Change-Point Detection Utilizing Normalized Entropy as a Fundamental Metric

Abstract: This paper introduces a concept for change-point detection based on normalized entropy as a fundamental metric, aiming to overcome the dependence of traditional entropy methods on assumptions about data distribution and absolute scales. Normalized entropy maps entropy values to the [0,1] interval through standardization, accurately capturing relative changes in data complexity. By utilizing a sliding window to compute normalized entropy, this approach transforms the challenge of detecting change points in complex time series, arising from variations in scale, distribution, and diversity, into the task of identifying significant features within the normalized entropy sequence, thereby avoiding interference from parametric assumptions and effectively highlighting distributional shifts. Experimental results show that normalized entropy exhibits significant numerical fluctuation characteristics and patterns near change points across various distributions and parameter combinations. The average deviation between fluctuation moments and actual change points is only 2.4% of the sliding window size, demonstrating strong adaptability. This paper provides theoretical support for change-point detection in complex data environments and lays a methodological foundation for precise and automated detection based on normalized entropy as a fundamental metric.