Covariance Density Neural Networks

TMLR Paper6664 Authors

Abstract:

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.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Bertrand_Thirion1

Submission Number: 6664