Abstract

Missing values in time-series is a frequently occurring problem in multi-sensor data analysis. The current state-of-the-art imputation networks don’t generalize well across the benchmarks. Further, some directly operate on space-time product graphs which may minimize the information loss but are prohibitively expensive. We propose Product Graph U-networks using Temporal pooling for Spa- tiotemporal imputation (P-GUTS). It uses pooled representations of the space-time sequence in the bottleneck part of the U-network and is memory efficient. Since datasets can have differing levels of redundancy, relying on a single view (pooled representation) of the data can be limiting. Therefore, P-GUTS uses multiple U-Nets with different pooling factors and aggregates the representations. We demonstrate the effectiveness of P-GUTS on multiple real-world imputation datasets and robustness across increasing missing rates. P-GUTS also gives encouraging results in spatiotemporal forecast- ing.

Abstract

Time-series data from sensor networks often has missing entries due to sensor failures, poor communication, scheduled downtime, etc. Missing data imputation improves perfor- mance of downstream tasks such as forecasting and anomaly detection. Therefore, highly accurate imputation methods are desirable. Multi-variate time series imputation methods using interpolation [1–3], or matrix factor- ization [4, 5] have limited accuracy. Auto-regressive methods like ARIMA [6] and RNNs like GRIN [7] are subject to error propagation and are slow. More recently, attention [8] has been successfully used to design effective networks for various time series tasks – imputation (SPIN, SPIN-H and Transformer) [9], forecasting [10, 11] and anomaly detection [12]. However, as evident from Figure 2, these state-of-the-art (SOTA) networks are effective only on certain datasets. It motivates a more general meta-network which can effectively aggregate these experts using a gating network. We provide the scope of improvement when these frozen experts are selected optimally using an oracle. The possible reduction in error can be as high as 28 − 40 percent by using existing imputation networks.

Abstract

We propose a data-driven method for direction-of-arrival (DOA) trajectory estimation. We use a deep complex architecture which leverages complex-valued representations to capture both magnitude and phase information in the received sensor array data. The network is designed to output the DOA trajectory parameters and amplitudes of the strongest source. Deviating from conventional methods, which attempt to estimate parameters for all sources simultaneously -- leading to assignment ambiguity and the problem of uncertain output dimensions, we adopt a sequential approach. The estimated source signal contribution is subtracted from the input to obtain a residual signal. This residual signal is then fed back into the network to identify the next strongest source and so on, making the proposed network reusable. We evaluate our network on simulated data of varying complexity. Results demonstrate the feasibility of such a reusable network and potential improvements can be explored in future.

Abstract

Time series data related to traffic and air quality are useful indicators for urban planning but they frequently have missing values. Imputation of multi-sensor time series data is thus a vital pre-processing step for forecasting, anomaly detection and other downstream tasks. We develop an efficient architecture – Sparse Attention-based Imputation Network for Time series (SAINT) – which outperforms the state-of- the-art imputation networks. Efficiency is achieved by separating the computations on the space-time product graph sequentially into channel independent temporal attention and sparse space-time transformer. This channel independent network can reduce overfitting to effectively repre- sent general temporal patterns. Sparse space-time transformer performs message passing on the spatial graph conditioned on time. We consider real-world datasets for evaluation – PEMS-BAY, METR-LA and AQI – which are gathered from sensor networks in major cities. We demonstrate the effectiveness and robustness of SAINT across complex missing data scenarios. Additionally, SAINT generalizes well to short-term forecasting and is practical for long-term forecasting with limited resources.

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

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

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

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