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 state-of-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.

中文翻译：

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EEG解码的最佳与近似通道选择方法及其在拓扑约束神经传感器网络中的应用

神经解码的通道选择或电极放置是脑电图（EEG）中经常遇到的问题。由于评估所有可能的信道组合通常是不可行的，因此通常必须在没有最优性保证的情况下采用启发式方法或凸近似。迄今为止，尚不清楚通过这些近似方法进行的选择与真正的最佳选择之间的差距有多大。本文的目的是在基于最小二乘的神经解码的情况下，为几种最新的频道选择方法量化这种最优差距。为此，我们将频道选择问题重新表述为混合整数二次程序（MIQP），它允许使用有效的MIQP求解器在可行的计算时间内找到最多100个候选通道的最佳通道组合。由于这揭示了组合问题的确切解决方案，因此可以在使用最先进的次优（但更快）的信道选择方法时量化性能损失。在听觉注意解码的上下文中，我们发现，基于效用度量的贪婪渠道选择与最优渠道选择相比，没有显示出明显的最优差距，而其他最新的贪婪或l1-norm惩罚方法确实做到了表现出明显的性能损失。此外，我们证明MIQP公式还提供了一种自然的方式来将拓扑约束纳入选择中，例如，用于将电极放置在具有电流分离约束的神经传感器网络中。此外，这种基于实用程序的贪婪选择与MIQP求解器的组合，即使在具有超过100个候选位置的大规模问题中，也可以执行拓扑约束的电极放置。