Amauri Lopes

2012 Special Issue: An extended echo state network using Volterra filtering and principal component analysis

Echo state networks (ESNs) can be interpreted as promoting an encouraging compromise between two seemingly conflicting objectives: (i) simplicity of the resulting mathematical model and (ii) capability to express a wide range of nonlinear dynamics. By imposing fixed weights to the recurrent connections, the echo state approach avoids the well-known difficulties faced by recurrent neural network training strategies, but still preserves, to a certain extent, the potential of the underlying structure due to the existence of feedback loops within the dynamical reservoir. Moreover, the overall training process is relatively simple, as it amounts essentially to adapting the readout, which usually corresponds to a linear combiner. However, the linear nature of the output layer may limit the capability of exploring the available information, since higher-order statistics of the signals are not taken into account. In this work, we present a novel architecture for an ESN in which the linear combiner is replaced by a Volterra filter structure. Additionally, the principal component analysis technique is used to reduce the number of effective signals transmitted to the output layer. This idea not only improves the processing capability of the network, but also preserves the simplicity of the training process. The proposed architecture is then analyzed in the context of a set of representative information extraction problems, more specifically supervised and unsupervised channel equalization, and blind separation of convolutive mixtures. The obtained results, when compared to those produced by already proposed ESN versions, highlight the benefits brought by the novel network proposal and characterize it as a promising tool to deal with challenging signal processing tasks.

Automatic genre classification of musical signals

We present a strategy to perform automatic genre classification of musical signals. The technique divides the signals into 21.3 milliseconds frames, from which 4 features are extracted. The values of each feature are treated over 1-second analysis segments. Some statistical results of the features along each analysis segment are used to determine a vector of summary features that characterizes the respective segment. Next, a classification procedure uses those vectors to differentiate between genres. The classification procedure has two main characteristics: (1) a very wide and deep taxonomy, which allows a very meticulous comparison between different genres, and (2) a wide pairwise comparison of genres, which allows emphasizing the differences between each pair of genres. The procedure points out the genre that best fits the characteristics of each segment. The final classification of the signal is given by the genre that appears more times along all signal segments. The approach has shown very good accuracy even for the lowest layers of the hierarchical structure.

Improving the MODEX algorithm for direction estimation

We propose a modification in the MODEX method for direction finding using array of sensors. This proposal alters the MODEX candidates for the estimation and, as a consequence, reduces the computational effort, improves the performance and preserves the optimum asymptotic efficiency for both uncorrelated and correlated (coherent) sources.

Experimental verification of an eye diagram reconstruction technique based on asynchronous undersampling

In this paper we experimentally demonstrate an eye diagram recovery technique, applied after asynchronous undersampling of a high speed optical communication signal. The resulting (reconstructed) eye diagrams are compared with the ones obtained by traditional (synchronous) techniques for different optical signal to noise ratios. This technique is being applied in the development of complete eye diagram analyzer equipment for BER estimation and network performance monitoring.

An echo state network architecture based on volterra filtering and PCA with application to the channel equalization problem

Echo state networks represent a promising alternative to the classical approaches involving recurrent neural networks, as they ally processing capability, due to the existence of feedback loops within the dynamical reservoir, with a simplified training process. However, the existing networks cannot fully explore the potential of the underlying structure, since the outputs are computed via linear combinations of the internal states. In this work, we propose a novel architecture for an echo state network that employs the Volterra filter structure in the output layer together with the Principal Component Analysis technique. This idea not only improves the processing capability of the network, but also preserves the simplicity of the training process. The proposed architecture has been analyzed in the context of the channel equalization problem, and the obtained results highlight the adequacy and the advantages of the novel network, which achieved a convincing performance, overcoming the other echo state networks, especially in the most challenging scenarios.

Application of natural computing algorithms to maximum likelihood estimation of direction of arrival

This work presents a study of the performance of populational meta-heuristics belonging to the field of natural computing when applied to the problem of direction of arrival (DOA) estimation, as well as an overview of the literature about the use of such techniques in this problem. These heuristics offer a promising alternative to the conventional approaches in DOA estimation, as they search for the global optima of the maximum likelihood (ML) function in a framework characterized by an elegant balance between global exploration and local improvement, which are interesting features in the context of multimodal optimization, to which the ML-DOA estimation problem belongs. Thus, we shall analyze whether these algorithms are capable of implementing the ML estimator, i.e., finding the global optima of the ML function. In this work, we selected three representative natural computing algorithms to perform DOA estimation: differential evolution, clonal selection algorithm, and the particle swarm. Simulation results involving different scenarios confirm that these methods can reach the performance of the ML estimator, regardless of the number of sources and/or their nature. Moreover, the number of points evaluated by such methods is quite inferior to that associated with a grid search, which gives support to their application.

Transmission Line Modeling: A Circuit Theory Approach

As shown in this paper, the classical transmission line equations for the distributed parameters model can be obtained from standard two-port network matrices avoiding the explicit use of partial differential equations. This is performed through a lemma derived directly from the Cayley--Hamilton theorem. The main advantage of this approach is that the modeling arises naturally in the frequency domain, allowing the consideration of frequency-dependent parameters (as, for instance, the resistance and inductance variations caused by the skin effect), normally not taken into account in time domain models.

Improving the threshold performance of maximum likelihood estimation of direction of arrival

We propose to improve the performance of some direction of arrival (DOA) estimators using array of sensors. We consider those maximum likelihood (ML) estimators that generate some DOA candidates and select one of them through an ML criterion. Our proposal modifies the candidate selection process substituting the traditional sample covariance matrix by a new one computed after filtering the received data with an optimum noise reduction filter. Simulation results indicate an improvement of the performance at low signal-to-noise ratios (SNR) and a considerable reduction of the threshold SNR. The computation of the new selection cost function implies in a small increase in the overall computational effort.

Empirical Methods to Determine the Number of Sources in Single-Channel Musical Signals

We present a sequence of empirical methods to determine the number of sources in musical signals when only one channel is available. Rather than building evidence through a statistical model-based approach, we instead develop a carefully tuned and tested two-stage system that is able to function effectively even in extremely underdetermined conditions. A first, more general procedure accurately determines the number of sources that are not closely harmonically related, while the second stage subsequently detects the presence of any remaining sources. The main advantages of this approach lie in its avoidance of the restrictive assumptions that can accompany more complex models in underdetermined cases, and in its use of robust heuristics to identify and exploit as much source-specific information as possible. These features make it possible to address even the most difficult cases in which sources are closely harmonically related, or even share the same fundamental frequency. We report an overall accuracy of nearly 80% on average, using both random and harmonically related mixtures of one to six sources taken from two widely available musical instrument databases-a notable result that demonstrates both the efficiency and the robustness of our proposed procedure.

Survey on automatic transcription of music

An automatic music transcriber is a device that detects, without human interference, the musical gestures required to play a particular piece. Many techniques have been proposed to solve the problem of automatic music transcription. This paper presents an overview on the theme, discussing digital signal processing techniques, pattern classification techniques and heuristic assumptions derived from music knowledge that were used to build some of the main systems found in the literature. The paper is focused on the motivations behind each technique, aiming to serve both as an introduction to the theme and as resource for the development of new solutions for automatic transcription.