Alexander Bertrand

Nick Seeuws, Maarten De Vos, Alexander Bertrand

Objective: Finding events of interest is a common task in biomedical signal processing. The detection of epileptic seizures and signal artefacts are two key examples. Epoch-based classification is the typical machine learning framework to detect such signal events because of the straightforward application of classical machine learning techniques. Usually, post-processing is required to achieve good performance and enforce temporal dependencies. Designing the right post-processing scheme to convert these classification outputs into events is a tedious, and labor-intensive element of this framework. Methods: We propose an event-based modeling framework that directly works with events as learning targets, stepping away from ad-hoc post-processing schemes to turn model outputs into events. We illustrate the practical power of this framework on simulated data and real-world data, comparing it to epoch-based modeling approaches. Results: We show that event-based modeling (without post-processing) performs on par with or better than epoch-based modeling with extensive post-processing. Conclusion: These results show the power of treating events as direct learning targets, instead of using ad-hoc post-processing to obtain them, severely reducing design effort. Significance: The event-based modeling framework can easily be applied to other event detection problems in signal processing, removing the need for intensive task-specific post-processing.

Nicolas Heintz, Tom Francart, Alexander Bertrand

Linear Discriminant Analysis (LDA) is one of the oldest and most popular linear methods for supervised classification problems. In this paper, we demonstrate that it is possible to compute the exact projection vector from LDA models based on unlabelled data, if some minimal prior information is available. More precisely, we show that only one of the following three pieces of information is actually sufficient to compute the LDA projection vector if only unlabelled data are available: (1) the class average of one of the two classes, (2) the difference between both class averages (up to a scaling), or (3) the class covariance matrices (up to a scaling). These theoretical results are validated in numerical experiments, demonstrating that this minimally informed Linear Discriminant Analysis (MILDA) model closely matches the performance of a supervised LDA model. Furthermore, we show that the MILDA projection vector can be computed in a closed form with a computational cost comparable to LDA and is able to quickly adapt to non-stationary data, making it well-suited to use as an adaptive classifier.

Thomas Strypsteen, Alexander Bertrand

We propose a dynamic sensor selection approach for deep neural networks (DNNs), which is able to derive an optimal sensor subset selection for each specific input sample instead of a fixed selection for the entire dataset. This dynamic selection is jointly learned with the task model in an end-to-end way, using the Gumbel-Softmax trick to allow the discrete decisions to be learned through standard backpropagation. We then show how we can use this dynamic selection to increase the lifetime of a wireless sensor network (WSN) by imposing constraints on how often each node is allowed to transmit. We further improve performance by including a dynamic spatial filter that makes the task-DNN more robust against the fact that it now needs to be able to handle a multitude of possible node subsets. Finally, we explain how the selection of the optimal channels can be distributed across the different nodes in a WSN. We validate this method on a use case in the context of body-sensor networks, where we use real electroencephalography (EEG) sensor data to emulate an EEG sensor network. We analyze the resulting trade-offs between transmission load and task accuracy.

Thomas Strypsteen, Alexander Bertrand

In this paper, we describe a conceptual design methodology to design distributed neural network architectures that can perform efficient inference within sensor networks with communication bandwidth constraints. The different sensor channels are distributed across multiple sensor devices, which have to exchange data over bandwidth-limited communication channels to solve, e.g., a classification task. Our design methodology starts from a user-defined centralized neural network and transforms it into a distributed architecture in which the channels are distributed over different nodes. The distributed network consists of two parallel branches of which the outputs are fused at the fusion center. The first branch collects classification results from local, node-specific classifiers while the second branch compresses each node's signal and then reconstructs the multi-channel time series for classification at the fusion center. We further improve bandwidth gains by dynamically activating the compression path when the local classifications do not suffice. We validate this method on a motor execution task in an emulated EEG sensor network and analyze the resulting bandwidth-accuracy trade-offs. Our experiments show that the proposed framework enables up to a factor 20 in bandwidth reduction with minimal loss (up to 2%) in classification accuracy compared to the centralized baseline on the demonstrated motor execution task. The proposed method offers a way to smoothly transform a centralized architecture to a distributed, bandwidth-efficient network amenable for low-power sensor networks. While the application focus of this paper is on wearable brain-computer interfaces, the proposed methodology can be applied in other sensor network-like applications as well.

Cem Ates Musluoglu, Alexander Bertrand

With the emergence of wireless sensor networks (WSNs), many traditional signal processing tasks are required to be computed in a distributed fashion, without transmissions of the raw data to a centralized processing unit, due to the limited energy and bandwidth resources available to the sensors. In this paper, we propose a distributed independent component analysis (ICA) algorithm, which aims at identifying the original signal sources based on observations of their mixtures measured at various sensor nodes. One of the most commonly used ICA algorithms is known as FastICA, which requires a spatial pre-whitening operation in the first step of the algorithm. Such a pre-whitening across all nodes of a WSN is impossible in a bandwidth-constrained distributed setting as it requires to correlate each channel with each other channel in the WSN. We show that an explicit network-wide pre-whitening step can be circumvented by leveraging the properties of the so-called Distributed Adaptive Signal Fusion (DASF) framework. Despite the lack of such a network-wide pre-whitening, we can still obtain the $Q$ least Gaussian independent components of the centralized ICA solution, where $Q$ scales linearly with the required communication load.

Nicolas Heintz, Tom Francart, Alexander Bertrand

Auditory attention decoding (AAD) algorithms exploit brain signals, such as electroencephalography (EEG), to identify which speaker a listener is focusing on in a multi-speaker environment. While state-of-the-art AAD algorithms can identify the attended speaker on short time windows, their predictions are often too inaccurate for practical use. In this work, we propose augmenting AAD with a hidden Markov model (HMM) that models the temporal structure of attention. More specifically, the HMM relies on the fact that a subject is much less likely to switch attention than to keep attending the same speaker at any moment in time. We show how a HMM can significantly improve existing AAD algorithms in both causal (real-time) and non-causal (offline) settings. We further demonstrate that HMMs outperform existing postprocessing approaches in both accuracy and responsiveness, and explore how various factors such as window length, switching frequency, and AAD accuracy influence overall performance. The proposed method is computationally efficient, intuitive to use and applicable in both real-time and offline settings.

Thomas Strypsteen, Alexander Bertrand

In this paper, we introduce Conditional Gumbel-Softmax as a method to perform end-to-end learning of the optimal feature subset for a given task and deep neural network (DNN) model, while adhering to certain pairwise constraints between the features. We do this by conditioning the selection of each feature in the subset on another feature. We demonstrate how this approach can be used to select the task-optimal nodes composing a wireless sensor network (WSN) while ensuring that none of the nodes that require communication between one another have too large of a distance between them, limiting the required power spent on this communication. We validate this approach on an emulated Wireless Electroencephalography (EEG) Sensor Network (WESN) solving a motor execution task. We analyze how the performance of the WESN varies as the constraints are made more stringent and how well the Conditional Gumbel-Softmax performs in comparison with a heuristic, greedy selection method. While the application focus of this paper is on wearable brain-computer interfaces, the proposed methodology is generic and can readily be applied to node deployment in wireless sensor networks and constrained feature selection in other applications as well.

Thomas Strypsteen, Alexander Bertrand

Many electroencephalography (EEG) applications rely on channel selection methods to remove the least informative channels, e.g., to reduce the amount of electrodes to be mounted, to decrease the computational load, or to reduce overfitting effects and improve performance. Wrapper-based channel selection methods aim to match the channel selection step to the target model, yet they require to re-train the model multiple times on different candidate channel subsets, which often leads to an unacceptably high computational cost, especially when said model is a (deep) neural network. To alleviate this, we propose a framework to embed the EEG channel selection in the neural network itself to jointly learn the network weights and optimal channels in an end-to-end manner by traditional backpropagation algorithms. We deal with the discrete nature of this new optimization problem by employing continuous relaxations of the discrete channel selection parameters based on the Gumbel-softmax trick. We also propose a regularization method that discourages selecting channels more than once. This generic approach is evaluated on two different EEG tasks: motor imagery brain-computer interfaces and auditory attention decoding. The results demonstrate that our framework is generally applicable, while being competitive with state-of-the art EEG channel selection methods, tailored to these tasks.

Tim De Ryck, Maarten De Vos, Alexander Bertrand

Change point detection (CPD) aims to locate abrupt property changes in time series data. Recent CPD methods demonstrated the potential of using deep learning techniques, but often lack the ability to identify more subtle changes in the autocorrelation statistics of the signal and suffer from a high false alarm rate. To address these issues, we employ an autoencoder-based methodology with a novel loss function, through which the used autoencoders learn a partially time-invariant representation that is tailored for CPD. The result is a flexible method that allows the user to indicate whether change points should be sought in the time domain, frequency domain or both. Detectable change points include abrupt changes in the slope, mean, variance, autocorrelation function and frequency spectrum. We demonstrate that our proposed method is consistently highly competitive or superior to baseline methods on diverse simulated and real-life benchmark data sets. Finally, we mitigate the issue of false detection alarms through the use of a postprocessing procedure that combines a matched filter and a newly proposed change point score. We show that this combination drastically improves the performance of our method as well as all baseline methods.

Jorge Plata-Chaves, Mohamad Hasan Bahari, Marc Moonen et al.

We study a distributed node-specific parameter estimation problem where each node in a wireless sensor network is interested in the simultaneous estimation of different vectors of parameters that can be of local interest, of common interest to a subset of nodes, or of global interest to the whole network. We assume a setting where the nodes do not know which other nodes share the same estimation interests. First, we conduct a theoretical analysis on the asymptotic bias that results in case the nodes blindly process all the local estimates of all their neighbors to solve their own node-specific parameter estimation problem. Next, we propose an unsupervised diffusion-based LMS algorithm that allows each node to obtain unbiased estimates of its node-specific vector of parameters by continuously identifying which of the neighboring local estimates correspond to each of its own estimation tasks. Finally, simulation experiments illustrate the efficiency of the proposed strategy.