Abstract

We address the problem of network connectivity inference by observing interacting time-series signals at the nodes. The evolving nodal signals depend on the connectivity structure of the network thus allowing us to successfully invert for it. Our approach is demonstrated using the example of heat diffusion dynamics. To learn the graph, we combine our knowledge of the dynamical equation and the observed graph signals. Specifically, we perform approximate numerical discretization of the dynamical equation leading to a system of linear equations in the unknown graph topology. Simulations indicate feasibility of this method for accurate network inference.

Abstract

In a prior study, a novel deterministic compartmental model known as the SEIHRK model was introduced, shedding light on the pivotal role of test kits as an intervention strategy for mitigating epidemics. Particularly in heterogeneous networks, it was empirically demonstrated that strategically distributing a limited number of test kits among nodes with higher degrees substantially diminishes the outbreak size. The network's dynamics were explored under varying values of infection rate. In this research, we expand upon these findings to investigate the influence of migration on infection dynamics within distinct communities of the network. Notably, we observe that nodes equipped with test kits and those without tend to segregate into two separate clusters when coupling strength is low, but beyond a critical threshold coupling coefficient, they coalesce into a unified cluster. Building on this clustering phenomenon, we develop a reduced equation model and rigorously validate its accuracy through comprehensive simulations. We show that this property is observed in both complete and random graphs.

Abstract

Functional MRI research using naturalistic stimuli (like movies) can help examine brain networks supporting empathy. Applying graph learning methods to whole-brain time-series signals, we propose a novel fMRI signal processing pipeline that includes high-pass filtering, voxel-level clustering, and windowed graph learning with a sparsity-based approach. The fMRI dataset is from passive viewing of an 8-minute movie shown to 14 healthy volunteers. The emotion rating of the movies by age-matched 40 participants is the ground truth. We considered a total of 54 regions extracted from the AAL Atlas for the study. The sparsity-based graph learning method consistently outperforms in capturing variations in the emotion scale, achieving over 88% match of the graph cluster labels averaged across participants. Temporal analysis reveals a high fit to the emotion scale supported by the method’s effectiveness in capturing dynamic connectomes through graph clustering, indicating the role of contextual inference in building empathy. While the edge-weight dynamics analysis underscores the superiority of sparsity-based learning, the connectome-network analysis highlights the crucial role of the Insula, Amygdala, and Thalamus in empathy, with lateral brain connections facilitating synchronized responses. Spectral filtering analysis by band-pass filter isolated the regions linked to emotional and empathy processing in scenes with high emotional context. We also observe strong similarities between the movies in graph cluster labels, connectome-network analysis, and spectral filtering-based analyses, revealing robust neural correlates of empathy. These findings contribute to a better understanding of the neural dynamics associated with empathy and identify regions specific to empathetic responses to naturalistic stimuli.

Abstract

Direction-of-arrival (DOA) estimation algorithms are crucial in localizing acoustic sources. Traditional localization methods rely on block-level processing to extract the directional information from multiple measurements processed together. However, these methods assume that DOA remains constant throughout the block, which may not be true in practical scenarios. Also, the performance of localization methods is limited when the true parameters do not lie on the parameter search grid. In this paper, two trajectory models are proposed, namely the polynomial and harmonic trajectory models, to capture the DOA dynamics. To estimate trajectory parameters, two gridless algorithms are adopted: (i) Sliding Frank–Wolfe (SFW), which solves the Beurling LASSO problem, and (ii) Newtonized orthogonal matching pursuit (NOMP), which is improved over orthogonal matching pursuit (OMP) using cyclic refinement. Furthermore, our analysis is extended to include multi-frequency processing. The proposed models and algorithms are validated using both simulated and real-world data. The results indicate that the proposed trajectory localization algorithms exhibit improved performance compared to grid-based methods in terms of resolution, robustness to noise, and computational efficiency.

Abstract

For a point set, Euclidean distance matrix (EDM) is the matrix consisting of squared distances between every pair of points in the set. It frequently appears in wide ranging applications such as sensor networks, acoustic arrays, crystallography, and self localization among others. Often the measured EDM are inaccurate (due to noise) and incomplete (due to limited availability of measurements) requiring denoising and completion algorithms, frequently both. In literature, methods based on rank alternation and semi-definite relaxation (SDR) have been successful but are restricted to processing a single noisy and/or incomplete input EDM. In this paper we propose extensions of these two algorithms which can process multiple noisy and incomplete EDM simultaneously. Simulations show that the proposed joint algorithms (which process multiple EDM) outperform the corresponding individual algorithms (which process individual EDM and combine the results). We focus on the challenging case of multiplicative noise.

Abstract

Accurate localization of sound sources is essential in many acoustic sensing and monitoring applications. In the absence of temporal continuity models, many methods produce unrealistic direction of arrival (DOA) estimates involving sudden changes. To address this, we propose an approach that trains a neural network to predict DOA derivatives in Cartesian coordi- nates (x′, y′, z′), which capture the rate of change in DOA (x, y, z) over time. By combining the predicted DOAs with the predicted derivatives, our method can suppress sudden DOA changes and generate smooth motion trajectories. We introduce an update rule that combines the predicted DOAs with the predicted derivatives to obtain the final DOAs. We validate our approach using the TAU-NIGENS Spatial Sound Events (TNSSE) 2021 dataset. Our results demonstrate that incorporating DOA derivatives improves the accuracy of DOA estimation, particularly in low signal-to- noise ratio scenarios

Abstract

The direction of arrival (DOA) estimation algorithms are crucial in localizing acoustic sources. Traditional localization methods rely on block-level processing to extract the directional information from multiple measurements processed together. However, these methods assume that DOA remains constant throughout the block, which may not be true in practical scenarios. Also, the performance of localization methods is limited when the true parameters do not lie on the parameter search grid. In this paper we propose two trajectory models, namely the polynomial and bandlimited trajectory models, to capture the DOA dynamics. To estimate trajectory parameters, we adopt two gridless algorithms: i) Sliding Frank-Wolfe (SFW), which solves the Beurling LASSO problem and ii) Newtonized Orthogonal Matching Pursuit (NOMP), which improves over OMP using cyclic refinement. Furthermore, we extend our analysis to include wideband processing. The simulation results indicate that the proposed trajectory localization algorithms exhibit improved performance compared to grid-based methods in terms of resolution, robustness to noise, and computational efficiency.

Abstract

We propose a data-based joint localization and tracking task called trajectory localization with source trajectories identified for a block (multiple measurements) of array data. This is in contrast to localization tasks where directions of arrival (DOA) are estimated per measurement. We employ parametric motion models with focus on linear trajectories. Deep learning based U-Net architecture is proposed to estimate the linear trajectory parameters. The results show that the proposed method gives better and fast trajectory estimates as compared to the trajectory localization (TL) methods of conventional beamforming (TL-CBF) and sparse Bayesian learning (TL-SBL).

Abstract

The particle flow Gaussian particle filter (PFGPF) uses an invertible particle flow to generate a proposal density. It approximates the predictive and posterior distributions as Gaussian densities. In this paper, we use a bank of PFGPF filters to construct a Particle flow Gaussian sum particle filter (PFGSPF), which approximates the prediction and posterior as Gaussian mixture model. This approximation is useful in complex estimation problems where a single Gaussian approximation is inadequate. We compare the performance of this proposed filter with the PFGPF and others in challenging numerical simulations. Index Terms— Gaussian mixture, invertible particle flow, Gaussian sum particle filer, Gaussian particle filter, PFGPF.

Abstract

The Internet of Things (IoT) relies heavily on exchange of data collected by nodes in a sensor network. This network data can be represented as a signal on a graph allowing tools from graph signal processing (GSP) to analyse it. Here, we utilize graph signal reconstruction algorithms to extrapolate missing sensor data from partially sampled network data. An important class of graph signal reconstruction algorithms operate by partitioning the graph vertices into local sets to achieve lower reconstruction errors and faster convergence. However, methods for identification of these local neighbourhoods have not been clearly studied in the literature. Here, we propose two flexible algorithms to generate local sets on a graph. These algorithms are based on the distance between the sampled and unsampled vertices. Our algorithms are competitive with the methods in literature while offering flexibility in the number of sampled vertices. We carry out simulation-based analysis of sampling strategies and proposed local set generation algorithms using local-set-based reconstruction algorithms.