A Domain-Informed Multi-Objective Framework for EEG Channel Selection in Motor Imagery BCIs

Abstract: Motor imagery (MI) classification using electroencephalography (EEG) signals is essential for advancing brain-computer interfaces (BCIs). Traditional EEG channel selection methods often face limitations, such as dependency on single-objective criteria and susceptibility to local optima. To address these challenges, this work proposes a multi-objective optimisation framework that employs non-dominated sorting genetic algorithm, multiple-objective particle swarm optimisation, and a multi-objective evolutionary algorithm based on decomposition. Our approach effectively balances spatial relevance, using a Gaussian kernel, and functional discriminability, which assesses intratrial task-related desynchronisation, thereby improving performance. We evaluated this framework on four EEG datasets: Physionet, OpenBMI, HighGamma, and BCIIV-2A. The proposed approach successfully identifies compact, relevant channel subsets concentrated around sensorimotor cortex regions linked to MI activity, addressing the prevalent challenges of dimensionality and complexity inherent to traditional techniques. Furthermore, the framework achieved classification performance of 87%, 71%, 75%, and 65% on the Physionet, OpenBMI, HighGamma, and BCIIV-2A datasets, respectively. By outperforming existing single-objective and accuracy-based methods, and those relying on fixed subsets, these findings demonstrate that this new multi-objective optimisation framework can enhance MI-based BCI performance while facilitating compact channel configurations with reduced computational complexity, making them better suited for wearable, portable, and real-time BCI applications.

• The paper formulates EEG channel selection as a constrained bi-objective problem that independently optimizes sensorimotor spatial relevance and trial-specific ITTRD-based discriminability across at most 16 channels.
• The paper evaluates NSGA-II, MOPSO, and MOEA/D on four public datasets, achieving a best result of 87% on PhysioNet with MOPSO and outperforming IMOCS’s reported 79.5% at the same channel count.
• The paper finds that selected channels consistently cluster around C3, C4, Cz, FCz, and CPz, but notes that greedy selection can deliver higher accuracy on some datasets and that MOPSO is sensitive to unnormalized objective scales.

Motivation and problem formulation

Channel selection for motor imagery (MI) brain-computer interfaces (BCIs) has historically been dominated by single-objective criteria or aggregated scores, which conflate spatial plausibility with classification utility. The paper under review formulates EEG channel selection as a constrained bi-objective optimisation problem that keeps two objectives explicitly independent: spatial relevance, computed via a Gaussian kernel centred on the sensorimotor reference electrodes C3/C4, and functional discriminability, quantified by intratrial task-related desynchronisation (ITTRD). The decision variable is a binary vector over $N$ channels, subject to a cardinality constraint $\|x\|_1 \leq L$ (with $L = 16$).

The ITTRD objective distinguishes this work from conventional ERD/ERS-based selection: rather than averaging spectral power changes across trials, it computes the percentage change between baseline and activation periods per trial using Welch's method, thereby preserving trial-specific neural characteristics. The authors argue that the two objectives are inherently conflicting—broader spatial coverage can dilute discriminative power—which motivates Pareto-based search rather than scalarisation.

Optimisation algorithms

Three population-based multi-objective evolutionary algorithms are instantiated on this formulation:

• NSGA-II: binary tournament selection, single-point crossover ($p_c = 0.7$), bit-flip mutation ($p_m = 0.1$), elitist non-dominated sorting with crowding distance; population 10 over 1000 generations.
• MOPSO: swarm of 10 particles with sigmoid velocity-to-position mapping, an external repository of 100 non-dominated solutions (10 grid divisions), inertia 0.5, acceleration coefficients $c_1 = c_2 = 2$, run for 100 iterations.
• MOEA/D: Tchebycheff decomposition into 19 scalar subproblems with neighbourhood size 10 and mating probability 0.7, over 1000 generations.

A greedy accuracy-driven baseline without domain knowledge (incremental forward selection using per-channel SVM accuracy, capped at 16 channels) serves as the comparator. Downstream decoding uses filter bank common spatial patterns (FBCSP, 36 features) plus 19 statistical/time-domain features per channel, reduced to the top 10 features via mRMR and classified with a grid-searched SVM.

Empirical results

The framework was evaluated on four public datasets spanning heterogeneous montages and cohorts: PhysioNet (109 subjects, 64 channels), OpenBMI (54 subjects, 62 channels), HighGamma (14 subjects, 128 channels), and BCIIV-2A (9 subjects, 22 channels). Feature selection consistently improved accuracy relative to the full feature set across all algorithms and datasets.

Dataset	Best MOO result	Channels	Greedy baseline
Physionet	87% (MOPSO)	16	93% (11.77 ch)
BCIIV-2A	63% (MOPSO/MOEA/D)	~6–11	65% (4.50 ch)
HighGamma	75% (NSGA-II)	~10.6	71% (7.70 ch)
OpenBMI	71% (MOPSO)	~15.8	69% (4.90 ch)

The headline comparison is against IMOCS [Handiru & Prasad]: MOPSO reaches 87% on PhysioNet versus IMOCS's reported 79.5% at the same channel count, evaluated on a substantially larger cohort of 109 subjects. This is the strongest quantitative claim in the paper.

Statistical analysis supports the superiority claim partially. One-way ANOVA found significant differences among methods on Physionet (F = 20.25), OpenBMI (F = 21.96), and BCIIV-2A (F = 9.20), all at $p < 0.001$, with Tukey HSD showing each MOO algorithm significantly outperforming greedy on those datasets. However, no significant differences were found on HighGamma (F = 1.56, p = 0.21), and no significant differences separated the three MOO algorithms from one another anywhere. Notably, the greedy baseline achieved the highest raw accuracy on Physionet (93%) and BCIIV-2A (65%) with fewer channels—the MOO advantage there rests on neurophysiological interpretability rather than accuracy.

Convergence behaviour and algorithm-specific pathologies

The convergence analysis reveals meaningful differences among the optimisers. NSGA-II converged stably (spatial relevance by generation 200–300; ITTRD by 400–500). MOEA/D converged rapidly but required up to 600 generations for ITTRD on harder datasets. MOPSO exhibited dataset-dependent instability: on Physionet, HighGamma, and BCIIV-2A its ITTRD objective froze near zero after early discovery of the global best, while on OpenBMI it oscillated to extreme values near −800 before recovering. The authors attribute this to the interaction between binary position updates and the sigmoid transformation combined with the scale imbalance between objectives—ITTRD's dynamic range far exceeds that of spatial relevance. This is an honest concession that the framework's objectives are not normalised, and it bounds MOPSO's reliability within this pipeline.

Spatial structure of selected channels

Topographic analysis of the Pareto-optimal subsets shows consistent clustering around central sensorimotor electrodes (C3, C4, Cz, FCz, CPz) across all three algorithms and datasets, with NSGA-II most tightly concentrated centrally, MOPSO broadest (including frontal/parietal sites), and MOEA/D intermediate. The authors contrast this with the greedy baseline, whose subsets were scattered across the scalp and frequently included non-sensorimotor channels—an observation they interpret as evidence that purely accuracy-driven selection exploits classifier-specific cues rather than physiologically meaningful signals. This interpretability argument is the core justification for accepting lower raw accuracy where greedy wins.

Limitations and open questions

Several limitations are acknowledged or evident. First, the greedy baseline outperforms the proposed methods in raw accuracy on two of four datasets, so the framework's value proposition depends on weighting interpretability and physiological plausibility alongside accuracy—a preference the paper asserts but does not formalise. Second, the absence of objective normalisation destabilises MOPSO, and no remedy is proposed. Third, evaluation is restricted to binary left/right-hand MI; extension to multi-class paradigms, SSVEP, and P300 remains untested. Fourth, the final solution among ten candidate Pareto subsets is chosen partly by requiring inclusion of C3 or C4 plus highest accuracy, introducing a mild circularity with the domain prior. Finally, subject-independent and real-time adaptive channel selection are identified as open problems, as is validation on wearable hardware with genuinely constrained electrode counts.

Conclusion

This paper contributes a domain-informed bi-objective formulation of EEG channel selection that preserves the independence of spatial relevance and functional discriminability, instantiated through NSGA-II, MOPSO, and MOEA/D. It delivers a strong, statistically supported improvement over prior aggregated-score methods on PhysioNet (87% vs. 79.5%) and demonstrates sensorimotor-consistent channel subsets across four public benchmarks. Its principal caveats—greedy baselines matching or exceeding accuracy on some datasets, MOPSO's sensitivity to objective scaling, and binary-task-only evaluation—define the concrete questions subsequent work must address.