arXiv subjects

Om Roy

Publications and source records attributed to Om Roy.

6 recordsLinked to original sources

arXiv2026

TVGL-CFM:Generating and Forecasting Time-Varying Trajectories of Dynamic Networks with Conditional Flow Matching

Many complex systems, including brain networks, financial markets, and gene-regulatory circuits, are better described by interaction structures that evolve over time than by a single fixed graph. The time-varying graphical lasso (TVGL) estimates this structure from multivariate signals as a temporally coherent sequence of sparse precision matrices. We introduce TVGL-CFM, a unified generative framework that learns distributions over complete SPD precision-matrix trajectories without requiring a pre-specified graph, supporting both class-conditional generation and history-conditioned forecasting. An SPD trajectory with T windows lies on the product Riemannian manifold (S++^p)^T. We construct a global log-Euclidean diffeomorphism from this product space to a Euclidean sequence space, enabling a non-autoregressive conditional flow-matching model with a Transformer backbone to generate all windows jointly and decode them to SPD matrices without post-hoc projection. For forecasting, we use two distinct data-dependent couplings so that the flow transforms an informative prior into a coherent future block. Across EEG motor-imagery data and three nonlinear dynamical systems, TVGL-CFM preserves class-discriminative dependency structure and forecasts future connectivity more accurately than several strongly matched baselines, opening new possibilities for generative dynamic graph models.

cs.LG↗

arXiv2026

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.

cs.LG↗

arXiv2026

Graph Variate Neural Networks

Modelling dynamically evolving spatio-temporal signals is a prominent challenge in the Graph Neural Network (GNN) literature. Notably, GNNs assume an existing underlying graph structure. While this underlying structure may not always exist or is derived independently from the signal, a temporally evolving functional network can always be constructed from multi-channel data. Graph Variate Signal Analysis (GVSA) defines a unified framework consisting of a network tensor of instantaneous connectivity profiles against a stable support usually constructed from the signal itself. Building on GVSA and tools from graph signal processing, we introduce Graph-Variate Neural Networks (GVNNs): layers that convolve spatio-temporal signals with a signal-dependent connectivity tensor combining a stable long-term support with instantaneous, data-driven interactions. This design captures dynamic statistical interdependencies at each time step without ad hoc sliding windows and admits an efficient implementation with linear complexity in sequence length. Across forecasting benchmarks, GVNNs consistently outperform strong graph-based baselines and are competitive with widely used sequence models such as LSTMs and Transformers. On EEG motor-imagery classification, GVNNs achieve strong accuracy highlighting their potential for brain-computer interface applications.

cs.LG↗

arXiv2025

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.

q-bio.NC↗

arXiv2025

A Hodge-FAST Framework for High-Resolution Dynamic Functional Connectivity Analysis of Higher Order Interactions in EEG Signals

We introduce a novel framework that integrates Hodge decomposition with Filtered Average Short-Term (FAST) functional connectivity to analyze dynamic functional connectivity (DFC) in EEG signals. This method leverages graph-based topology and simplicial analysis to explore transient connectivity patterns at multiple scales, addressing noise, sparsity, and computational efficiency. The temporal EEG data are first sparsified by keeping only the most globally important connections, instantaneous connectivity at these connections is then filtered by global long-term stable correlations. This tensor is then decomposed into three orthogonal components to study signal flows over higher-order structures such as triangle and loop structures. Our analysis of Alzheimer-related MCI patients show significant temporal differences related to higher-order interactions that a pairwise analysis on its own does not implicate. This allows us for the first time to capture higher-dimensional interactions at high temporal resolution in noisy EEG signal recordings.

eess.SP↗

arXiv2024

Graph Permutation Entropy: Extensions to the Continuous Case, A step towards Ordinal Deep Learning, and More

Nonlinear dynamics play an important role in the analysis of signals. A popular, readily interpretable nonlinear measure is Permutation Entropy. It has recently been extended for the analysis of graph signals, thus providing a framework for non-linear analysis of data sampled on irregular domains. Here, we introduce a continuous version of Permutation Entropy, extend it to the graph domain, and develop a ordinal activation function akin to the one of neural networks. This is a step towards Ordinal Deep Learning, a potentially effective and very recently posited concept. We also formally extend ordinal contrasts to the graph domain. Continuous versions of ordinal contrasts of length 3 are also introduced and their advantage is shown in experiments. We also integrate specific contrasts for the analysis of images and show that it generalizes well to the graph domain allowing a representation of images, represented as graph signals, in a plane similar to the entropy-complexity one. Applications to synthetic data, including fractal patterns and popular non-linear maps, and real-life MRI data show the validity of these novel extensions and potential benefits over the state of the art. By extending very recent concepts related to permutation entropy to the graph domain, we expect to accelerate the development of more graph-based entropy methods to enable nonlinear analysis of a broader kind of data and establishing relationships with emerging ideas in data science.

nlin.CD↗