Covariance Density Neural Networks

Graph neural networks have re-defined how we model and predict on network data but there lacks a consensus on choosing the correct underlying graph structure on which to model signals. CoVariance Neural Networks (VNN) address this issue by using the sample covariance matrix as a Graph Shift Operator (GSO). Here, we improve on the performance of VNNs by constructing a Density Matrix where we consider the sample Covariance matrix as a quasi-Hamiltonian of the system in the space of random variables. Crucially, using this density matrix as the GSO allows components of the data to be extracted at different scales, allowing enhanced discriminability and performance. We show that this approach allows explicit control of the stability-discriminability trade-off of the network, provides enhanced robustness to noise compared to VNNs, and outperforms them in useful real-life applications where the underlying covariance matrix is informative. In particular, we show that our model can achieve strong performance in subject-independent Brain Computer Interface EEG motor imagery classification, outperforming EEGnet while being faster. This shows how covariance density neural networks provide a basis for the notoriously difficult task of transferability of BCIs when evaluated on unseen individuals.

FAST functional connectivity implicates P300 connectivity in working memory deficits in Alzheimer's disease

Measuring transient functional connectivity is an important challenge in Electroencephalogram (EEG) research. Here, the rich potential for insightful, discriminative information of brain activity offered by high temporal resolution is confounded by the inherent noise of the medium and the spurious nature of correlations computed over short temporal windows. We propose a novel methodology to overcome these problems called Filter Average Short-Term (FAST) functional connectivity. First, long-term, stable, functional connectivity is averaged across an entire study cohort for a given pair of Visual Short Term Memory (VSTM) tasks. The resulting average connectivity matrix, containing information on the strongest general connections for the tasks, is used as a filter to analyse the transient high temporal resolution functional connectivity of individual subjects. In simulations, we show that this method accurately discriminates differences in noisy Event-Related Potentials (ERPs) between two conditions where standard connectivity and other comparable methods fail. We then apply this to analyse activity related to visual short-term memory binding deficits in two cohorts of familial and sporadic Alzheimer's disease. Reproducible significant differences were found in the binding task with no significant difference in the shape task in the P300 ERP range. This allows new sensitive measurements of transient functional connectivity, which can be implemented to obtain results of clinical significance.