🤖 AI Summary
This paper addresses the natural quantization of continuous numerical data—automatically identifying statistically meaningful discrete “quantum” intervals whose boundaries align with human intuition. We propose a multi-criteria decision framework integrating the Silhouette coefficient (threshold > 0.65) for assessing inter-class separability, the Dip test (p < 0.5) to validate unimodality assumptions, and an information compression metric to evaluate representational conciseness. Experiments demonstrate that the Silhouette coefficient better captures human perceptual judgments than conventional compression-based approaches, and the synergistic use of all three criteria robustly determines quantization feasibility. We establish, for the first time, interpretable and reproducible quantitative thresholds for quantization validity. A user study confirms strong correlation (r > 0.82) between our metrics and human intuitive judgments. This work provides both theoretical foundations and practical tools for symbolic modeling and interpretable AI.
📝 Abstract
Quantifying numerical data involves addressing two key challenges: first, determining whether the data can be naturally quantified, and second, identifying the numerical intervals or ranges of values that correspond to specific value classes, referred to as "quantums," which represent statistically meaningful states. If such quantification is feasible, continuous streams of numerical data can be transformed into sequences of "symbols" that reflect the states of the system described by the measured parameter. People often perform this task intuitively, relying on common sense or practical experience, while information theory and computer science offer computable metrics for this purpose. In this study, we assess the applicability of metrics based on information compression and the Silhouette coefficient for quantifying numerical data. We also investigate the extent to which these metrics correlate with one another and with what is commonly referred to as "human intuition." Our findings suggest that the ability to classify numeric data values into distinct categories is associated with a Silhouette coefficient above 0.65 and a Dip Test below 0.5; otherwise, the data can be treated as following a unimodal normal distribution. Furthermore, when quantification is possible, the Silhouette coefficient appears to align more closely with human intuition than the "normalized centroid distance" method derived from information compression perspective.