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Identifying abnormal patterns in electroencephalography (EEG) remains the cornerstone of diagnosing several neurological diseases. The current clinical EEG review process relies heavily on expert visual review, which is unscalable and error-prone. In an effort to augment the expert review process, there is a significant interest in mining population-level EEG patterns using unsupervised approaches. Current approaches rely either on two-dimensional decompositions (e.g., principal and independent component analyses) or deep representation learning (e.g., auto-encoders, self-supervision). However, most approaches do not leverage the natural multi-dimensional structure of EEGs and lack interpretability. In this study, we propose a tensor decomposition approach using the canonical polyadic decomposition to discover a parsimonious set of population-level EEG patterns, retaining the natural multi-dimensional structure of EEGs (time x space x frequency). We then validate their clinical value using a cohort of patients including varying stages of cognitive impairment. Our results show that the discovered patterns reflect physiologically meaningful features and accurately classify the stages of cognitive impairment (healthy vs mild cognitive impairment vs Alzheimer's dementia) with substantially fewer features compared to classical and deep learning-based baselines. We conclude that the decomposition of population-level EEG tensors recovers expert-interpretable EEG patterns that can aid in the study of smaller specialized clinical cohorts.