Binary Brain-State Classification

Updated 13 August 2025

Binary brain-state classification is the process of assigning neurobiological measurements to one of two cognitive or physiological states using statistical, machine learning, and signal processing techniques.
Key techniques include advanced feature extraction (e.g., FPCA, spectral transformations, topological descriptors), dimensionality reduction, and robust classifiers that achieve high accuracy on noisy, high-dimensional data.
Applications in mental state detection, clinical diagnostics, and brain-computer interfaces underline its significance, while challenges such as data scarcity and model interpretability remain.

Binary brain-state classification is the process of assigning a neurobiological measurement (such as neuroimaging or electrophysiological time series) to one of two possible cognitive or physiological brain states. Over the past decade, advances in feature engineering, metric learning, dimensionality reduction, topological data analysis, and sophisticated statistical or deep learning models have enabled accurate discrimination between binary brain states in high-dimensional, noisy, and heterogeneous neural data. This field integrates statistical theory, machine learning, signal processing, and neuroinformatics to enable applications such as mental state detection, disease diagnosis, and closed-loop brain-computer interfaces.

1. Feature Extraction and Representation Techniques

Feature engineering is foundational for binary brain-state classification. Because brain signals are high-dimensional, redundant, and noisy, effective feature reduction and transformation are critical. Major approaches include:

Functional Principal Component Analysis (FPCA): FPCA decomposes temporal brain signals at each sensor or voxel into a small set of principal component scores via the Karhunen–Loève expansion, retaining components until ≈90% variance is explained (Croteau et al., 2015). This yields local features capturing the primary modes of variation.
Spectral Domain Phase Features: Transformation of fMRI time series using the discrete Fourier or Hilbert transforms enables classification based on phase features, which have been shown to dramatically increase discriminative power (with SVM accuracy improving from 76.4% on raw data to 97.5% and 99.0% after DFT and DHT, respectively) (Ramasangu et al., 2016). A random sieve function is applied before transformation to randomize and reduce data dimensionality.
Topological Descriptors via Persistent Homology: Persistent homology captures the birth and death of topological features (connected components, loops, voids) as the scale parameter changes across sensors/voxels, leading to global descriptors (total persistence, variance, kurtosis) that summarize the topological structure of brain activity (Croteau et al., 2015, Nasrin et al., 2019, Ferrà et al., 2023).
Connectivity and Network-Based Features: Features derived from pairwise or higher-order brain region connectivity have high discriminative capacity:
- Mutual Information Networks: Compute pairwise coherence-based mutual information, convert to edge weights, then derive graph-theoretic metrics (global/local efficiency, clustering, modularity) (Croteau et al., 2015).
- Ensemble-Based Graphs: Edges encode the difference in posterior classification confidence for pairs of regions using ensemble logistic regression base models, providing richer discriminatory information than traditional correlations (Vlasenko et al., 8 Aug 2025).
- Hyperconnectome Representations: Many-to-many connectivity (hyperedges linking multiple regions) is encoded and embedded into low-dimensional latent space via hypergraph convolutional layers (Banka et al., 2020).
- Riemannian Covariance Features: By treating symmetric positive definite covariance matrices of neural time series as points on a Riemannian manifold, differences between states are captured using geodesic distances, respecting intrinsic geometry (Marin-Llobet et al., 7 Apr 2025).
ε-Complexity and Nuclear Features: Model-free scalar features quantifying the intrinsic complexity (via reconstruction error scaling laws) or energy (dominant singular values from SVD) of multichannel EEG records have been shown to provide highly compact and robust discriminants for binary classes (Darkhovsky et al., 2016, Qazi et al., 2019).

2. Classification Algorithms and Regularization

The extracted features serve as input for a range of classifiers, each chosen based on the structure of the data and its dimensionality:

Logistic Regression with Elastic Net Regularization: For high-dimensional feature spaces, symmetric multinomial (or binary) logistic regression with elastic net regularization (combined L₁/L₂ penalty) is used to avoid overfitting and enforce balanced selection (Croteau et al., 2015).
Support Vector Machines (SVMs) and Naive Bayes: Classical approaches such as SVMs and Naive Bayes remain effective, especially with phase-based spectral features or low-dimensional representations. Linear SVMs operate on phase or amplitude coefficients, rapidly separating states with properly engineered features (Ramasangu et al., 2016, Darkhovsky et al., 2016).
Random Forests: In scenarios with low-dimensional, highly informative features (e.g., ε-complexity coefficients), random forest classifiers offer robust performance (accuracy ≈ 83.6% for EEG schizophrenia/healthy discrimination) (Darkhovsky et al., 2016).
Minimum Distance to Mean (MDM): On Riemannian manifolds of covariance matrices, MDM classifiers using geodesic distances to class Fréchet means have outperformed both CNNs and vector-based Euclidean classifiers in accuracy and computational efficiency for intracortical LFP state decoding (Marin-Llobet et al., 7 Apr 2025).
Bayesian Neural Networks (BNNs): Probabilistic classifiers that explicitly model weight uncertainties through Bayesian statistics and variational inference enable robust classification under data/model uncertainty, as shown for fNIRS-based motor state discrimination (accuracy ≈ 86.44%, AUC ≈ 0.855) (Siddique et al., 2021).
Convolutional Neural Networks (CNNs) and BiLSTM: Shallow CNNs extracting spectral-temporal features from EEG or fMRI data yield high accuracy, especially with careful data splitting and augmentation for cross-channel generalization. BiLSTMs and 1D-CNNs trained on z-scored fMRI BOLD time series leverage temporal dynamics, achieving ≈81% overall accuracy and revealing that visual and control networks are key discriminants (Kucukosmanoglu et al., 14 Aug 2024, Ajra et al., 23 Jul 2024).

3. Dimensionality Reduction and Data Complexity

Effective handling of the high ambient dimensionality is crucial:

FPCA and PCA: Reduce each channel's time series to a handful of principal components, compressing thousands of time points into a few summary scores (Croteau et al., 2015). In topological classifiers, PCA is used to test sensitivity to variance versus “shape,” revealing that accuracy is less sensitive to increased explained variance beyond a few critical dimensions (Ferrà et al., 2023).
Random Sieve Functions: Randomly mask out subsets of features/voxels prior to transformation, which reduces input dimensionality while maintaining random coverage and avoiding systematic bias (Ramasangu et al., 2016).
Adaptive Non-Euclidean Screening: The Metric Kolmogorov Filter (MK-Filter) screens thousands of SPD matrices and other non-vector predictors, using a Kolmogorov–Smirnov-type statistic defined on arbitrary metric spaces (including Wasserstein and Log-Cholesky measures), controlling false discovery rate and facilitating selection of only the most informative connectivities for presentation in downstream classifiers (He et al., 19 Mar 2024).
Low-Dimensional Model-Free Summaries: Nuclear features (dominant singular values) and ε-complexity coefficients (A, B, and derivatives) yield highly compressed representations, delivering both computational efficiency and resistance to overfitting (Darkhovsky et al., 2016, Qazi et al., 2019).

4. Interpretability, Topological and Graph-Theoretic Insights

Interpretability is advanced via statistical, geometric, and topological summaries:

Graph and Hypergraph Topologies: Ensemble-graphs enable edge-level interpretability—each edge carries a probability-derived confidence in favor of one brain state over the other, also facilitating identification of central/critical brain regions in disease or cognitive task discrimination (Vlasenko et al., 8 Aug 2025). Hyperconnectome frameworks encode many-to-many relations and enable localization of discriminative motifs (Banka et al., 2020).
Persistent Homology and Topological Classification: Topological classifiers assess the change in persistence silhouettes when a new sample is virtually added to each class, providing a formal intuition about the “shape” of class manifolds and their intrinsic dimension. This approach is largely insensitive to explained variance, in contrast to traditional classifiers (Ferrà et al., 2023). Bayesian topological learning further integrates prior knowledge, handles noise and nonstationarity, and quantifies class membership via Bayes factors on persistence diagrams (Nasrin et al., 2019).
Model Explainability via Permutation Importance: Deep learning approaches for fMRI state classification use permutation-based feature importance: shuffling the activity of a region leads to a measured drop in classification accuracy, tightly linking prediction confidence with neuroanatomical contributions. Visual and attentional networks consistently dominate in discriminative power (Kucukosmanoglu et al., 14 Aug 2024).

5. Performance Evaluation and Empirical Comparisons

Binary brain-state classifiers are evaluated using standard classification metrics:

Accuracy and F1 Score: Reported cross-validation and test accuracies range from ≈61% (variance-only features) to >99% (ensemble-graph logistic regression, phase-transformed EEG, nuclear features on frontal EEG in EOEC tasks) (Croteau et al., 2015, Ramasangu et al., 2016, Qazi et al., 2019, Vlasenko et al., 8 Aug 2025).
AUC and ROC: In iEEG seizure classification, area under the ROC curve (AUC) improvements of ≈9.13% are realized by node-centric graph learning methods over edge-centric baselines (Ghoroghchian et al., 2020).
Model Comparison: Riemannian MDM consistently outperforms both CNNs and Euclidean classifiers, producing mean F1 macro scores ≈0.75 with significantly reduced training time (up to 400× speedup compared to CNNs) (Marin-Llobet et al., 7 Apr 2025). Ensemble-based graph representations yield accuracy increases of about 15.6 percentage points over classical correlation graphs when used in GNNs (Vlasenko et al., 8 Aug 2025).
Parameter Robustness and Statistical Significance: Many methods employ multiple random seeds or repeated cross-validations to ensure stability. For instance, SVMs with phase features maintain standard deviations ≤2% over 50 random sieve samplings (Ramasangu et al., 2016).

6. Applications and Broader Implications

The methodological advances in binary brain-state classification support a range of applied contexts:

Clinical Diagnostics: Identification of disease-specific biomarkers (e.g., abnormal connectivity in autism via metric screening of SPD matrices (He et al., 19 Mar 2024); EEG-based detection of schizophrenia (Darkhovsky et al., 2016)).
Brain-Computer Interfaces (BCIs): Real-time binary state decoding for prosthetic control, communication interfaces, and adaptive neurofeedback (Qazi et al., 2019, Marin-Llobet et al., 7 Apr 2025). Binarization methods (random projections) support deployment on resource-constrained edge devices with minimal degradation in accuracy (Hersche et al., 2020).
Neurocognitive Monitoring: Behavioral and task monitoring (e.g., finger tapping vs. rest via fNIRS (Siddique et al., 2021); cognitive performance discrimination via fMRI and DNNs (Kucukosmanoglu et al., 14 Aug 2024)).
Personalized Electrode and Feature Selection: Single-channel EEG models using CNNs reveal certain individual channels (especially frontal or central) can suffice for robust classification, aligning with the drive for wearable and portable BCI implementations (Ajra et al., 23 Jul 2024).
General Non-Euclidean Data Analysis: Approaches such as the MK-Filter and ensemble graph representations generalize to modalities and data types beyond traditional EEG/fMRI, covering arbitrary metric and manifold-valued objects (He et al., 19 Mar 2024, Vlasenko et al., 8 Aug 2025).

7. Limitations, Open Problems, and Prospective Directions

Despite significant progress, several limitations and emerging research directions are identified:

Data Scarcity and Estimation Reliability: Especially in invasive (intracortical) recordings, the limited number of samples can challenge accurate covariance estimation and undermine complex model learning. Shrinkage estimators (e.g., Oracle Approximating Shrinkage) and robust statistics are necessary to address variance-bias tradeoffs (Marin-Llobet et al., 7 Apr 2025).
High-Dimensional, Non-Euclidean Complexity: Many robust screening and classification methods depend on well-chosen metrics or geometric formulations—mis-specification can reduce discriminative power and raise computational costs (He et al., 19 Mar 2024, Marin-Llobet et al., 7 Apr 2025).
Interpretability and Black-Box Models: As deep neural models eclipse classical classifiers in accuracy, achieving neuroscientific interpretability (especially identifying causal contributions of specific networks) remains a vital concern. Permutation-based or attention-based importance measures, as well as topological summaries, are active areas for bridging this gap (Kucukosmanoglu et al., 14 Aug 2024, Ferrà et al., 2023).
Extension to Multimodal and Longitudinal Analysis: Current binary classifiers are now being extended to multiclass, regression, and temporally adaptive frameworks, as well as to multimodal fusion of EEG, fMRI, MEG, and beyond (Vlasenko et al., 8 Aug 2025).
Energy and Resource Constraints: Real-time deployment, especially on wearables or implantables, mandates low-memory and low-energy classifiers. Binarization, memory-augmented neural networks, and ultra-compact nuclear/complexity features are promising here (Hersche et al., 2020, Qazi et al., 2019).
Statistical Control and Model-Free Inference: Procedures with provable control of false discovery rate (e.g., adaptive thresholds in the MK-Filter) are essential for whole-brain screening amidst massive multiple testing (He et al., 19 Mar 2024).

A plausible implication is that future advances will further integrate information-theoretic, geometric, and deep learning frameworks with improved statistical control, permitting even more robust and interpretable binary brain-state classification across modalities and real-world application settings.