Table 3 Performance comparison of different methods for item recommendation task on five datasets

MIs

HR@5

0.4033

0.5976

0.5153

0.5477

0.5213

0.4136

0.5250

0.5951

–

–

NDCG@5

0.2921

0.3942

0.3957

0.4078

0.3890

0.2923

0.3625

0.4207

3.16%

8.9e–2

HR@10

0.4551

0.5869

0.5612

0.5698

0.5890

0.4741

0.5548

0.6874

16.71%

1.1e–4\(^\star \)

NDCG@10

0.3007

0.4056

0.4034

0.4248

0.4038

0.3136

0.3890

0.4569

7.56%

4.9e–2\(^\star \)

HR@20

0.4568

0.5935

0.5655

0.5786

0.5992

0.4947

0.5660

0.6957

16.10%

8.2e–4\(^\star \)

NDCG@20

0.3215

0.4104

0.4099

0.4292

0.4127

0.3531

0.3977

0.4599

7.15%

4.2e–2\(^\star \)

Auto

HR@5

0.4417

0.6097

0.5559

0.6068

0.5023

0.4319

0.5501

0.6207

1.80%

1.3e–2\(^\star \)

NDCG@5

0.2721

0.4660

0.4146

0.4703

0.3140

0.2812

0.3007

0.3861

–

–

HR@10

0.4668

0.6107

0.5663

0.6456

0.5662

0.4638

0.5945

0.7039

9.03%

4.9e–2\(^\star \)

NDCG@10

0.3102

0.4448

0.4200

0.4874

0.3871

0.3008

0.3915

0.4833

–

–

HR@20

0.4725

0.6187

0.5925

0.6591

0.5810

0.4850

0.6110

0.7099

7.71%

7.2e–2

NDCG@20

0.3320

0.4471

0.3274

0.3842

0.4020

0.3122

0.4201

0.4929

10.24%

4.8e–2\(^\star \)

LB

HR@5

0.4359

0.5269

0.5311

0.4973

0.4903

0.4759

0.4779

0.5531

4.14%

7.5e–3\(^\star \)

NDCG@5

0.2805

0.3639

0.3295

0.3538

0.3656

0.3032

0.3137

0.3992

9.19%

6.1e–4\(^\star \)

HR@10

0.4620

0.5279

0.5347

0.5016

0.5243

0.4904

0.5021

0.6075

13.62%

2.0e–3\(^\star \)

NDCG@10

0.2917

0.3791

0.3362

0.3581

0.3907

0.3426

0.3383

0.4251

8.80%

2.0e–2\(^\star \)

HR@20

0.4801

0.5323

0.5404

0.5189

0.5309

0.5011

0.5201

0.6089

12.68%

3.1e–3\(^\star \)

NDCG@20

0.3382

0.4421

0.3434

0.3618

0.4102

0.3213

0.3566

0.4315

–

–

Beer

HR@5

0.3625

0.4938

0.4611

0.5173

0.4526

0.3820

0.3661

0.5617

8.58%

4.1e–2\(^\star \)

NDCG@5

0.2496

0.3624

0.3633

0.3558

0.2926

0.2817

0.2457

0.3715

2.26%

2.7e–3

HR@10

0.3998

0.5793

0.5673

0.5769

0.4725

0.3947

0.3870

0.5921

2.21%

7.3e–3\(^\star \)

NDCG@10

0.2651

0.3963

0.3706

0.3616

0.3322

0.2920

0.2681

0.4107

3.63%

0.17

HR@20

0.4195

0.5868

0.5908

0.5838

0.5026

0.4218

0.4102

0.5026

–

–

NDCG@20

0.3005

0.3556

0.3987

0.3348

0.3539

0.3198

0.3108

0.4211

5.62%

0.18

Yelp

HR@5

0.4331

0.4868

0.5166

0.5326

0.4903

0.4741

0.4726

0.5637

5.84%

3.9e–2\(^\star \)

NDCG@5

0.2521

0.3601

0.3492

0.3439

0.3107

0.3112

0.2635

0.3826

6.25%

3.6e–2\(^\star \)

HR@10

0.4537

0.5159

0.5227

0.5411

0.5130

0.5001

0.4807

0.6139

13.45%

1.2e–2\(^\star \)

NDCG@10

0.2813

0.3956

0.3682

0.3457

0.3261

0.3138

0.2840

0.4217

6.60%

0.10

HR@20

0.4807

0.5338

0.5556

0.5469

0.5337

0.5238

0.5010

0.6219

11.93%

3.8e–3\(^\star \)

NDCG@20

0.3101

0.3964

0.3685

0.3514

0.3740

0.3329

0.3124

0.4361

10.02%

4.5e–2\(^\star \)

Statistic

Win/Loss

(18/0)

(17/1)

(17/1)

(16/2)

(18/0)

(18/0)

(18/0)

F-rank\(^{a} \)

1.33

6.23

5.13

5.67

4.65

2.30

3.00

7.68