Channel Activity Coefficient (CAC) for EEG

• CAC is a scalar score for EEG channel selection that integrates classification accuracy, chance-normalized performance, and prediction confidence.
• It computes a multiplicative product of relative discriminatory quotient, accuracy–chance ratio, and confidence (1-H) to reliably rank channels.
• CAC offers a task-independent, reusable channel ranking that improves downstream BCI model performance compared to conventional, task-specific methods.

Channel Activity Coefficient (CAC) is a task-independent scalar score for EEG channel selection introduced within the Activity Coefficient-based Channel Selection (ACCS) framework. It is designed to quantify how reliably an individual EEG channel distinguishes “active” brain states from resting states by combining relative classification accuracy, chance-normalized accuracy, and prediction confidence into a single product score. In the formulation reported for high-density EEG–BCI systems, CAC is computed channel-wise from a univariate active-versus-rest discriminator and then used to rank electrodes, with the top-ranked subset serving as a reusable channel set across downstream tasks and models (Pandey et al., 10 Aug 2025).

1. Formal definition

In the ACCS framework, EEG channels are indexed by $i = 1, \ldots, C$. For each channel $i$, a simple one-dimensional CNN is trained to discriminate, using that channel alone, between active and rest trials. From held-out test predictions, three quantities are computed for each channel (Pandey et al., 10 Aug 2025):

• $A_i$: the channel-specific classification accuracy
• $H_i$: the Shannon entropy of the two-class soft-prediction vector $p = (p_1, p_2)$
• $A_{\max}, A_{\min}$: the maximal and minimal per-channel accuracies over all $i$

Three intermediate scores are then defined:

$$RDQ_i = \frac{A_i - A_{\min}}{A_{\max} - A_{\min} + \epsilon}$$

The Relative Discriminatory Quotient (RDQ) measures where channel $i$ sits between the worst and best channels.

$$ACR_i = \log_2 \left( \frac{A_i + \epsilon}{0.5 + \epsilon} \right)$$

The Accuracy–Chance Ratio (ACR) compares channel accuracy to chance level $i$0, with the base-2 logarithm mapping above-chance performance to positive values and below-chance performance to negative values.

$i$1

This is the Shannon entropy of the predicted class probabilities; consequently, $i$2 increases as predictions become more confident.

The final Channel Activity Coefficient is

$i$3

Here $i$4 is a small constant to prevent division-by-zero or log-of-zero, with $i$5 given as an example. By construction, $i$6 is large only if channel $i$7 both attains high accuracy and yields confident low-entropy predictions relative to other channels and relative to chance (Pandey et al., 10 Aug 2025).

2. Statistical rationale and design principles

The CAC metric is explicitly grounded in three statistical-information principles (Pandey et al., 10 Aug 2025).

First, discriminability scaling via RDQ rewards channels that perform close to the strongest discriminators and penalizes those near the weakest. This makes the score relative to the empirical range of channel performance rather than absolute in isolation.

Second, chance-normalized accuracy via ACR penalizes trivial predictors that hover around random guessing, compresses the dynamic range through the $i$8 mapping, and symmetrically punishes sub-chance channels. This component prevents a channel from appearing useful merely because its raw accuracy is numerically nonzero.

Third, prediction confidence via $i$9 incorporates soft-decision certainty. The reported motivation is that a channel may achieve high average accuracy while still producing diffuse posterior distributions; low entropy is therefore treated as an indicator of robustness.

The multiplicative form makes CAC jointly sensitive to the level and reliability of task-relevant fluctuations in each channel. The paper’s central claim is that this construction remains task-independent in the downstream sense: it does not require labels or models for the final BCI problem, only a generic active/rest discriminator (Pandey et al., 10 Aug 2025). This suggests that CAC is not a direct measure of semantic task structure, but rather a measure of channel utility under an operational notion of neural activity.

3. Algorithmic realization in ACCS

The ACCS workflow consists of preprocessing, channel-wise model training, and score computation (Pandey et al., 10 Aug 2025).

During preprocessing, each raw EEG channel is band-pass filtered, for example at 1–40 Hz, and notch-filtered at 50/60 Hz to remove line noise. Continuous recordings are segmented into fixed-duration trials, with 5 s active-versus-rest epochs given as an example for the KARAOne dataset at 1 kHz. Baseline removal and per-trial amplitude normalization are then applied.

During channel-wise model training, each channel $A_i$0 is handled independently. The procedure is:

1. collect that channel’s active/rest epochs across all trials;
2. split the data into train/validation/test sets, with 70/15/15 given as an example;
3. train a 1D-CNN plus self-attention classifier for 50 epochs with batch size 32, optimizing binary cross-entropy using Adam with initial learning rate $A_i$1 and ReduceLROnPlateau decay;
4. record test-time predicted probabilities $A_i$2 and channel accuracy $A_i$3.

During score computation, $A_i$4 and $A_i$5 are computed over all channels, after which $A_i$6, $A_i$7, entropy $A_i$8, and finally $A_i$9 are evaluated for each channel.

The framework is therefore modular: the only required supervision is binary active/rest labeling at the per-channel stage, whereas downstream classification is separated from channel scoring. A plausible implication is that ACCS shifts optimization effort from repeated task-specific channel search to one reusable channel-ranking phase.

4. Ranking, subset formation, and computational properties

Once $H_i$0 has been computed, the scores may be normalized across channels, for example by min-max scaling, although the paper notes that this step is optional (Pandey et al., 10 Aug 2025). Channels are then sorted in descending order and a single hyperparameter $H_i$1 specifies how many to retain. In the reported experiments, $H_i$2 was chosen because of common 16-electrode caps in BCI research.

The resulting subset is simply the top-$H_i$3 channels by CAC. No threshold beyond $H_i$4 is required, although the paper notes that a minimum acceptable CAC such as $H_i$5 could be imposed if desired.

The dominant computational cost is the training of $H_i$6 separate CNNs. If $H_i$7 is the number of epochs, $H_i$8 the average number of samples per channel, and $H_i$9 the per-sample forward/backward flop count of the CNN, the total complexity is reported as

$p = (p_1, p_2)$0

Once all CNNs have been trained, score computation and sorting require only

$p = (p_1, p_2)$1

which is negligible by comparison (Pandey et al., 10 Aug 2025).

For the reported configuration with $p = (p_1, p_2)$2, $p = (p_1, p_2)$3, and $p = (p_1, p_2)$4 $p = (p_1, p_2)$5 subjects $p = (p_1, p_2)$6 classes $p = (p_1, p_2)$7 trials$p = (p_1, p_2)$8 samples $p = (p_1, p_2)$9 points, and using a lightweight 1D-CNN, end-to-end CAC computation can be carried out in a few hours on a single GPU. Channel-wise training can also be parallelized across multiple GPUs to reduce wall-clock time.

5. Empirical behavior and comparative performance

The reported empirical results position ACCS as a task-independent alternative to task-specific channel selection methods (Pandey et al., 10 Aug 2025). Table 4 in the paper compares relative accuracy gains over five binary and one multi-class imagined-speech tasks across the following categories:

Method category	Methods	Task-independent
Task-independent methods	PCA	Y
Task-dependent methods	Mutual Information (MI), ECA-Net, NSGA-II, XCDC, SBFS	N
ACCS	ACCS	Y

The principal reported findings are that ACCS delivers an average +34.97% gain on the multi-class task, compared with +12.85% for PCA, and that it matches or exceeds five task-specific algorithms on the same evaluation set (Pandey et al., 10 Aug 2025). Under the same DDA+SVM classifier, ACCS is reported as consistently more effective than MI (+21.52%), XCDC (+24.69%), and SBFS (+29.85%).

A central operational distinction is reusability. MI and SBFS must be re-run for each new classification problem, whereas ACCS yields a single reusable 16-channel set that boosts performance across downstream models including CNNs, SVMs, and LSTMs, and across tasks including phonemes and words. This suggests that the paper treats channel selection not as a classifier-specific wrapper optimization problem, but as a more stable property of the recording montage under active/rest contrast.

6. Reported effects, spatial patterns, and scope conditions

In Experiment 3, five distinct classifiers were benchmarked on full 64-channel EEG and on the 16 channels selected by ACCS (Pandey et al., 10 Aug 2025). The reported improvements include:

• EEGNet+SPDNet: +39.52% increase on the 11-class imagined-speech task
• DDA+SVM: +34.97% on the multi-class problem and +7.96% to +10.07% on various binary sub-tasks
• Cepstral ANN: +4.02% to +12.81% across binary tasks

These results are interpreted in the paper as evidence that removing noisy or redundant electrodes can improve classification broadly rather than only for a single architecture.

The spatial visualization in Fig. 3 reportedly shows that frontal and motor-cortical electrodes cluster among the top 16 by average CAC, while peripheral and occipital sites generally rank low (Pandey et al., 10 Aug 2025). The paper describes this as automatically recovering neurophysiologically plausible regions for speech imagery. A plausible implication is that CAC does not merely optimize statistical separability but may also align with known cortical relevance under the specific imagined-speech setting examined.

The same source also states several limitations. Active/rest discrimination may fail to capture subtler cognitive phenomena such as affective states. Training separate models per channel increases upfront compute, and the paper notes that lightweight alternatives such as shallow classifiers could reduce this burden. CAC also presumes that “activity” over baseline is the principal indicator of usefulness; for ERP-driven tasks, channels with low spontaneous activity but high evoked responses might be under-weighted (Pandey et al., 10 Aug 2025).

Potential extensions identified in the source include replacing the CNN with a faster univariate time–frequency feature extractor such as wavelet energy, generalizing from binary active/rest to multi-state baselines, integrating source-localization priors, and applying CAC in online adaptive BCI through periodic channel re-evaluation as subject state drifts. These proposals indicate that CAC is presented not as a closed metric family but as a scoring principle that can be re-instantiated under different feature extractors, baseline definitions, and adaptation regimes.