Kernel-Based Inference of Functions Over Graphs

Abstract The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting—and prevalent in several fields of study—problem is that of inferring a function defined over the nodes of a network. This work presents a versatile kernel-based framework for tackling this inference problem that naturally subsumes and generalizes the reconstruction approaches put forth recently for the signal processing by the community studying graphs. Both the static and the dynamic settings are considered along with effective modeling approaches for addressing real-world problems. The analytical discussion herein is complement…

Location-Free Spectrum Cartography

Spectrum cartography constructs maps of metrics such as channel gain or received signal power across a geographic area of interest using spatially distributed sensor measurements. Applications of these maps include network planning, interference coordination, power control, localization, and cognitive radios to name a few. Since existing spectrum cartography techniques require accurate estimates of the sensor locations, their performance is drastically impaired by multipath affecting the positioning pilot signals, as occurs in indoor or dense urban scenarios. To overcome such a limitation, this paper introduces a novel paradigm for spectrum cartography, where estimation of spectral maps rel…

Implicit Wiener Filtering for Speech Enhancement In Non-Stationary Noise

Integration of different cardiac electrophysiological models into a single simulation pipeline

Clinical translation of computational models of the heart has been hampered by the absence of complete and rigorous technical and clinical validation, as well as benchmarking of the developed tools. To address this issue, a dataset containing the cardiac anatomy and fibre orientations from magnetic resonance images (MRI), as well as epicardial transmembrane potentials from optical mapping acquired on ex-vivo porcine hearts, have previously been made available to the community. Image processing techniques were developed to integrate MRI images with electrical information. Different models were tested and compared with the integrated data1, including: i) a new methodology to customize and reg…

Fast Distributed Subspace Projection via Graph Filters

A significant number of linear inference problems in wireless sensor networks can be solved by projecting the observed signal onto a given subspace. Decentralized approaches avoid the need for performing such an operation at a central processor, thereby reducing congestion and increasing the robustness and the scalability of the network. Unfortunately, existing decentralized approaches either confine themselves to a reduced family of subspace projection tasks or need an infinite number of iterations to obtain the exact projection. To remedy these limitations, this paper develops a framework for computing a wide class of subspace projections in a decentralized fashion by relying on the notio…

Localization-Free Power Cartography

Author's accepted manuscript (postprint). © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Spectrum cartography constructs maps of metrics such as channel gain or received signal power across a geographic area of interest using measurements of spatially distributed sensors. Applications of these maps include network planning, interference coordination, power con…

Online topology estimation for vector autoregressive processes in data networks

An important problem in data sciences pertains to inferring causal interactions among a collection of time series. Upon modeling these as a vector autoregressive (VAR) process, this paper deals with estimating the model parameters to identify the underlying causality graph. To exploit the sparse connectivity of causality graphs, the proposed estimators minimize a group-Lasso regularized functional. To cope with real-time applications, big data setups, and possibly time-varying topologies, two online algorithms are presented to recover the sparse coefficients when observations are received sequentially. The proposed algorithms are inspired by the classic recursive least squares (RLS) algorit…

Inference of Spatio-Temporal Functions over Graphs via Multi-Kernel Kriged Kalman Filtering

Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel-based kriged Kalman filter that accounts for the spatio-temporal variations, and offers efficient online reconstruction, even for dynamically evolving network topologies. The kernel-based learning framework bypasses the need for statistical information by capitalizing on the smoothness that graph signals exhibit with respect to the underlying graph. To address the challenge o…

Analysis of Microstructure of the Cardiac Conduction System Based on Three-Dimensional Confocal Microscopy

The specialised conducting tissues present in the ventricles are responsible for the fast distribution of the electrical impulse from the atrio-ventricular node to regions in the subendocardial myocardium. Characterisation of anatomical features of the specialised conducting tissues in the ventricles is highly challenging, in particular its most distal section, which is connected to the working myocardium via Purkinje-myocardial junctions. The goal of this work is to characterise the architecture of the distal section of the Purkinje network by differentiating Purkinje cells from surrounding tissue, performing a segmentation of Purkinje fibres at cellular scale, and mathematically describin…

Locally optimal invariant detector for testing equality of two power spectral densities

This work addresses the problem of determining whether two multivariate random time series have the same power spectral density (PSD), which has applications, for instance, in physical-layer security and cognitive radio. Remarkably, existing detectors for this problem do not usually provide any kind of optimality. Thus, we study here the existence under the Gaussian assumption of optimal invariant detectors for this problem, proving that the uniformly most powerful invariant test (UMPIT) does not exist. Thus, focusing on close hypotheses, we show that the locally most powerful invariant test (LMPIT) only exists for univariate time series. In the multivariate case, we prove that the LMPIT do…

An Abstract Generic Framework for Web Site Verification

In this paper, we present an abstract framework for Web site verification which improves the performance of a previous, rewriting-based Web verification methodology. The approximated framework is formalized as a source-to-source transformation which is parametric w.r.t. the chosen abstraction. This transformation significantly reduces the size of the Web documents by dropping or merging contents that do not influence the properties to be checked. This allows us to reuse all verification facilities of the previous system WebVerdi-M to efficiently analyze Web sites. In order to ensure that the verified properties are not affected by the abstraction, we develop a methodology which derives the …

Fast Decentralized Linear Functions via Successive Graph Shift Operators

Decentralized signal processing performs learning tasks on data distributed over a multi-node network which can be represented by a graph. Implementing linear transformations emerges as a key task in a number of applications of decentralized signal processing. Recently, some decentralized methods have been proposed to accomplish that task by leveraging the notion of graph shift operator, which captures the local structure of the graph. However, existing approaches have some drawbacks such as considering special instances of linear transformations, or reducing the family of transformations by assuming that a shift matrix is given such that a subset of its eigenvectors spans the subspace of i…

Blind Radio Tomography

From the attenuation measurements collected by a network of spatially distributed sensors, radio tomography constructs spatial loss fields (SLFs) that quantify absorption of radiofrequency waves at each location. These SLFs can be used for interference prediction in (possibly cognitive) wireless communication networks, for environmental monitoring or intrusion detection in surveillance applications, for through-the-wall imaging, for survivor localization after earthquakes or fires, etc. The cornerstone of radio tomography is to model attenuation as the bidimensional integral of the SLF of interest scaled by a weight function. Unfortunately, existing approaches (i) rely on heuristic assumpti…

Online Topology Identification from Vector Autoregressive Time Series

Causality graphs are routinely estimated in social sciences, natural sciences, and engineering due to their capacity to efficiently represent the spatiotemporal structure of multivariate data sets in a format amenable for human interpretation, forecasting, and anomaly detection. A popular approach to mathematically formalize causality is based on vector autoregressive (VAR) models and constitutes an alternative to the well-known, yet usually intractable, Granger causality. Relying on such a VAR causality notion, this paper develops two algorithms with complementary benefits to track time-varying causality graphs in an online fashion. Their constant complexity per update also renders these a…

Data-Driven Spectrum Cartography via Deep Completion Autoencoders

Spectrum maps, which provide RF spectrum metrics such as power spectral density for every location in a geographic area, find numerous applications in wireless communications such as interference control, spectrum management, resource allocation, and network planning to name a few. Spectrum cartography techniques construct these maps from a collection of measurements collected by spatially distributed sensors. Due to the nature of the propagation of electromagnetic waves, spectrum maps are complicated functions of the spatial coordinates. For this reason, model-free approaches have been preferred. However, all existing schemes rely on some interpolation algorithm unable to learn from data. …

Inter-Model Consistency and Complementarity: Learning from ex-vivo Imaging and Electrophysiological Data towards an Integrated Understanding of Cardiac Physiology

International audience; Computational models of the heart at various scales and levels of complexity have been independently developed, parameterised and validated using a wide range of experimental data for over four decades. However, despite remarkable progress, the lack of coordinated efforts to compare and combine these computational models has limited their impact on the numerous open questions in cardiac physiology. To address this issue, a comprehensive dataset has previously been made available to the community that contains the cardiac anatomy and fibre orientations from magnetic resonance imaging as well as epicardial transmembrane potentials from optical mapping measured on a per…

Effect of Scar Development on Fast Electrophysiological Models of the Human Heart: In-Silico Study on Atlas-Based Virtual Populations

The main goal of this work is to study the effect of scar development in the electrophysiological function of the human left ventricle by statistically analyzing large-scale simulation data including hypertrophic and dilated hearts. Electrophysiological simulations are obtained by solving the classical Eikonal equation in both the ventricular tissue and a customized Purkinje system. This Purkinje system is obtained assuming a geodesic rule to connect different Purkinje-myocardial junctions into a tree-like structure. Infarction shape and function is modeled with taking into account the occlusion in coronary arteries. Infarct, core and border zones of the scar are estimated by calculating bl…

Implicit Wiener Filtering for Speech Enhancement In Non-Stationary Noise

Speech quality is degraded in the presence of background noise, which reduces the quality of experience (QoE) of the end-user and therefore motivates the usage of speech enhancement algorithms. A large number of approaches have been proposed in this context. However most of them have focused on the case where the noise is stationary, an assumption that seldom holds in practice. For instance, in mobile telephony, noise sources with a marked non-stationary spectral signature include vehicles, machines, and other speakers to name a few. On the other hand, the usage of frequency-domain information in existing algorithms for speech enhancement in non-stationary noise environments can be made mor…

Defending Surveillance Sensor Networks Against Data-Injection Attacks Via Trusted Nodes

By injecting false data through compromised sensors, an adversary can drive the probability of detection in a sensor network-based spatial field surveillance system to arbitrarily low values. As a countermeasure, a small subset of sensors may be secured. Leveraging the theory of Matched Subspace Detection, we propose and evaluate several detectors that add robustness to attacks when such trusted nodes are available. Our results reveal the performance-security tradeoff of these schemes and can be used to determine the number of trusted nodes required for a given performance target.

Non-cooperative Aerial Base Station Placement via Stochastic Optimization

Autonomous unmanned aerial vehicles (UAVs) with on-board base station equipment can potentially provide connectivity in areas where the terrestrial infrastructure is overloaded, damaged, or absent. Use cases comprise emergency response, wildfire suppression, surveillance, and cellular communications in crowded events to name a few. A central problem to enable this technology is to place such aerial base stations (AirBSs) in locations that approximately optimize the relevant communication metrics. To alleviate the limitations of existing algorithms, which require intensive and reliable communications among AirBSs or between the AirBSs and a central controller, this paper leverages stochastic…

Towards High Resolution Computational Models of the Cardiac Conduction System: A Pipeline for Characterization of Purkinje-Ventricular-Junctions

The cardiac conduction system (CCS) has been in the spot light of the clinical and modeling community in recent years because of its fundament role in physiology and pathophysiology of the heart. Experimental research has focused mainly on investigating the electrical properties of the Purkinje-ventricular-junctions (PVJs). The structure of the PVJs has only been described through schematic drawings but not thoroughly studied. In this work confocal microscopy was used with the aim of three-dimensional characterization of PVJs. Adult rabbit hearts were labeled with fluorescent dyes, imaged with confocal microscopy and Purkinje fibers differentiated from other cardiac tissue by their lack of …

Robust Transmit Beamforming for Underlay D2D Communications on Multiple Channels

Underlay device-to-device (D2D) communications lead to improvement in spectral efficiency by simultaneously allowing direct communication between the users and the existing cellular transmission. However, most works in resource allocation for D2D communication have considered single antenna transmission and with a focus on perfect channel state information (CSI). This work formulates a robust transmit beamforming design problem for maximizing the aggregate rate of all D2D pairs and cellular users (CUs). Assuming complex Gaussian distributed CSI error, our formulation guarantees probabilistically a signal to interference plus noise ratio (SINR) above a specified threshold. In addition, we al…

Dynamic network identification from non-stationary vector autoregressive time series

Learning the dynamics of complex systems features a large number of applications in data science. Graph-based modeling and inference underpins the most prominent family of approaches to learn complex dynamics due to their ability to capture the intrinsic sparsity of direct interactions in such systems. They also provide the user with interpretable graphs that unveil behavioral patterns and changes. To cope with the time-varying nature of interactions, this paper develops an estimation criterion and a solver to learn the parameters of a time-varying vector autoregressive model supported on a network of time series. The notion of local breakpoint is proposed to accommodate changes at individu…

Deep Completion Autoencoders for Radio Map Estimation

Radio maps provide metrics such as power spectral density for every location in a geographic area and find numerous applications such as UAV communications, interference control, spectrum management, resource allocation, and network planning to name a few. Radio maps are constructed from measurements collected by spectrum sensors distributed across space. Since radio maps are complicated functions of the spatial coordinates due to the nature of electromagnetic wave propagation, model-free approaches are strongly motivated. Nevertheless, all existing schemes for radio occupancy map estimation rely on interpolation algorithms unable to learn from experience. In contrast, this paper proposes a…

Aerial Spectrum Surveying: Radio Map Estimation with Autonomous UAVs

Radio maps are emerging as a popular means to endow next-generation wireless communications with situational awareness. In particular, radio maps are expected to play a central role in unmanned aerial vehicle (UAV) communications since they can be used to determine interference or channel gain at a spatial location where a UAV has not been before. Existing methods for radio map estimation utilize measurements collected by sensors whose locations cannot be controlled. In contrast, this paper proposes a scheme in which a UAV collects measurements along a trajectory. This trajectory is designed to obtain accurate estimates of the target radio map in a short time operation. The route planning a…

Underlay Device-to-Device Communications on Multiple Channels

Author´s accepted manuscript (postprint). © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Since the spectral efficiency of wireless communications is already close to its fundamental bounds, a significant increase in spatial efficiency is required to meet future traffic demands. Device-to-device (D2D) communications provide such an increase by allowing nearby u…

Inference of Spatiotemporal Processes over Graphs via Kernel Kriged Kalman Filtering

Inference of space-time signals evolving over graphs emerges naturally in a number of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel-based kriged Kalman filtering approach that leverages the spatio-temporal dynamics to allow for efficient online reconstruction, while also coping with dynamically evolving network topologies. Laplacian kernels are employed to perform kriging over the graph when spatial second-order statistics are unknown, as is often the case. Numerical tests with synthetic and real data ill…

Flexible modeling for anatomically-based cardiac conduction system construction.

We present a method to automatically deploy the peripheral section of the cardiac conduction system in ventricles. The method encodes anatomical information thorough rules that ensure that Purkinje network structures generated are realistic and comparable to those observed in ex-vivo studies. The core methodology is based in non-deterministic production rules that are parameterized by means of statistical functions. Input parameters allow the construction of a great diversity of Purkinje structures that could be incorporated in fine element ventricular models to perform electrophysiology simulations. Resulting Purkinje trees show good geometrical approximations of Purkinje core network and …

Randomized Block Frank–Wolfe for Convergent Large-Scale Learning

Owing to their low-complexity iterations, Frank-Wolfe (FW) solvers are well suited for various large-scale learning tasks. When block-separable constraints are present, randomized block FW (RB-FW) has been shown to further reduce complexity by updating only a fraction of coordinate blocks per iteration. To circumvent the limitations of existing methods, the present work develops step sizes for RB-FW that enable a flexible selection of the number of blocks to update per iteration while ensuring convergence and feasibility of the iterates. To this end, convergence rates of RB-FW are established through computational bounds on a primal sub-optimality measure and on the duality gap. The novel b…

Reliable Underlay Device-to-Device Communications on Multiple Channels

Device-to-device (D2D) communications provide a substantial increase in spectrum usage and efficiency by allowing nearby users to communicate directly without passing their packets through the base station (BS). In previous works, proper channel assignment and power allocation algorithms for sharing of channels between cellular users and D2D pairs, usually require exact knowledge of the channel-state-information (CSI). However, due to the non-stationary wireless environment and the need to limit the communication and computation overheads, obtaining perfect CSI in the D2D communication scenario is generally not possible. In this work, we propose a joint channel assignment and power allocati…

Cooperative compressive power spectrum estimation in wireless fading channels

This paper considers multiple wireless sensors that cooperatively estimate the power spectrum of the signals received from several sources. We extend our previous work on cooperative compressive power spectrum estimation to accommodate the scenario where the statistics of the fading channels experienced by different sensors are different. The signals received from the sources are assumed to be time-domain wide-sense stationary processes. Multiple sensors are organized into several groups, where each group estimates a different subset of lags of the temporal correlation. A fusion centre (FC) combines these estimates to obtain the power spectrum. As each sensor group computes correlation esti…

Testing Equality of Multiple Power Spectral Density Matrices

This paper studies the existence of optimal invariant detectors for determining whether P multivariate processes have the same power spectral density. This problem finds application in multiple fields, including physical layer security and cognitive radio. For Gaussian observations, we prove that the optimal invariant detector, i.e., the uniformly most powerful invariant test, does not exist. Additionally, we consider the challenging case of close hypotheses, where we study the existence of the locally most powerful invariant test (LMPIT). The LMPIT is obtained in the closed form only for univariate signals. In the multivariate case, it is shown that the LMPIT does not exist. However, the c…

DECENTRALIZED SUBSPACE PROJECTION IN LARGE NETWORKS

A great number of applications in wireless sensor networks involve projecting a vector of observations onto a subspace dictated by prior information. Accomplishing such a task in a centralized fashion entails great power consumption, congestion at certain nodes, and suffers from robustness issues. A sensible alternative is to compute such projections in a decentralized fashion. To this end, recent works proposed schemes based on graph filters, which compute projections exactly with a finite number of local exchanges among sensor nodes. However, existing methods to obtain these filters are confined to reduced families of projection matrices or small networks. This paper proposes a method tha…

Fast Graph Filters for Decentralized Subspace Projection

A number of inference problems with sensor networks involve projecting a measured signal onto a given subspace. In existing decentralized approaches, sensors communicate with their local neighbors to obtain a sequence of iterates that asymptotically converges to the desired projection. In contrast, the present paper develops methods that produce these projections in a finite and approximately minimal number of iterations. Building upon tools from graph signal processing, the problem is cast as the design of a graph filter which, in turn, is reduced to the design of a suitable graph shift operator. Exploiting the eigenstructure of the projection and shift matrices leads to an objective whose…