Utility Metrics for Assessment and Subset Selection of Input Variables for Linear Estimation [Tips &amp; Tricks]

Bertrand, Alexander

doi:10.1109/msp.2018.2856632

Cited by 24 publications

(64 citation statements)

References 12 publications

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“…In the remaining of this paper, we will refer to this method as the decoder magnitude-based (DMB) greedy method or DMB-G. However, in [21] it was argued that the magnitude of the entries in the decoderŵ do not necessarily reflect the importance of the corresponding channel as it is scaling dependent and it does not properly take interactions across channels into account. Instead, it was argued to quantify the importance or 'utility' of a channel k by the increase in the least squared error (LSE) if channel k were to be removed and the decoder would be fully re-optimized.…”

Section: B Greedy Channel Selectionmentioning

confidence: 99%

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

Narayanan¹,

Patrinos²,

Bertrand³

2021

IEEE Trans. Neural Syst. Rehabil. Eng.

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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.

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Section: B Greedy Channel Selectionmentioning

confidence: 99%

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

Narayanan¹,

Patrinos²,

Bertrand³

2021

IEEE Trans. Neural Syst. Rehabil. Eng.

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“…To select channels we used the utility metric (Bertrand, 2018), which quantifies the effective loss, i.e., the increase in the LS cost, if a group of columns (corresponding to one channel or a set of channels and all their τ − 1 corresponding time-shifted version) would be removed and if the model (1) would be reoptimized afterwards:…”

Section: Channel Selectionmentioning

confidence: 99%

“…Note that a naive implementation of computing U g would require solving one LS squares problem like (1), for each possible removal of a candidate group, which would lead to a large computational cost for problems with large dimensions and/or involving a large number of groups. Fortunately, this can be circumvented, as shown by Bertrand (2018), with a final computational complexity that scales linearly in the number of groups, given the solution of (1) when none of the channels are removed. The basic workflow for finding the best k groups of EEG channels can be summarized as follows (Narayanan and Bertrand, 2019): we compute the utility metric for each of the groups and remove the group with the lowest utility.…”

Section: Channel Selectionmentioning

confidence: 99%

“…The utility metric for each (group of) channel(s) can be directly computed ‡ fromŵ (i) and C (i) (we refer to Bertrand (2018) and Narayanan and Bertrand (2019) for more details). We then ranked the groups according to their corresponding utilities, and removed the channel(s) corresponding to the group g with the lowest utility.…”

Section: Channel Selectionmentioning

confidence: 99%

“…In this work, we propose a channel selection strategy based on the utility metric (Bertrand, 2018), which allows a quick quantitative assessment of the influence of a channel (or a group of channels) on the reconstruction error. In the subject-specific scenario, we use the utility metric to remove channels one by one, each time removing the channel with least influence on the reconstruction error.…”

Section: Introductionmentioning

confidence: 99%

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Effect of number and placement of EEG electrodes on measurement of neural tracking of speech

Montoya-Martínez

Vanthornhout

Bertrand

et al. 2019

Preprint

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Measurement of neural tracking of natural running speech from the 15 electroencephalogram (EEG) is an increasingly popular method in auditory neuroscience 16 and has applications in audiology. The method involves decoding the envelope of the 17 speech signal from the EEG signal, and calculating the correlation with the envelope 18 that was presented to the subject. Typically EEG systems with 64 or more electrodes 19 are used. However, in practical applications, set-ups with fewer electrodes are required. 20 Here, we determine the optimal number of electrodes, and the best position to place 21 a limited number of electrodes on the scalp. We propose a channel selection strategy, 22 aiming to induce the selection of symmetric EEG channel groups in order to avoid 23 hemispheric bias. The proposed method is based on a utility metric, which allows 24 a quick quantitative assessment of the influence of each group of EEG channels on 25 the reconstruction error. We consider two use cases: a subject-specific case, where 26 the optimal number and positions of the electrodes is determined for each subject 27 individually, and a subject-independent case, where the electrodes are placed at the same 28 positions (in the 10-20 system) for all the subjects. We evaluated our approach using 64-29 channel EEG data from 90 subjects. Surprisingly, in the subject-specific case we found 30 that the correlation between actual and reconstructed envelope first increased with 31 decreasing number of electrodes, with an optimum at around 20 electrodes, yielding 38% 32 higher correlations using the optimal number of electrodes. In the subject-independent 33 case, we obtained a stable decoding performance when decreasing from 64 to 32 channels. 34When the number of channels was further decreased, the correlation decreased. For 35 a maximal decrease in correlation of 10%, 32 well-placed electrodes were sufficient in 36 87% of the subjects. Practical electrode placement recommendations are given for 8, 37 16, 24 and 32 electrode systems. 38 42 also has applications in domains such as audiology, as part of an objective measure 43 of speech intelligibility (Vanthornhout et al., 2018; Lesenfants et al., 2019), and coma 44 science (Braiman et al., 2018). 45The relationship between the stimulus and the brain response can be studied using 46 two different models (e.g., Crosse et al., 2016; Lalor and Foxe, 2010; Ding and Simon, 47 2012; Verschueren et al., 2019; Vanthornhout et al., 2018): in the forward model (also 48 know as encoding model), we determine a linear mapping from the stimulus to the 49 brain response. On the other hand, in the backward model (also known as stimulus 50 reconstruction), we determine the linear mapping from the brain response to the stimulus. 51Backward models are referred to as decoding models, because they attempt to reverse 52 the data generation process. Both the forward and backward models involve the solution 53 of a linear least squares (LS) regression problem. The quality of the reconstruction is 54 ...

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

Strypsteen

Bertrand

2021

J. Neural Eng.

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Objective. To develop an efficient, embedded electroencephalogram (EEG) channel selection approach for deep neural networks, allowing us to match the channel selection to the target model, while avoiding the large computational burdens of wrapper approaches in conjunction with neural networks. Approach. We employ a concrete selector layer to jointly optimize the EEG channel selection and network parameters. This layer uses a Gumbel-softmax trick to build continuous relaxations of the discrete parameters involved in the selection process, allowing them be learned in an end-to-end manner with traditional backpropagation. As the selection layer was often observed to include the same channel twice in a certain selection, we propose a regularization function to mitigate this behavior. We validate this method on two different EEG tasks: motor execution and auditory attention decoding. For each task, we compare the performance of the Gumbel-softmax method with a baseline EEG channel selection approach tailored towards this specific task: mutual information and greedy forward selection with the utility metric respectively. Main results. Our experiments show that the proposed framework is generally applicable, while performing at least as well as (and often better than) these state-of-the-art, task-specific approaches. Significance. The proposed method offers an efficient, task- and model-independent approach to jointly learn the optimal EEG channels along with the neural network weights.

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Utility Metrics for Assessment and Subset Selection of Input Variables for Linear Estimation [Tips & Tricks]

Cited by 24 publications

References 12 publications

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

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

Effect of number and placement of EEG electrodes on measurement of neural tracking of speech

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

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