A Distributed Adaptive Algorithm for Non-Smooth Spatial Filtering Problems in Wireless Sensor Networks

A wireless sensor network often relies on a fusion center to process the data collected by each of its sensing nodes. Such an approach relies on the continuous transmission of raw data to the fusion center, which typically has a major impact on the sensors' battery life. To address this issue in the particular context of spatial filtering and signal fusion problems, we recently proposed the Distributed Adaptive Signal Fusion (DASF) algorithm, which distributively computes a spatial filter expressed as the solution of a smooth optimization problem involving the network-wide sensor signal statistics. In this work, we show that the DASF algorithm can be extended to compute the filters associated with a certain class of non-smooth optimization problems. This extension makes the addition of sparsity-inducing norms to the problem's cost function possible, allowing sensor selection to be performed in a distributed fashion, alongside the filtering task of interest, thereby further reducing the network's energy consumption. We provide a description of the algorithm, prove its convergence, and validate its performance and solution tracking capabilities with numerical experiments.

Stimulus-Informed Generalized Canonical Correlation Analysis for Group Analysis of Neural Responses

Various new brain-computer interface technologies or neuroscience applications require decoding stimulus-following neural responses to natural stimuli such as speech and video from, e.g., electroencephalography (EEG) signals. In this context, generalized canonical correlation analysis (GCCA) is often used as a group analysis technique, which allows the extraction of correlated signal components from the neural activity of multiple subjects attending to the same stimulus. GCCA can be used to improve the signal-to-noise ratio of the stimulus-following neural responses relative to all other irrelevant (non-)neural activity, or to quantify the correlated neural activity across multiple subjects in a group-wise coherence metric. However, the traditional GCCA technique is stimulus-unaware: no information about the stimulus is used to estimate the correlated components from the neural data of several subjects. Therefore, the GCCA technique might fail to extract relevant correlated signal components in practical situations where the amount of information is limited, for example, because of a limited amount of training data or group size. This motivates a new stimulus-informed GCCA (SI-GCCA) framework that allows taking the stimulus into account to extract the correlated components. We show that SI-GCCA outperforms GCCA in various practical settings, for both auditory and visual stimuli. Moreover, we showcase how SI-GCCA can be used to steer the estimation of the components towards the stimulus. As such, SI-GCCA substantially improves upon GCCA for various purposes, ranging from preprocessing to quantifying attention.

Minimally Informed Linear Discriminant Analysis: training an LDA model with unlabelled data

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.

Distributed Adaptive Signal Fusion for Fractional Programs

The distributed adaptive signal fusion (DASF) framework allows to solve spatial filtering optimization problems in a distributed and adaptive fashion over a bandwidth-constrained wireless sensor network. The DASF algorithm requires each node to sequentially build a compressed version of the original network-wide problem and solve it locally. However, these local problems can still result in a high computational load at the nodes, especially when the required solver is iterative. In this paper, we study the particular case of fractional programs, i.e., problems for which the objective function is a fraction of two continuous functions, which indeed require such iterative solvers. By exploiting the structure of a commonly used method for solving fractional programs and interleaving it with the iterations of the standard DASF algorithm, we obtain a distributed algorithm with a significantly reduced computational cost compared to the straightforward application of DASF as a meta-algorithm. We prove convergence and optimality of this "fractional DASF" (FDASF) algorithm and demonstrate its performance via numerical simulations.

A distributed neural network architecture for dynamic sensor selection with application to bandwidth-constrained body-sensor networks

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.

A Distributed Adaptive Algorithm for Node-Specific Signal Fusion Problems in Wireless Sensor Networks

Wireless sensor networks consist of sensor nodes that are physically distributed over different locations. Spatial filtering procedures exploit the spatial correlation across these sensor signals to fuse them into a filtered signal satisfying some optimality condition. However, gathering the raw sensor data in a fusion center to solve the problem in a centralized way would lead to high energy and communication costs. The distributed adaptive signal fusion (DASF) framework has been proposed as a generic method to solve these signal fusion problems in a distributed fashion, which reduces the communication and energy costs in the network. The DASF framework assumes that there is a common goal across the nodes, i.e., the optimal filter is shared across the network. However, many applications require a node-specific objective, while all these node-specific objectives are still related via a common latent data model. In this work, we propose the DANSF algorithm which builds upon the DASF framework, and extends it to allow for node-specific spatial filtering problems.

A Distributed Adaptive Algorithm for Non-Smooth Spatial Filtering Problems

Computing the optimal solution to a spatial filtering problems in a Wireless Sensor Network can incur large bandwidth and computational requirements if an approach relying on data centralization is used. The so-called distributed adaptive signal fusion (DASF) algorithm solves this problem by having the nodes collaboratively solve low-dimensional versions of the original optimization problem, relying solely on the exchange of compressed views of the sensor data between the nodes. However, the DASF algorithm has only been shown to converge for filtering problems that can be expressed as smooth optimization problems. In this paper, we explore an extension of the DASF algorithm to a family of non-smooth spatial filtering problems, allowing the addition of non-smooth regularizers to the optimization problem, which could for example be used to perform node selection, and eliminate nodes not contributing to the filter objective, therefore further reducing communication costs. We provide a convergence proof of the non-smooth DASF algorithm and validate its convergence via simulations in both a static and adaptive setting.

Stimulus-Informed Generalized Canonical Correlation Analysis of Stimulus-Following Brain Responses

In brain-computer interface or neuroscience applications, generalized canonical correlation analysis (GCCA) is often used to extract correlated signal components in the neural activity of different subjects attending to the same stimulus. This allows quantifying the so-called inter-subject correlation or boosting the signal-to-noise ratio of the stimulus-following brain responses with respect to other (non-)neural activity. GCCA is, however, stimulus-unaware: it does not take the stimulus information into account and does therefore not cope well with lower amounts of data or smaller groups of subjects. We propose a novel stimulus-informed GCCA algorithm based on the MAXVAR-GCCA framework. We show the superiority of the proposed stimulus-informed GCCA method based on the inter-subject correlation between electroencephalography responses of a group of subjects listening to the same speech stimulus, especially for lower amounts of data or smaller groups of subjects.

Bandwidth-efficient distributed neural network architectures with application to body sensor networks

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.

EventNet: Detecting Events in EEG

Neurologists are often looking for various "events of interest" when analyzing EEG. To support them in this task various machine-learning-based algorithms have been developed. Most of these algorithms treat the problem as classification, thereby independently processing signal segments and ignoring temporal dependencies inherent to events of varying duration. At inference time, the predicted labels for each segment then have to be post processed to detect the actual events. We propose an end-to-end event detection approach (EventNet), based on deep learning, that directly works with events as learning targets, stepping away from ad-hoc postprocessing schemes to turn model outputs into events. We compare EventNet with a state-of-the-art approach for artefact and and epileptic seizure detection, two event types with highly variable durations. EventNet shows improved performance in detecting both event types. These results show the power of treating events as direct learning targets, instead of using ad-hoc postprocessing to obtain them. Our event detection framework can easily be extended to other event detection problems in signal processing, since the deep learning backbone does not depend on any task-specific features.