State–of–the–art report on nonlinear representation of sources and channels

This report consists of two complementary parts, related to the modeling of two important sources of nonlinearities in a communications system. In the first part, an overview of important past work related to the estimation, compression and processing of sparse data through the use of nonlinear models is provided. In the second part, the current state of the art on the representation of wireless channels in the presence of nonlinearities is summarized. In addition to the characteristics of the nonlinear wireless fading channel, some information is also provided on recent approaches to the sparse representation of such channels

Comparative assessment of goods and services provided by grazing regulation and reforestation in degraded Mediterranean rangelands

Several management actions are applied to restore ecosystem services in degraded Mediterranean rangelands, which range from adjusting the grazing pressure to the removal of grazers and pine plantations. Four such actions were assessed in Quercus coccifera L. shrublands in northern Greece: (i) moderate grazing by goats and sheep; (ii) no grazing; (iii) no grazing plus pine (Pinus pinaster Aiton) plantation in forest gaps (gap reforestation); and (iv) no grazing plus full reforestation of shrubland areas, also with P. pinaster. In addition, heavy grazing was also assessed to serve as a control action. We comparatively assessed the impact of these actions on key provisioning, regulating and supporting ecosystem services by using ground‐based indicators. Depending on the ecosystem service considered, the management actions were ranked differently. However, the overall provision of services was particularly favoured under moderate and no grazing management options, with moderate grazing outranking any other action in provisioning services and the no grazing action presenting the most balanced provision of services. Pine reforestations largely contributed to water and soil conservation and C sequestration but had a negative impact on plant diversity when implemented at the expense of removing natural vegetation in the area. Heavy grazing had the lowest provision of ecosystem services. It is concluded that degraded rangelands can be restored by moderating the grazing pressure rather than completely banning livestock grazing or converting them into pine plantations

Robust Subspace Tracking with Missing Entries: The Set-Theoretic Approach

In this paper, an Adaptive Projected Subgradient Method (APSM) based algorithm for robust subspace tracking is introduced. A properly chosen cost function is constructed at each time instance and the goal is to seek for points, which belong to the zero level set of this function; i.e., the set of points which score a zero loss. At each iteration, an outlier detection mechanism is employed, in order to conclude whether the current data vector contains outlier noise or not. In the sequel, a sparsity-promoting greedy algorithm is employed for the outlier vector estimation allowing the purification of the corrupted data from the outlier noise, prior to any further processing. Furthermore, the case where the observation vectors are partially observed is attacked via a prediction procedure, which estimates the values of the unobserved (missing) coefficients. A theoretical analysis is carried out and the simulation experiments, within the contexts of robust subspace estimation and robust matrix completion, demonstrate the enhanced performance of the proposed scheme compared to recently developed state of the art algorithms. © 1991-2012 IEEE

Online Distributed Learning over Networks in RKH Spaces Using Random Fourier Features

We present a novel diffusion scheme for online kernel-based learning over networks. So far, a major drawback of any online learning algorithm, operating in a reproducing kernel Hilbert space (RKHS), is the need for updating a growing number of parameters as time iterations evolve. Besides complexity, this leads to an increased need of communication resources in a distributed setting. In contrast, we propose to approximate the solution as a fixed-size vector (of larger dimension than the input space) using the previously introduced framework of random Fourier features. This paves the way to use standard linear combine-then-adapt techniques. To the best of our knowledge, this is the first time that a complete protocol for distributed online learning in RKHS is presented. Conditions for asymptotic convergence and boundness of the networkwise regret are also provided. The simulated tests illustrate the performance of the proposed scheme. © 1991-2012 IEEE

Adaptive robust distributed learning in diffusion sensor networks

In this paper, the problem of adaptive distributed learning in diffusion networks is considered. The algorithms are developed within the convex set theoretic framework. More specifically, they are based on computationally simple geometric projections onto closed convex sets. The paper suggests a novel combine-project-adapt protocol for cooperation among the nodes of the network; such a protocol fits naturally with the philosophy that underlies the projection-based rationale. Moreover, the possibility that some of the nodes may fail is also considered and it is addressed by employing robust statistics loss functions. Such loss functions can easily be accommodated in the adopted algorithmic framework; all that is required from a loss function is convexity. Under some mild assumptions, the proposed algorithms enjoy monotonicity, asymptotic optimality, asymptotic consensus, strong convergence and linear complexity with respect to the number of unknown parameters. Finally, experiments in the context of the system-identification task verify the validity of the proposed algorithmic schemes, which are compared to other recent algorithms that have been developed for adaptive distributed learning. © 2011 IEEE

Trading off complexity with communication costs in distributed adaptive learning via Krylov subspaces for dimensionality reduction

In this paper, the problemof dimensionality reduction in adaptive distributed learning is studied. We consider a network obeying the ad-hoc topology, in which the nodes sense an amount of data and cooperate with each other, by exchanging information, in order to estimate an unknown, common, parameter vector. The algorithm, to be presented here, follows the set-theoretic estimation rationale; i.e., at each time instant and at each node of the network, a closed convex set is constructed based on the received measurements, and this defines the region in which the solution is searched for. In this paper, these closed convex sets, known as property sets, take the form of hyperslabs. Moreover, in order to reduce the number of transmitted coefficients, which is dictated by the dimension of the unknown vector, we seek for possible solutions in a subspace of lower dimension; the technique will be developed around the Krylov subspace rationale. Our goal is to find a point that belongs to the intersection of this infinite number of hyperslabs and the respective Krylov subspaces. This is achieved via a sequence of projections onto the property sets and the Krylov subspaces. The case of highly correlated inputs that degrades the performance of the algorithm is also considered. This is overcome via a transformation whichwhitens the input. The proposed schemes are brought in a decentralized form by adopting the combine-adapt cooperation strategy among the nodes. Full convergence analysis is carried out and numerical tests verify the validity of the proposed schemes in different scenarios in the context of the adaptive distributed system identification task. © 2013 IEEE