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Fig 1.

(I) and (II) the difference between the data before and after performing the clustering. I. Before, II. After.

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Fig 2.

The Pseudocode of MBHA algorithm.

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Fig 3.

The flowchart for the MBHA algorithm.

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Table 1.

Benchmark test functions.

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Table 2.

Parameter setting.

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Table 3.

The results of the standard and modified Black Hole Algorithm.

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Table 4.

The Wilcoxon signed rank test.

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Fig 4.

The convergence of (f1).

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Fig 5.

The convergence of (f2).

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Fig 6.

The convergence of (f3).

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Fig 7.

The convergence of (f4).

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Fig 8.

The convergence of (f5).

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Fig 9.

The convergence of (f6).

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Table 5.

Main characteristics of the test datasets.

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Table 6.

The sum of intra-cluster distances and error rate obtained by MBHA and STANDARD algorithms on different datasets.

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Table 7.

The results of the statistical analysis tests.

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Table 8.

The sum of intra-cluster distances and error rate obtained by MBHA and modified algorithms on different datasets.

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