. Author manuscript; available in PMC: 2017 Feb 1.

Published in final edited form as: Pattern Recognit. 2016 Feb;50:155–177. doi: 10.1016/j.patcog.2015.08.009

Table 2.

Clustering performance of the involved clustering algorithms on artificial datasets.

Dataset

Validity index

Algorithm

FCM (m=2)

FCM

MEC

FC-QR

QWGSD-FC

PCM

ECM

LSSMTC

CombKM

STC

TI-KT-CM

TII-KT-CM

X_{T}^{I}

NMI-mean

0.7747

0.8005

0.7669

0.8080

0.7978

0.8103

0.7373

0.7932

0.8426 ➂

0.7802

0.8926 ➁

0.9110 ➀

NMI-std

5.23E-17

0.0743

1.17E-16

0.0349

0.0148

8.28E-17

RI-mean

0.9177

0.9331 ➂

0.9066

0.9262

0.9288

0.866

0.859

0.9313

0.9116

0.9203

0.9639 ➁

0.9752 ➀

RI-std

2.34E-16

0.0511

1.36E-16

1.17E-16

0.0404

0.0047

DBI-mean

0.8011

0.8198

0.8059

0.7664

0.8088

0.6827 ➀

0.9079

0.8376

0.7646 ➂

0.8104

0.7641 ➁

DBI-std

9.79E-17

1.12E-16

0.0490

3.70E-17

0.055

0.0376

9.79E-16

X_{T}^{II}

NMI-mean

0.8544

0.8576

0.8539

0.8634 ➂

0.8571

0.7925

0.8059

0.8119

0.8500

0.8772 ➁

0.8977 ➀

NMI-std

1.33E-16

1.36E-16

0.0011

RI-mean

0.9510

0.9528

0.9542

0.9534

0.9561 ➂

0.9181

0.9343

0.8814

0.9518

0.9600 ➁

0.9715 ➀

RI-std

1.36E-16

0.0005

DBI-mean

0.7499

0.7407.3 ➂

0.7729

0.7272 ➀

0.777

0.7939

0.9316

0.7611

0.7437

0.7414

0.7324 ➁

DBI-std

5.23E-17

7.85E-17

1.11E-16

2.34E-16

7.49E-05

1.36E-16

X_{T}^{III}

NMI-mean

0.7744

0.7839

0.7945

0.8022

0.8034

0.7949

0.8268 ➂

0.6715

0.7748

0.7871

0.8443 ➁

0.8763 ➀

NMI-std

1.17E-16

1.36E-16

0.0406

2.34E-16

RI-mean

0.8724

0.8798

0.8932

0.9049

0.8972

0.8399

0.9097 ➂

0.8329

0.9025

0.9074

0.9180 ➁

0.9656 ➀

RI-std

1.24E-16

0.0357

DBI-mean

0.7782

0.7738

0.7945

0.7849

0.7637 ➂

0.7727

0.7384 ➀

0.9223

0.7912

0.7582 ➁

0.7982

0.7738

DBI-std

1.17E-16

1.12E-16

0.0389

1.17E-16

X_{T}^{IV}

NMI-mean

0.6913

0.7023

0.6464

0.7039

0.7108

0.7376 ➁

0.6958

0.6178

0.6265

0.6850

0.7212 ➂

0.7397 ➀

NMI-std

1.48E-16

1.23E-16

1.17E-16

0.0848

1.17E-16

0.0026

RI-mean

0.8880

0.8923

0.8006

0.8817

0.8969

0.9101 ➁

0.8594

0.8617

0.8286

0.8820

0.9010 ➂

0.9123 ➀

RI-std

1.17E-16

0.0776

1.17E-16

0.0015

1.17E-16

DBI-mean

0.8856

0.8734

0.8796

0.8556 ➀

0.8965

0.8718 ➂

0.956

1.1627

0.8705 ➁

0.8889

0.8899

DBI-std

1.17E-16

1.12E-16

2.34E-16

1.36E-16

0.088

1.17E-16

0.0029

1.17E-16