.

For each dataset, it is first split into 60% for training and 40% for testing. All experiments are repeated 10 times independently with random splits. The mean of 10 trials is regarded as the final result. Three evaluation metrics are provided:

  • The area under receiver operating characteristic (ROC) curve

  • Precision @ rank n (P@N)

  • Execution time

You could replicate this process by running benchmark.py.

We also provide the hardware specification for reference.

Specification

Value

Platform

PC

OS

Microsoft Windows 10 Enterprise

CPU

Intel i7-6820HQ @ 2.70GHz

RAM

32GB

Software

PyCharm 2018.02

Python

Python 3.6.2

Core

Single core (no parallelization)

ROC Performance

ROC Performances (average of 10 independent trials)

Data

#Samples

# Dimensions

Outlier Perc

ABOD

CBLOF

FB

HBOS

IForest

KNN

LOF

MCD

OCSVM

PCA

arrhythmia

452

274

14.6018

0.7688

0.7835

0.7781

0.8219

0.8005

0.7861

0.7787

0.7790

0.7812

0.7815

cardio

1831

21

9.6122

0.5692

0.9276

0.5867

0.8351

0.9213

0.7236

0.5736

0.8135

0.9348

0.9504

glass

214

9

4.2056

0.7951

0.8504

0.8726

0.7389

0.7569

0.8508

0.8644

0.7901

0.6324

0.6747

ionosphere

351

33

35.8974

0.9248

0.8134

0.8730

0.5614

0.8499

0.9267

0.8753

0.9557

0.8419

0.7962

letter

1600

32

6.2500

0.8783

0.5070

0.8660

0.5927

0.6420

0.8766

0.8594

0.8074

0.6118

0.5283

lympho

148

18

4.0541

0.9110

0.9728

0.9753

0.9957

0.9941

0.9745

0.9771

0.9000

0.9759

0.9847

mnist

7603

100

9.2069

0.7815

0.8009

0.7205

0.5742

0.8159

0.8481

0.7161

0.8666

0.8529

0.8527

musk

3062

166

3.1679

0.1844

0.9879

0.5263

1.0000

0.9999

0.7986

0.5287

0.9998

1.0000

1.0000

optdigits

5216

64

2.8758

0.4667

0.5089

0.4434

0.8732

0.7253

0.3708

0.4500

0.3979

0.4997

0.5086

pendigits

6870

16

2.2707

0.6878

0.9486

0.4595

0.9238

0.9435

0.7486

0.4698

0.8344

0.9303

0.9352

pima

768

8

34.8958

0.6794

0.7348

0.6235

0.7000

0.6806

0.7078

0.6271

0.6753

0.6215

0.6481

satellite

6435

36

31.6395

0.5714

0.6693

0.5572

0.7581

0.7022

0.6836

0.5573

0.8030

0.6622

0.5988

satimage-2

5803

36

1.2235

0.8190

0.9917

0.4570

0.9804

0.9947

0.9536

0.4577

0.9959

0.9978

0.9822

shuttle

49097

9

7.1511

0.6234

0.6272

0.4724

0.9855

0.9971

0.6537

0.5264

0.9903

0.9917

0.9898

vertebral

240

6

12.5000

0.4262

0.3486

0.4166

0.3263

0.3905

0.3817

0.4081

0.3906

0.4431

0.4027

vowels

1456

12

3.4341

0.9606

0.5856

0.9425

0.6727

0.7585

0.9680

0.9410

0.8076

0.7802

0.6027

wbc

378

30

5.5556

0.9047

0.9227

0.9325

0.9516

0.9310

0.9366

0.9349

0.9210

0.9319

0.9159

P@N Performance

Precision @ N Performances (average of 10 independent trials)

Data

#Samples

# Dimensions

Outlier Perc

ABOD

CBLOF

FB

HBOS

IForest

KNN

LOF

MCD

OCSVM

PCA

arrhythmia

452

274

14.6018

0.3808

0.4539

0.4230

0.5111

0.4961

0.4464

0.4334

0.3995

0.4614

0.4613

cardio

1831

21

9.6122

0.2374

0.5876

0.1690

0.4476

0.5041

0.3323

0.1541

0.4317

0.5011

0.6090

glass

214

9

4.2056

0.1702

0.0726

0.1476

0.0000

0.0726

0.0726

0.1476

0.0000

0.1726

0.0726

ionosphere

351

33

35.8974

0.8442

0.6088

0.7056

0.3295

0.6369

0.8602

0.7063

0.8806

0.7000

0.5729

letter

1600

32

6.2500

0.3801

0.0749

0.3642

0.0715

0.1003

0.3312

0.3641

0.1933

0.1510

0.0875

lympho

148

18

4.0541

0.4483

0.7517

0.7517

0.8467

0.9267

0.7517

0.7517

0.5183

0.7517

0.7517

mnist

7603

100

9.2069

0.3555

0.3348

0.3299

0.1188

0.3135

0.4204

0.3343

0.3462

0.3962

0.3846

musk

3062

166

3.1679

0.0507

0.7766

0.2230

0.9783

0.9680

0.2733

0.1695

0.9742

1.0000

0.9799

optdigits

5216

64

2.8758

0.0060

0.0000

0.0244

0.2194

0.0301

0.0000

0.0234

0.0000

0.0000

0.0000

pendigits

6870

16

2.2707

0.0812

0.2768

0.0658

0.2979

0.3422

0.0984

0.0653

0.0893

0.3287

0.3187

pima

768

8

34.8958

0.5193

0.5413

0.4480

0.5424

0.5111

0.5413

0.4555

0.4962

0.4704

0.4943

satellite

6435

36

31.6395

0.3902

0.4152

0.3902

0.5690

0.5676

0.4994

0.3893

0.6845

0.5346

0.4784

satimage-2

5803

36

1.2235

0.2130

0.8846

0.0555

0.6939

0.8754

0.3809

0.0555

0.6481

0.9356

0.8041

shuttle

49097

9

7.1511

0.1977

0.2943

0.0695

0.9551

0.9546

0.2184

0.1424

0.7506

0.9542

0.9501

vertebral

240

6

12.5000

0.0601

0.0000

0.0644

0.0071

0.0343

0.0238

0.0506

0.0071

0.0238

0.0226

vowels

1456

12

3.4341

0.5710

0.0831

0.3224

0.1297

0.1875

0.5093

0.3551

0.2186

0.2791

0.1364

wbc

378

30

5.5556

0.3060

0.5055

0.5188

0.5817

0.5088

0.4952

0.5188

0.4577

0.5125

0.4767

Execution Time

Time Elapsed in Seconds (average of 10 independent trials)

Data

#Samples

# Dimensions

Outlier Perc

ABOD

CBLOF

FB

HBOS

IForest

KNN

LOF

MCD

OCSVM

PCA

arrhythmia

452

274

14.6018

0.3667

0.2123

0.5651

0.1383

0.2669

0.1075

0.0743

1.4165

0.0473

0.0596

cardio

1831

21

9.6122

0.3824

0.1255

0.7741

0.0053

0.2672

0.2249

0.0993

0.5418

0.0883

0.0035

glass

214

9

4.2056

0.0352

0.0359

0.0317

0.0022

0.1724

0.0173

0.0025

0.0325

0.0010

0.0011

ionosphere

351

33

35.8974

0.0645

0.0459

0.0728

0.0082

0.1864

0.0302

0.0070

0.0718

0.0048

0.0018

letter

1600

32

6.2500

0.3435

0.1014

0.7361

0.0080

0.2617

0.1882

0.0935

1.1942

0.0888

0.0041

lympho

148

18

4.0541

0.0277

0.0353

0.0266

0.0037

0.1712

0.0111

0.0021

0.0327

0.0014

0.0012

mnist

7603

100

9.2069

7.4192

1.1339

48.2750

0.0480

1.9314

7.3431

6.7901

4.7448

5.0203

0.1569

musk

3062

166

3.1679

2.3860

0.4134

13.8610

0.0587

1.2736

2.2057

1.9835

25.5501

1.3774

0.1637

optdigits

5216

64

2.8758

2.7279

0.4977

14.2399

0.0303

0.7783

2.1205

1.7799

1.8599

1.5618

0.0519

pendigits

6870

16

2.2707

1.4339

0.2847

3.8185

0.0090

0.5879

0.8659

0.5936

2.2209

0.9666

0.0062

pima

768

8

34.8958

0.1357

0.0698

0.0908

0.0019

0.1923

0.0590

0.0102

0.0474

0.0087

0.0013

satellite

6435

36

31.6395

1.7970

0.4269

7.5566

0.0161

0.6449

1.2578

0.9868

2.6916

1.3697

0.0245

satimage-2

5803

36

1.2235

1.5209

0.3705

5.6561

0.0148

0.5529

1.0587

0.7525

2.3935

1.1114

0.0151

shuttle

49097

9

7.1511

14.3611

1.2524

59.2131

0.0953

3.3906

9.4958

11.1500

12.1449

44.6830

0.0378

vertebral

240

6

12.5000

0.0529

0.0444

0.0339

0.0014

0.1786

0.0161

0.0025

0.0446

0.0015

0.0010

vowels

1456

12

3.4341

0.3380

0.0889

0.3125

0.0044

0.2751

0.1125

0.0367

0.9745

0.0469

0.0023

wbc

378

30

5.5556

0.1014

0.0691

0.0771

0.0063

0.2030

0.0287

0.0078

0.0864

0.0062

0.0035