Evaluation of Classification Accuracy for Abnormal Gait Patterns Using Quaternion Waveforms

In recent years, gait analysis in physical therapy has increasingly required the use of quantitative techniques in addition to visual observation. While conventional accelerometer or camera-based methods have limitations, quaternion waveforms derived from smartphone-mounted inertial sensors (IMUs) have attracted attention as a high-resolution and flexible tool for motion analysis. This study aimed to examine how accurately multiple abnormal gait patterns can be classified using quaternion waveforms and to evaluate their effectiveness through classification modeling and quantitative analysis. Twenty-two healthy adults were recruited and asked to perform one trial each of normal gait and four types of simulated abnormal gait: Trendelenburg gait, circumduction gait, Duchenne gait with hip abduction, and Duchenne gait without hip abduction. A smartphone (iPhone, iOS 17.4.1) with a built-in IMU app capable of recording triaxial acceleration, angular velocity, and quaternion data was attached to the lower back. Gait cycles were segmented based on Z-axis acceleration and resampled to 100 points for each of the four quaternion components (400 dimensions total), followed by normalization. The waveforms were analyzed using Z-score transformation, principal component analysis (PCA), and K-means clustering (K=5). A classification model using a support vector machine (SVM) was built, and its performance was evaluated using accuracy, F1-score, and cross-validation. As the result, the PCA revealed a cumulative contribution ratio of 41.7%, with the Z-axis (pelvic elevation and depression) contributing the most. Clustering successfully separated Trendelenburg gait from other patterns. The SVM model achieved an overall accuracy of 86.9%, correctly identifying all instances of Trendelenburg gait. PCA and clustering revealed variability in waveform structures and classification challenges among abnormal gait patterns. Moreover, the SVM analysis demonstrated that discrimination performance varied across gait types, suggesting that specific features in quaternion waveforms play a critical role in classification accuracy.