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Segmenting an image of a nucleus is one of the most essential tasks in a leukemia diagnostic system. Accurate and rapid segmentation methods help the physicians identify the diseases and provide better treatment at the appropriate time. Recently, hybrid clustering algorithms have started being widely used for image segmentation in medical image processing. In this article, a novel hybrid histogram-based soft covering rough k-means clustering (HSCRKM) algorithm for leukemia nucleus image segmentation is discussed. This algorithm combines the strengths of a soft covering rough set and rough k-means clustering. The histogram method was utilized to identify the number of clusters to avoid random initialization. Different types of features such as gray level co-occurrence matrix (GLCM), color, and shape-based features were extracted from the segmented image of the nucleus. Machine learning prediction algorithms were applied to classify the cancerous and non-cancerous cells. The proposed strategy is compared with an existing clustering algorithm, and the efficiency is evaluated based on the prediction metrics. The experimental results show that the HSCRKM method efficiently segments the nucleus, and it is also inferred that logistic regression and neural network perform better than other prediction algorithms.