Tri-Conditional Biomechanical Signature Extraction: A Hybrid Framework Integrating Multivariate Functional Clustering, Cross-Modal Regression, and Inter-Subject Classification for Discriminative Gait Pattern Analysis

Gait analysis traditionally relies on isolated scalar parameters that discard the temporal coordination essential for clinical interpretation, limiting both biomechanical interpretability and machine learning efficacy. This study introduces the Tri-Conditional Biomechanical Signature Extraction (TC-BSE) framework, a novel hybrid architecture that simultaneously integrates multivariate functional clustering, cross-modal regression, and inter-subject classification to extract discriminative gait signatures from the UCI Multivariate Gait Data. Operating on sixth-order tensor representations (10 subjects × 3 bracing conditions × 10 replications × 2 legs × 3 joints × 101 timepoints), TC-BSE preserves the native multivariate structure of lower-limb kinematics while modeling three synergistic analytical conditions: (1) functional clustering identifies four latent gait prototypes with moderate validity (silhouette score = 0.264), revealing subject-invariant coordination strategies; (2) cross-modal regression quantifies phase-dependent joint couplings, achieving R² = 0.803 in predicting knee kinematics from ankle-hip trajectories with 31% performance degradation during swing versus stance phase; and (3) inter-subject classification extracts condition-invariant signatures yielding 84.3% subject identification accuracy despite orthotic perturbations. The framework's novelty lies in its tri-conditional integration, where clustering provides structural context for regression modeling, regression residuals enhance cluster discriminability, and both inform classification boundaries yielding signatures that simultaneously exhibit functional coherence, biomechanical interpretability, and subject-level discriminability. This approach advances gait analysis beyond reductionist feature engineering toward holistic signature synthesis, with translational impact for condition-robust biometric authentication, personalized orthotic tuning, and movement-strategy stratification in clinical rehabilitation. All analyses employed subject-wise cross-validation to prevent data leakage; limitations include the constrained sample size (n=10 healthy adults), necessitating cautious generalization.