Deep Sleep Classification via EEG Signal Criticality: A Passive BCI Approach for Sleep-Improvement Neurofeedback

The gist: Criticality-derived features from Detrended Fluctuation Analysis (DFA) provide a high-accuracy, robust sensing mechanism for deep sleep classification, achieving a mean balanced accuracy of 87.17% with Naive Bayes classification.

Passive BCI Framework

Automated sleep staging is presented as a fundamental application of passive Brain-Computer Interfaces (pBCI), which decode spontaneous neural states to enable closed-loop interventions independent of user intent. This framework is particularly robust for automated sleep staging, which monitors the brain’s spontaneous, ongoing neural oscillations to infer physiological state without any voluntary participation from the user. A BCI is classified as passive when it satisfies three core criteria: the use of spontaneous brain activity as input, the absence of conscious intent from the user, and the output being a state estimation rather than a direct command. Sleep staging maps perfectly to this architecture because during sleep, the user is unconscious and unable to voluntarily modulate neural patterns. The system must decode hidden physiological markers such as sleep spindles, K-complexes, and slow-wave activity to classify the internal state (e.g., N3 vs. REM).

EEG Criticality Feature Derivation

The study leverages EEG signal criticality as a primary feature set for deep sleep classification. Criticality is the study of neural systems operating at a phase transition between order and disorder, which offers a unique window into the brain’s self-organization during the descent into deep sleep. The DFA procedure for each 30-second EEG epoch involves four primary steps:

1. Integration: The original time series x(i) is transformed into an integrated profile Y(i) = ∑ i k=1 [x(k)−⟨x⟩] to convert the noise-like signal into a random walk-like profile, revealing underlying scaling properties.

2. Segmentation: The integrated profile is partitioned into Nn = int(N/n) non-overlapping segments of equal length n.

3. Local Detrending: For each segment ν, a local polynomial trend yν,n (of order k = 1) is calculated via least-squares fitting and subtracted from the integrated profile to remove non-stationary drifts.

4. Fluctuation Function Calculation (q=2): The root-mean-square fluctuation is computed by averaging the variance over all segments: F(n) = vuut 1 2Nn 2Nn ∑ ν=1 [F2(ν,n)].

The output is characterized by the scaling exponent α (equivalent to the Hurst exponent H), determined as the slope of logF(n) versus logn. A value of α ≈ 0.5 indicates white noise (randomness), while α ≈ 1.0 suggests 1/f noise, characteristic of healthy, self-organized criticality. Significant deviations from these values serve as primary metrics for pathological decline and loss of signal complexity.

Data Acquisition and Cohort Characteristics

The research dataset was acquired following proper authorization from the National Sleep Research Resource (NSRR) [2606.13017p5], drawing upon a selected portion of the Study of Osteoporotic Fractures (SOF) records [2606.13017p5]. The cohort consisted of 290 older women who obtained a Mini-Mental State Examination (MMSE) score exceeding 24 during PSG administration and attended a subsequent evaluation five years later. Participants were divided into three groups according to their results on the Tengmodified Mini-Mental State Examination (3MS) administered at follow-up: cognitively normal (score of 88 or above), Mild Cognitive Impairment (MCI) (score between 78 − 88), and dementia (score below 78). The polysomnography electrode configuration comprised C3, C4, A1, and A2 channels with a sampling frequency of 128 Hz. EEG recordings were divided into 30-second epochs and hand-scored to classify wakefulness, REM sleep, or non-REM phases (N1, N2, N3 and N4), with N3 and N4 merged into a unified N3 stage.

Manifold Visualization of Sleep Dynamics

Unsupervised Uniform Manifold Approximation and Projection (UMAP) was applied to the full 347,232-epoch DFA feature set to visualize the manifold structure of the DFA scaling features. This technique constructs a low-dimensional embedding based solely on the underlying topological structure of the data, allowing for an unbiased observation of how neural scaling properties naturally cluster across different sleep stages. The resulting embedding highlights a clear topological separation of the N3 sleep stage from the continuum of awake, N1, N2, and REM sleep. The N3 stage is characterized by high-amplitude delta activity and distinct long-range temporal correlations, occupying a restricted, high-density region of the manifold. This isolation reflects the unique criticality of deep sleep compared to the more stochastic or fragile dynamics of lighter sleep stages.

Machine Learning Model Selection

Six classifiers were benchmarked via 10-fold cross-validation using balanced accuracy to determine the optimal state-sensing engine. The selected models spanned linear, instance-based, probabilistic, and connectionist architectures:

**: Linear Models included Linear Discriminant Analysis (LDA) and Linear Support Vector Classification (Linear SVC) to establish a baseline for linear separability. These models performed poorly, indicating that DFA-derived criticality features reside on a distinct, non-linear manifold. LDA achieved only 57.21% balanced accuracy. Linear SVM performed the worst at 51.01% balanced accuracy. These poor results are indicative of a mismatch between model architecture and feature geometry. Probabilistic and Neural Models included Gaussian Naive Bayes, which achieved the highest mean balanced accuracy of 87.17% (±0.24%), and a four-layer Feedforward Neural Network (FNN) with ReLU activation, which attained the second-highest performance at 81.58% (±0.68%). Random Forest also performed well, achieving 80.97% balanced accuracy. K-Nearest Neighbors (KNN) achieved 80.35% balanced accuracy. The highest score was achieved by Naive Bayes with accuracy of 87.17%(±0.24%). All features were standardized using a StandardScaler within the cross-validation pipeline to ensure zero mean and unit variance. The performance was quantified using Balanced Accuracy, defined as the arithmetic mean of class-specific recall. All features were standardized using a StandardScaler within the cross-validation pipeline to ensure zero mean and unit variance. The highest score was achieved by Naive Bayes with accuracy of 87.17% (±0.24%). The full list of values can be seen in Table 1.

1. Improve automated sleep staging by implementing a state-sensing engine based on Naive Bayes classification to achieve a mean balanced accuracy of 87.17%. This allows the system to decode hidden physiological markers—such as sleep spindles, K-complexes, and slow-wave activity—to classify internal states (e.g., N3 vs. REM) with high accuracy, supporting closed-loop interventions like Closed-Loop Auditory Stimulation (CLAS).

2. Enhance the system's predictive utility for cognitive decline by using channel-wise DFA to quantify long-range temporal correlations, as this metric shows a consistent and statistically robust elevation of H values during the N3 sleep stage across healthy aging and cognitive groups. This enables the AI to serve as an early-stage biomarker for identifying shifts in neural scaling properties associated with conditions like Alzheimer’s disease.

3. Develop a non-linear decoding strategy by utilizing UMAP manifold learning to characterize the geometric structure of DFA features, thereby demonstrating that the N3 stage—characterized by high-amplitude delta activity and distinct long-range temporal correlations—occupies a restricted, high-density region of the manifold. This insight dictates that the decision boundary for accurate N3 detection must be non-linear, validating the selection of non-linear classifiers over linear models like LDA (57.21%).

Automated sleep staging is a fundamental application of passive Brain-Computer Interfaces (pBCI), decoding spontaneous neural states to enable closed-loop interventions independent of user intent. This study evaluates criticality features derived from Detrended Fluctuation Analysis (DFA) for the specific identification of deep sleep (N3). We analyzed 347,232 EEG epochs from 290 older women using UMAP manifold learning to visualize state transitions. Subsequently, six classifiers were benchmarked via 10-fold cross-validation, using balanced accuracy to determine the optimal "state-sensing" engine for neurofeedback.Naive Bayes achieved the highest mean balanced accuracy (87.17% plus or minus 0.24%), significantly outperforming a fully connected deep neural network (FNN: 81.58%) and Random Forest (80.97%). Linear models (LDA: 57.21%; SVM: 51.01%) performed poorly, indicating that DFA-derived criticality features reside on a distinct, non-linear manifold. Probabilistic decoding of EEG criticality provides a high-accuracy sensing mechanism for pBCIs. This robust classification pipeline supports the development of state-dependent neurofeedback, such as targeted auditory stimulation, to enhance cognitive recovery.