This paper introduces a novel divergence measure between two probability distributions, parameterized by a constant \(\alpha \in [0,1]\) . The proposed divergence generalizes well-known measures such as the Kullback–Leibler (KL) and Jensen–Shannon (JS) divergences, providing a flexible and unified framework for distribution comparison. We analyze its key mathematical properties, including convexity, differentiability, and symmetry, and explore its relationships with other divergence measures and invariance characteristics. Furthermore, we demonstrate its practical effectiveness through applications in clustering, anomaly detection, and machine learning, supported by experiments on the Iris and MNIST datasets. Detailed results and visualizations highlight the advantages of the proposed divergence, particularly in adaptive and dynamic scenarios.
