Abstract
Distance measures play a central role in evolving the clustering technique. Due to the rich mathematical background and natural implementation of
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distance measures, researchers were motivated to use them in almost every clustering process. Beside
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distance measures, there exist several distance measures. Sargent introduced a special type of distance measures
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\begin{document}$m(\phi)$\end{document}
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and
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which is closely related to
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. In this paper, we generalized the Sargent sequence spaces through introduction of
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\begin{document}$M(\phi)$\end{document}
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and
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sequence spaces. Moreover, it is shown that both spaces are
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-spaces, and one is a dual of another. Further, we have clustered the two-moon dataset by using an induced
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-distance measure (induced by the Sargent sequence space
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) in the k-means clustering algorithm. The clustering result established the efficacy of replacing the Euclidean distance measure by the
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-distance measure in the k-means algorithm.