Optimal Versus Approximate Channel Selection Methods for EEG Decoding With Application to Topology-Constrained Neuro-Sensor Networks

Abstract

Channel selection or electrode placement for neural decoding is a commonly encountered problem in electroencephalography (EEG). Since evaluating all possible channel combinations is usually infeasible, one usually has to settle for heuristic methods or convex approximations without optimality guarantees. To date, it remains unclear how large the gap is between the selection made by these approximate methods and the truly optimal selection. The goal of this paper is to quantify this optimality gap for several state-of-the-art channel selection methods in the context of least-squares based neural decoding. To this end, we reformulate the channel selection problem as a mixed-integer quadratic program (MIQP), which allows the use of efficient MIQP solvers to find the optimal channel combination in a feasible computation time for up to 100 candidate channels. As this reveals the exact solution to the combinatorial problem, it allows to quantify the performance losses when using stateof-the-art sub-optimal (yet faster) channel selection methods. In a context of auditory attention decoding, we find that a greedy channel selection based on the utility metric does not show a significant optimality gap compared to optimal channel selection, whereas other state-of-the-art greedy or l1-norm penalized methods do show a significant loss in performance. Furthermore, we demonstrate that the MIQP formulation also provides a natural way to incorporate topology constraints in the selection, e.g., for electrode placement in neuro-sensor networks with galvanic separation constraints. Furthermore, a combination of this utility-based greedy selection with an MIQP solver allows to perform a topology constrained electrode placement, even in large scale problems with more than 100 candidate positions.

EEG miniaturization limits for stimulus decoding with EEG sensor networks

“…The BEST analysis confirmed a significant increase in MESD (decrease in AAD performance) for N < 15 compared to the best achievable MESD using N = 86 channels (see figure 4(a)). In [26,32], a similar significant drop in AAD performance was observed for N < 10 channels. The discrepancy between the position of the turnover point can probably be explained by the different performance metrics that were used.…”

End-to-end learnable EEG channel selection for deep neural networks with Gumbel-softmax

“…Additionally, our use of a regularization function for distinct selections can be extended with additional constraints on the channels to be selected. For example, one possibility is selecting the channels that not only optimize performance, but also minimize the inter-electrode distance as much as possible, as is required in the design of miniaturized EEG sensor networks [7,34].…”

End-to-end learnable EEG channel selection for deep neural networks with Gumbel-softmax

“…In the field of AAD on the other hand, there is no clear set of EEG/speech features that perform the same role. Instead, we employ a greedy channel selection procedure based on the least-squares utility metric as described in [7], which is currently the state-of-theart channel selection method in EEG-based speech decoding paradigms [32]. In this setting, a linear decoder is trained to reconstruct the matching speech stimulus from the EEG signal, which constitutes a least-squares (LS) regression problem.…”

“…Additionally, our use of a regularization function for distinct selections can be extended with additional constraints on the channels to be selected. For example, one possibility is selecting the channels that not only optimize performance, but also minimize the inter-electrode distance as much as possible, as is required in the design of miniaturized EEG sensor networks [7,32].…”