Discovering Minority Sub-clusters and Local Difficulty Factors from Imbalanced Data: Supplement

1 Dataset visualizations

Two-dimensional dataset visualizations. Left column: clusters differentiated using shapes and colors. Right column: types of minority class examples in color-coded as: safe - green, borderline - orange, rare - red, outlier - black.

Clusters

Example types

clover

clover^b

clover^u

clover^r

clover_s

clover_s^u

dis

dis^b

dis^u

dis^r

dis_s

dis_s^u

hyp

hyp^b

hyp^u

hyp^r

hyp_s

hyp_s^u

joined

joined^b

joined^u

joined^r

joined_s

joined_s^u

normal

normal^b

normal^u

normal^r

normal_s

normal_s^u

rothyp

rothyp^b

rothyp^u

rothyp^r

rothyp_s

rothyp_s^u

2 Result summary

3 Comparisons and statistical tests

3.1 AMI - best models

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Friedman rank sum test
Friedman chi-squared = 34.039, df = 2, p-value = 4.061e-08

ImScan	ImKmeans	ImGrid
1.71	1.87	2.43

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3.2 AMI - mean models

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Friedman rank sum test
Friedman chi-squared = 2.8129, df = 2, p-value = 0.245

ImGrid	ImScan	ImKmeans
1.85	2.06	2.09

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3.3 G-mean - best models

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Friedman rank sum test
Friedman chi-squared = 95.191, df = 3, p-value < 2.2e-16

Napierala	ImScan	ImGrid	ImKmeans
1.75	2.17	2.45	3.63

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3.4 G-mean - mean models

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Friedman rank sum test
Friedman chi-squared = 139.69, df = 3, p-value < 2.2e-16

Napierala	ImGrid	ImScan	ImKmeans
1.56	1.85	2.88	3.71

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3.5 Time (mean models)

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Friedman rank sum test
Friedman chi-squared = 227.35, df = 3, p-value < 2.2e-16

Napierala	ImGrid	ImScan	ImKmeans
1	2.08	2.92	4

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4 Balance between AMI and G-mean

4.1 beta*AMI + (1-beta)*G-mean for best models

4.2 beta*AMI + (1-beta)*G-mean for mean models