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 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.

Highlights

  • Electroencephalography (EEG) is a popular non-invasive technology to record macro-scale electrophysiological activity in the brain

  • In the context of an auditory attention decoding (AAD) task, we demonstrate that, unlike-least absolute shrinkage and selection operator (LASSO) or decoder weight-based greedy selection, the greedy method based on the LS-utility metric does not perform significantly worse than the optimal mixed-integer quadratic program (MIQP)-based channel selection, while improving 3-4 orders of magnitude in computation time

  • We found the greedy method based on the LS-utility metric to perform similar to the optimal channel selection in an AAD task for standard cap EEG channels but requiring considerably less computation time, thereby providing a practical solution for the channel selection problem

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Summary

Introduction

Electroencephalography (EEG) is a popular non-invasive technology to record macro-scale electrophysiological activity in the brain. Most high-end EEG systems record from 20 up to 256 scalp electrodes [1], [2]. While using a large number of electrodes allows to record at a high spatial resolution, such high-density recordings come with several disadvantages; they require more expensive equipment, they lead to longer set-up times, they require more data storage/processing, and the higher dimensionality may cause overfitting in data-driven.

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