Geometric Representation and Data Generation for Sequential Data Analysis

Abstract

Sequential data, including human motion sequences, skeletal rehabilitation movements, and biomedical time-series signals, play an important role in intelligent healthcare, human–computer interaction, and assistive systems. Effective analysis of such data requires modeling temporal dynamics while preserving structural characteristics and addressing practical challenges such as nonlinear geometry, limited data availability, and class imbalance. Traditional Euclidean-based approaches often struggle to capture intrinsic structural dependencies in motion data, while real-world biomedical signals frequently suffer from data imbalance that affects classification reliability.

This thesis investigates sequential data analysis with an emphasis on geometric representation and data generation strategies, and further examines classification robustness in imbalanced biomedical time-series scenarios.

First, Symmetric Positive Definite (SPD) manifold-based representations are developed for hand gesture recognition and rehabilitation assessment. For gesture sequences, region-based SPD descriptors capture spatial correlations, while temporal dynamics are integrated through Log-Euclidean fusion to form a spatio-temporal representation. For rehabilitation evaluation, motion data are modeled on the SPD manifold and evaluated using multiple discriminative strategies to assess correct and incorrect movements, demonstrating strong cross-subject performance on public datasets.

Second, to address the limited availability and variability of skeleton sequence datasets, a lightweight generative framework is proposed for motion data synthesis. The method combines a Neural Gas Network for coarse sequence generation with a spatiotemporal refinement network to enhance anatomical plausibility, temporal smoothness, and motion realism. Experimental results demonstrate improvements over existing approaches across multiple motion quality metrics. The generated data increase dataset diversity and contribute to improved robustness of downstream assessment models.

Finally, recognizing that real-world sequential data may exhibit severe class imbalance, this thesis extends the investigation to biomedical time-series classification using cardiotocography (CTG) signals. A multifusion strategy integrating undersampling, threshold optimization, and ensemble classifiers is proposed to improve pathological case detection under imbalanced distributions. Experimental results show substantial improvements in identifying minority pathological cases compared with baseline models, underscoring the importance of decision-level optimization in healthcare sequential data analysis.

In summary, this thesis contributes to sequential data analysis through geometric representation methods for structured motion modeling, data generation techniques for enhancing dataset diversity, and classification strategies for handling imbalanced biomedical signals. The proposed approaches improve modeling effectiveness and robustness across motion understanding and healthcare-related applications.