Robust and accurate decoding of gesture from non-invasive surface electromyography (sEMG) is important for various applications including spatial computing, healthcare, and entertainment, and has been actively pursued by researchers and industry. Majority of sEMG-based gesture decoding algorithms employ deep neural networks that are designed for Euclidean data, and may not be suitable for analyzing multi-dimensional, non-stationary time-series with long-range dependencies such as sEMG. State-of-the-art sEMG-based decoding methods also demonstrate high variability across subjects and sessions, requiring re-calibration and adaptive fine-tuning to boost performance. To address these shortcomings, this work proposes a geometric deep learning model that learns on symmetric positive definite (SPD) manifolds and leverages unsupervised domain adaptation to desensitize the model to subjects and sessions. The model captures the features in time and across sensors with multiple kernels, projects the features onto SPD manifold, learns on manifolds and projects back to Euclidean space for classification. It uses a domain-specific batch normalization layer to address variability between sessions, alleviating the need for re-calibration or fine-tuning. Experiments with publicly available benchmark gesture decoding datasets (Ninapro DB6, Flexwear-HD) demonstrate the superior generalizability of the model compared to Euclidean and other SPD-based models in the inter-session scenario, with up to 8.83 and 4.63 points improvement in accuracy, respectively. Detailed analyses reveal that the model extracts muscle-specific information for different tasks and ablation studies highlight the importance of modules introduced in the work. The proposed method pushes the state-of-the-art in sEMG-based gesture recognition and opens new research avenues for manifold-based learning for muscle signals.
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