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But before the realization of the dimension decreasing procedure, we should introduce the mathematical criterion of the self-descriptiveness.
Until the variances of the points are equal to the maximum variance of intervals derived from the last step, this decreasing procedure continues.
If the value of s 1 2 Open image in new window equals s 2 2 Open image in new window in this decreasing procedure, both s 1 2 Open image in new window and s 2 2 Open image in new window decrease in the next iteration.
If the values of s 1 2 Open image in new window and s 2 2 Open image in new window equal s 3 2 Open image in new window in this decreasing procedure, all three variances decrease in the next iteration, and this procedure continues until q is equal to qc.
As indicated in the figure, the single-objective optimization is a monotonic decreasing procedure, while docking with the multi-objective strategy can hinder single SF to fall into its energy minimum.
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