A multi-dimensional framework for quantifying dance movement complexity with hierarchical structure analysis

Dance is a highly expressive form of human motion that involves coordinated changes in body posture, timing, rhythm, and spatial use. However, the analysis of dance movement complexity is still frequently based on subjective judgement, making it difficult to compare performances across dancers, styles, choreographic structures, and learning stages. This paper proposes a systematic framework for quantifying the complexity of dance movements from pose-based motion data and for analyzing the hierarchical organization of complexity within a performance. Raw video or motion-capture input is transformed into a standardized time series of human body keypoints. After interpolation, smoothing, alignment, and scale normalization, the motion sequence is represented through joint positions, velocities, accelerations, angular changes, and segment-level descriptors. Complexity is then decomposed into five interpretable dimensions: kinematic variation, temporal complexity, spatial complexity, structural diversity, and information-theoretic irregularity. These dimensions are computed locally over temporal windows and globally over complete performances, producing both a multi-dimensional complexity profile and an optional aggregate index. A hierarchical structure analysis is further introduced to connect joint-level behavior, short motion units, phrase-level segments, and complete choreographies. The framework supports standardized and reproducible comparison between dance styles, dancers, and choreographic sections while preserving interpretability. The proposed method provides a reproducible basis for dance analysis, intelligent feedback, digital performance evaluation, and broader computational studies of complex human movement.