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Despite different approaches, including various K\u2010Means versions, suboptimal outcomes persist due to inadequate initial centroid choices and reliance on common normalization techniques like min\u2010max normalization. In this study, we propose an improved algorithm that selects initial centroids more effectively by utilizing a novel formula to differentiate between instance attributes, creating a single weight for differentiation. We introduce a preprocessing phase for dataset normalization without forcing values into a specific range, yielding significantly improved results compared to unnormalized datasets and those normalized using min\u2010max techniques. For our experiments, we used five real datasets and five simulated datasets. The proposed algorithm is evaluated using various metrics and an external benchmark measure, such as the Adjusted Rand Index (ARI), and compared with the traditional K\u2010Means algorithm and 11 other modified K\u2010Means algorithms. Experimental evaluations on these datasets demonstrate the superiority of our proposed methodologies, achieving an impressive average accuracy rate of up to 95.47% and an average ARI score of 0.95. Additionally, the number of iterations required is reduced compared to the conventional K\u2010Means algorithm. 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