Change-Point Detection Utilizing Normalized Entropy as a Fundamental Metric

This paper proposes a change-point detection concept based on normalized entropy as a fundamental metric, aiming to overcome the limitations of traditional entropy-based methods that depend on distributional assumptions and absolute scale. Normalized entropy maps entropy values to the [0,1] interval through standardization, thereby accurately capturing relative changes in data complexity. The proposed method employs a sliding window to compute normalized entropy, transforming the problem of detecting change points in complex time series — induced by changes in scale, distribution, and diversity — into the problem of identifying salient features within the normalized entropy sequence. This circumvents the interference of parametric assumptions and effectively highlights distributional shifts. Experimental results demonstrate that normalized entropy exhibits pronounced numerical fluctuation characteristics and patterns near change points under various distributions and parameter combinations; the mean deviation between fluctuation moments and actual change points is only 2.4% of the sliding window size, indicating strong adaptability. This work provides theoretical support for change-point detection in complex data environments and lays a methodological foundation for precise, automated change-point detection using normalized entropy as a base metric.