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Table 4 Statistical significance test which compares KPCA with other classifiers: whole data, PCA, t-test, PAM and Lasso

From: New bandwidth selection criterion for Kernel PCA: Approach to dimensionality reduction and classification problems

Kernel function

Data set

I

II

III

IV

V

VI

VII

VIII

IX

 

Whole data

1.0000

1.0000

0.9250

0.0015

0.5750

0.0400

0.0628

0.0200

0.0150

 

PCA

0.0050

0.0021

0.0003

0.0015

2.83E-08

5.00E-07

0.0250

0.0005

0.0140

RBF

t-test

1.0000

1.0000

1.0000

1.0000

6.50E-04

4.35E-04

0.0110

0.0005

1.0000

 

PAM

1.0000

6.10E-05

0.0002

0.0800

0.1450

0.0462

1.0000

0.0002

0.0015

 

Lasso

0.0278

1.000

0.0001

0.0498

1.0000

0.0015

1.0000

0.00003

0.0200

 

Whole data

1.0000

0.3095

1.0000

1.0000

1.0000

1.0000

1.0000

0.0009

1.0000

 

PCA

7.00E-05

0.0011

1.30E-09

7.70E-09

1.28E-08

2.72E-05

6.15E-07

0.357

0.230

lin

t-test

1.0000

0.2150

0.7200

1.0000

0.0559

0.0443

1.0000

0.5450

1.0000

 

PAM

0.0400

0.0003

0.0422

0.0015

0.0004

0.0001

0.0015

1.0000

0.0300

 

Lasso

0.4950

0.4950

0.0049

2.12E-06

0.0005

0.0493

0.0025

1.0000

2.12E-06

 

Whole data

1.0000

0.0100

1.0000

4.16E-11

0.00450

5.90E-08

7.70E-08

1.0000

1.0000

 

PCA

0.0130

0.0003

4.35E-07

4.50E-05

7.70E-08

0.0040

3.28E-08

2.72E-05

5.00E-11

poly

t-test

1.0000

1.0000

0.0250

1.0000

0.0443

0.2100

1.0000

0.0005

1.0000

 

PAM

0.1200

0.0005

0.0100

0.0400

0.0300

1.0000

0.0015

0.0200

0.0650

 

Lasso

0.0100

1.0000

4.61E-05

1.76E-08

0.5000

1.0000

0.0006

0.0010

0.4350

  1. P-values of two-sided signed test are given.
  2. p-value: False Discovery Rate (FDR) corrected.