Luiz F. O. Chamon

Combination of adaptive filters with coefficients feedback

In parallel combinations of adaptive filters, the component filters are usually run independently to be later on combined, leading to a stagnation phase before reaching a lower error. Conditional transfers of coefficients between the filters have been introduced in an attempt to address this issue. The present work proposes a more natural way of accelerating the convergence to steady-state, using a cyclic feedback of the overall weights to all component filters, instead of a unidirectional conditional transfer. It is shown that, depending on the cycle length, the resulting recursion is equivalent to either: (i) the independent combination, (ii) a variable step size adaptive filter, or (iii) a new hybrid algorithm. Comments on the universality of the approach are presented along with a technique to design the cycle length. Comparisons in stationary and non-stationary system identification scenarios demonstrate the superior performance of this new combination method.

Near-optimality of greedy set selection in the sampling of graph signals

Sampling has been extensively studied in graph signal processing, having found applications in estimation, clustering, and video compression. Still, sampling set selection remains an open issue. Indeed, although conditions for graph signal reconstruction from noiseless samples were derived, the presence of noise makes sampling set selection combinatorial and NP-hard in general. Performance bounds are available only for randomized sampling schemes, even though greedy search remains ubiquitous in practice. This work sets out to justify the success of greedy sampling by introducing the concept of approximate supermodularity and updating the classical greedy bound to account for this class of functions. Then, it quantifies the approximate supermodularity of two important reconstruction figures of merit, namely the log det of the error covariance matrix and the mean-square error, showing that they can be optimized with worst-case guarantees using greedy sampling.

Greedy Sampling of Graph Signals

Sampling is a fundamental topic in graph signal processing, having found applications in estimation, clustering, and video compression. In contrast to traditional signal processing, the irregularity of the signal domain makes selecting a sampling set nontrivial and hard to analyze. Indeed, though conditions for graph signal interpolation from noiseless samples exist, they do not lead to a unique sampling set. The presence of noise makes choosing among these sampling sets a hard combinatorial problem. Although greedy sampling schemes are commonly used in practice, they have no performance guarantee. This work takes a twofold approach to address this issue. First, universal performance bounds are derived for the Bayesian estimation of graph signals from noisy samples. In contrast to currently available bounds, they are not restricted to specific sampling schemes and hold for any sampling sets. Second, this paper provides near-optimal guarantees for greedy sampling by introducing the concept of approximate submodularity and updating the classical greedy bound. It then provides explicit bounds on the approximate supermodularity of the interpolation mean-square error showing that it can be optimized with worst case guarantees using greedy search even though it is not supermodular. Simulations illustrate the derived bound for different graph models and show an application of graph signal sampling to reduce the complexity of kernel principal component analysis.

A data reusage algorithm based on incremental combination of LMS filters

This work introduces a new data reuse algorithm based on the incremental combination of LMS filters. It is able to outperform the Affine Projection Algorithm (APA) in its standard form, another well-known data reuse adaptive filter. First, the so called true gradient data reuse LMS-sometimes referred to as data reuse LMS-is shown to be a limiting case of the regularized APA. Afterwards, an incremental counterpart of its recursion is inspired by distributed optimization and adaptive networks scenarios. Simulations in different scenarios show the efficiency of the proposed data reuse algorithm, that is able to match and even outperform the APA in the mean-square sense at lower computational complexity.

THERE'S PLENTY OF ROOM AT THE BOTTOM: INCREMENTAL COMBINATIONS OF SIGN-ERROR LMS FILTERS

The introduction of data reuse in the incremental topology made it possible for combinations of LMS filters to outperform algorithms such as the Affine Projection Algorithm (APA) with lower complexity. This work poses and extends the concept of combinations as a complexity reduction technique by proposing an incremental combination of sign-error LMS filters that matches and even outperforms stand-alone LMS filters with reduced complexity. This combination is then analyzed and used as a building block in a larger combination that is able to match the APA at a reduced computational cost. Numerical simulations illustrate the performance of this novel combination in different scenarios.

Universal bounds for the sampling of graph signals

Sampling is a fundamental topic in graph signal processing with applications in estimation, clustering, and video compression. In contrast to traditional signal processing, however, the irregularity of the signal domain makes the selection of the sampling points non-trivial and hard to analyze. Indeed, although graph signal reconstruction is well-understood in the noiseless case, performance bounds for the interpolation of noisy samples exist mainly for randomized sampling schemes. This paper addresses this issue by deriving a lower bound on the mean-square interpolation error for graph signals. This bound is universal in the sense that it is not restricted to a specific sampling method and holds for all sampling sets. Simulations illustrate the tightness of the bound, which is then used to evaluate the performance of greedy sampling. Finally, a solution to the complexity issues of kernel principal component analysis is proposed using graph signal sampling.

Towards spatially universal adaptive diffusion networks

Adaptive networks (ANs) rely on local adaptive filters (AFs) and a cooperation protocol to achieve a common goal, e.g., estimating a set of parameters. This protocol fuses the information from the rest of the network based on local combiners whose design impacts directly the network performance. Indeed, although diffusion schemes improve network performance on average, heterogeneity in signal statistics implies that indiscriminate cooperation may not be the best policy for good nodes. In this work, these observations lead to the introduction of different concepts of spatial universality which motivate a new adaptive combiner structure. The goal of the new combiner is to enforce that the cooperative AFs perform at least as well as the best individual non-cooperative AF, without discarding information from other nodes. The new structure has lower complexity and outperforms existing techniques, as illustrated by simulations. Network learning analysis is also provided.

The Application of the Singular Value Decomposition (SVD) for the Decoupling of the Vibratory Reproduction System of an Aircraft Cabin Simulator

Mechanical systems excited by vibratory point-sources, tend to suffer from interference among axes, due to characteristics of the reproduction system or difficulties associated with the application of the excitation forces on the system’s masscenter. Thus, when it is necessary to excite the system independently in different directions, control techniques are needed for the correct reproduction of the desired signals. This work presents the developments for the reproduction of vibrations in two directions, on platforms employed as the base of seats of an aircraft cabin simulator. Each platform is independently excited by two orthogonal shakers, located in the geometrical center of the latter. Based on an evaluation of the degree of coupling between both orthogonal axes, signal processing solutions for the decoupling problem are proposed. Using SVD to diagonalize the transfer-function-matrix, an independent base for the system was identified. Some preliminary evaluations using inverse static filters show that the proposed method can provide the desired results.

Closing the Network Diagnostics Gap with Vigil

Closing the Network Diagnostics Gap with Vigil Behnaz Arzani, Selim Ciraci, Luiz Chamon, Yibo Zhu, Hongqiang Liu, Jitu Padhye, Geoff Outhred, Boon Thau Loo Vigil started with an ambitious goal: For every TCP retransmission in our data centers, we wanted to pinpoint the network link that caused the packet drop that triggered the retransmission with negligible diagnostic overhead or changes to the networking infrastructure. This goal may sound like an overkill—after all, TCP is supposed to be able to deal with a few packet losses. Packet losses might occur due to simple congestion instead of network equipment failures. Even network failures might be transient. Above all, there is a danger of drowning in a sea of data without generating any actionable intelligence.