Pedro J. Zufiria

On the discrete-time dynamics of the basic Hebbian neural network node

In this paper, the dynamical behavior of the basic node used for constructing Hebbian artificial neural networks (NNs) is analyzed. Hebbian NNs are employed in communications and signal processing applications, among others. They have been traditionally studied on a continuous-time formulation whose validity is justified via some analytical procedures that presume, among other hypotheses, a specific asymptotic behavior of the learning gain. The main contribution of this paper is the study of a deterministic discrete-time (DDT) formulation that characterizes the average evolution of the node, preserving the discrete-time form of the original network and gathering a more realistic behavior of the learning gain. The new deterministic discrete-time model provides some unstability results (critical for the case of large similar variance signals) which are drastically different to the ones known for the continuous-time formulation. Simulation examples support the presented results, illustrating the practical limitations of the basic Hebbian model.

Fault Detection Schemes for Continuous-Time Stochastic Dynamical Systems

In this paper the fault detection (FD) task in stochastic continuous-time dynamical systems is addressed. A new family of FD approaches is presented, which is based on the application of hypothesis testing on continuous-time estimators. The given FD schemes are widely analyzed in the framework of their characteristics, such as fault detectability, false alarms and missed detection. A collection of sufficient detectability conditions are given for a class of faults (referred here as generic), characterizing the faults which can be detected with certain formalized guarantee by the given FD schemes, and providing also an upper bound for the detection time in a probabilistic sense. The application and comparative performance of these FD approaches is illustrated for different faults in a simulation example.

Peer to Peer Energy Trading with Electric Vehicles

This paper presents a novel peer-to-peer energy trading system between two sets of electric vehicles, which significantly reduces the impact of the charging process on the power system during business hours. This trading system is also economically beneficial for all the users involved in the trading process. An activity-based model is used to predict the daily agenda and trips of a synthetic population for Flanders (Belgium). These drivers can be initially classified into three sets; after discarding the set of drivers who will be short of energy without charging chances due to their tight schedule, we focus on the two remaining relevant sets: those who complete all their daily trips with an excess of energy in their batteries and those who need to (and can) charge their vehicle during some daily stops within their scheduled trips. These last drivers have the chance to individually optimize their energy cost in the time-space dimensions, taking into account the grid electricity price and their mobility constraints. Then, collecting all the available offer/demand information among vehicles parked in the same area at the same time, an aggregator determines an optimal peer-to-peer price per area and per time slot, allowing customers with excess of energy in their batteries to share with benefits this good with other users who need to charge their vehicles during their daily trips. Results show that, when applying the proposed trading system, the energy cost paid by these drivers at a specific time slot and in a specific area can be reduced up to 71%.

Image compression via optimal vector quantization: a comparison between SOM, LBG and k-means algorithms

An application of optimal vector quantization on image compression is studied. A neural network structure for obtaining the optimal codebook for the vector quantizer (VQ) is employed. This structure is based on Kohonens self-organizing map (SOM), whose learning algorithm provides an optimal codebook for a training sequence. It is demonstrated that the SOM complies, in general, with the Max-Lloyds conditions for optimal VQ. In this line, it is shown that the obtained codebook minimizes the averaged distortion over the training sequence, provided that the certain regularity conditions are satisfied. Finally, SOM-VQ convergence properties and squared-mean-error results are compared with LBG as well as k-means algorithms.<<ETX>>

Extended backpropagation for invariant pattern recognition neural networks

This paper presents some improvements on a neural network structure composed by a multilayer perceptron (MLP) with a preprocessing neural net, in order to perform translation, rotation and scale invariant pattern recognition. The preprocessing network has been modified and backpropagation (BP) has been generalized for training the preprocessing net as well as the multilayer perceptron. The new structure and weight selection procedure lead to a more noise tolerant neural net which also performs a better pattern classification.

Analysis of the sanger hebbian neural network

In this paper, the behavior of the Sanger hebbian artificial neural networks [6] is analyzed. Hebbian neural networks are employed in communications and signal processing applications, among others, due to their capability to implement Principal Component Analysis (PCA). Different improvements over the original model due to Oja have been developed in the last two decades. Among them, Sanger model was designed to directly provide the eigenvectors of the correlation matrix[8]. The behavior of these models has been traditionally considered on a continuous-time formulation whose validity is justified via some analytical procedures that presume, among other hypotheses, an specific asymptotic behavior of the learning gain. In practical applications, these assumptions cannot be guaranteed. This paper addresses the study of a deterministic discrete-time (DDT) formulation that characterizes the average evolution of the net, preserving the discrete-time form of the original network and gathering a more realistic behavior of the learning gain[13]. The dynamics behavior Sanger model is analyzed in this more realistic context. The results thoroughly characterize the relationship between the learning gain and the eigenvalue structure of the correlation matrix.

On the role of singularities in Branin's method from dynamic and continuation perspectives

A global analysis of Branins method (originally due to Davidenko) for finding all the real zeros of a vector function is carried out. The analysis is based on a global study of this method perceived of as a dynamical system. Since Branins algorithm is closely related to homotopy methods, this paper sheds some light on the global performance of these methods when employed for locating all the zeros of a vector function. Following the dynamical system approach, the performance of Branins algorithm is related to the existence of extraneous singularities as well as to the relative spatial distribution of the zeros of the vector function and singular manifolds. Branins conjectures regarding the types and the role of extraneous singularities are examined and counterexamples are provided to disprove them. We conclude that the performance of Branins method for locating all the zeros of a vector function is questionable even in the absence of extraneous singularities.

Analysis of Hebbian models with lateral weight connections

In this paper, the behavior of some hebbian artificial neural networks with lateral weights is analyzed. Hebbian neural networks are employed in communications and signal processing applications for implementing on-line Principal Component Analysis (PCA). Different improvements over the original Oja model have been developed in the last two decades. Among them, models with lateral weights have been designed to directly provide the eigenvectors of the correlation matrix [1,5,6,9]. The behavior of hebbian models has been traditionally studied by resorting to an associated continuous-time formulation under some questionable assumptions which are not guaranteed in real implementations. In this paper we employ the alternative deterministic discrete-time (DDT) formulation that characterizes the average evolution of these nets and gathers the influence of the learning gains time evolution [12]. The dynamic behavior of some of these hebbian models is analytically characterized in this context and several simulations complement this comparative study.

Dynamic behavior of DCT and DDT formulations for the Sanger neural network

In this paper, the behavior of the Sanger hebbian artificial neural networks is analyzed. Hebbian networks are employed to implement principal component analysis (PCA), and several improvements over the original model due to Oja have been developed in the last two decades. Among them, Sanger model is designed to directly provide the eigenvectors of the correlation matrix. The behavior of these models has been traditionally considered on a deterministic continuous-time (DCT) formulation whose validity is justified under some hypotheses on the specific asymptotic behavior of the learning gain. In practical applications, these assumptions cannot be guaranteed. This paper addresses a comparative study with a deterministic discrete-time (DDT) formulation that characterizes the average evolution of the net, preserving the discrete-time form of the original network and gathering a more realistic behavior of the learning gain. The results thoroughly characterize the relationship between the learning gain and the eigenvalue structure of the correlation matrix.

Entropy Characterization of Random Network Models

This paper elaborates on the Random Network Model (RNM) as a mathematical framework for modelling and analyzing the generation of complex networks. Such framework allows the analysis of the relationship between several network characterizing features (link density, clustering coefficient, degree distribution, connectivity, etc.) and entropy-based complexity measures, providing new insight on the generation and characterization of random networks. Some theoretical and computational results illustrate the utility of the proposed framework.