Asymmetric label switching is an effective and principled method for creating a diverse ensemble of learners for imbalanced classification problems. This technique can be combined with other rebalancing mechanisms, such as those based on cost policies or class proportion modifications. In this study, and under the Bayesian theory framework, we specify the optimal decision thresholds for the combination of these mechanisms. In addition, we propose using a gating network to aggregate the learners contributions as an additional mechanism to improve the overall performance of the system.

Ordinal classification of imbalanced data is a challenging problem that appears in many real world applications. The challenge is to simultaneously consider the order of the classes and the class imbalance, which can notably improve the performance metrics. The Bayesian formulation allows to deal with these two characteristics jointly: It takes into account the prior probability of each class and the decision costs, which can be used to include the imbalance and the ordinal information, respectively. We propose to use the Bayesian formulation to train neural networks, which have shown excellent results in many classification tasks. A loss function is proposed to train networks with a single neuron in the output layer and a threshold based decision rule. The loss is an estimate of the Bayesian classification cost, based on the Parzen windows estimator, which is fitted for a thresholded decision. Experiments with several real datasets show that the proposed method provides competitive results in different scenarios, due to its high flexibility to specify the relative importance of the errors in the classification of patterns of different classes, considering the order and independently of the probability of each class.

A new method for example-dependent cost (EDC) classification is proposed. The method constitutes an extension of a recently introduced training algorithm for neural networks. The surrogate cost function is an estimate of the Bayesian risk, where the estimates of the conditional probabilities for each class are defined in terms of a 1-D Parzen window estimator of the output of (discriminative) neural networks. This probability density is modeled with the objective of allowing an easy minimization of a sampled version of the Bayes risk. The conditional probabilities included in the definition of the risk are not explicitly estimated, but the risk is minimized by a gradient-descent algorithm. The proposed method has been evaluated using linear classifiers and neural networks, with both shallow (a single hidden layer) and deep (multiple hidden layers) architectures. The experimental results show the potential and flexibility of the proposed method, which can handle EDC classification under imbalanced data situations that commonly appear in this kind of problems.

Classification over imbalanced datasets is a highly interesting topic given that many real-world classification problems present a concrete class with a much smaller number of patterns than the others. In this work we shall explore the use of large, fully connected and potentially deep MLPs in such problems. We will consider simple MLPs, with ReLU activations, softmax outputs and categorical cross-entropy loss, showing that, when properly regularized, these relatively straightforward MLP models yield state of the art results in terms of the areas under the ROC curve for both two-class problems (the usual focus in imbalanced classification) as well as for multi-class problems.

The standard Gaussian Process regression (GP) is usually formulated under stationary hypotheses: The noise power is considered constant throughout the input space and the covariance of the prior distribution is typically modeled as depending only on the difference between input samples. These assumptions can be too restrictive and unrealistic for many real-world problems. Although nonstationarity can be achieved using specific covariance functions, they require a prior knowledge of the kind of nonstationarity, not available for most applications. In this paper we propose to use the Laplace approximation to make inference in a divisive GP model to perform nonstationary regression, including heteroscedastic noise cases. The log-concavity of the likelihood ensures a unimodal posterior and makes that the Laplace approximation converges to a unique maximum. The characteristics of the likelihood also allow to obtain accurate posterior approximations when compared to the Expectation Propagation (EP) approximations and the asymptotically exact posterior provided by a Markov Chain Monte Carlo implementation with Elliptical Slice Sampling (ESS), but at a reduced computational load with respect to both, EP and ESS.

Standard Gaussian process regression (GPR) assumes constant noise power throughout the input space and stationarity when combined with the squared exponential covariance function. This can be unrealistic and too restrictive for many real-world problems. Nonstationarity can be achieved by specific covariance functions, though prior knowledge about this nonstationarity can be difficult to obtain. On the other hand, the homoscedastic assumption is needed to allow GPR inference to be tractable. In this paper, we present a divisive GPR model which performs nonstationary regression under heteroscedastic noise using the pointwise division of two nonparametric latent functions. As the inference on the model is not analytically tractable, we propose a variational posterior approximation using expectation propagation (EP) which allows for accurate inference at reduced cost. We have also made a Markov chain Monte Carlo implementation with elliptical slice sampling to assess the quality of the EP approximation. Experiments support the usefulness of the proposed approach.

Using functional weights in a conventional linear combination architecture is a way of obtaining expressive power and represents an alternative to classical trainable and implicit nonlinear transformations. In this brief, we explore this way of constructing binary classifiers, taking advantage of the possibility of generating functional weights by means of a gate with fixed radial basis functions. This particular form of the gate permits training the machine directly with maximal margin algorithms. We call the resulting scheme "feature combiners with gate generated weights for classification." Experimental results show that these architectures outperform support vector machines (SVMs) and Real AdaBoost ensembles in most considered benchmark examples. An increase in the computational design effort due to cross-validation demands is the price to be paid to obtain this advantage. Nevertheless, the operational effort is usually lower than that needed by SVMs.

In this brief, we propose to increase the capabilities of standard real AdaBoost (RAB) architectures by replacing their linear combinations with a fusion controlled by a gate with fixed kernels. Experimental results in a series of well-known benchmark problems support the effectiveness of this approach in improving classification performance. Although the need for cross-validation processes obviously leads to higher training requirements and more computational effort, the operation load is never much higher; in many cases it is even lower than that of competitive RAB schemes.

The combination of filters concept is a simple and flexible method to circumvent various compromises hampering the operation of adaptive linear filters. Recently, applications which require the identification of not only linear, but also nonlinear systems are widely studied. In this paper, we propose a combination of adaptive Volterra filters as the most versatile nonlinear models with memory. Moreover, we develop a novel approach that shows a similar behavior but significantly reduces the computational load by combining Volterra kernels rather than complete Volterra filters. Following an outline of the basic principles, the second part of the paper focuses on the application to nonlinear acoustic echo cancellation scenarios. As the ratio of the linear to nonlinear echo signal power is, in general, a priori unknown and time-variant, the performance of nonlinear echo cancellers may be inferior to a linear echo canceller if the nonlinear distortion is very low. Therefore, a modified version of the combination of kernels is developed obtaining a robust behavior regardless of the level of nonlinear distortion. Experiments with noise and speech signals demonstrate the desired behavior and the robustness of both the combination of Volterra filters and the combination of kernels approaches in different application scenarios.

This work explores the possibility of improving the performance of Real Adaboost ensemble classifiers by replacing their standard linear combination of learners by a gating scheme. This more powerful fusion method is defined following the epoch-by-epoch construction of boosting ensembles. Preliminary experimental results support the potential of this new approach.

Adaptive combinations of adaptive filters are gaining popularity as a flexible and versatile solution to improve adaptive filters performance. In the recent years, combination schemes have focused on two different approaches: Convex and affine combinations, developing principally practical implementations with just two component filters. However, combinations of a higher number of adaptive filters can offer additional advantages, mainly in tracking environments. In this paper, we introduce a practical adaptation scheme for the affine combination of an arbitrary number of filters, including a steady-state analysis where the proposed rule is compared with the optimal combination. Several experiments both in tracking and stationary scenarios serve to demonstrate the appropriate performance of this approach.

For regression tasks, traditional neural networks (NNs) have been superseded by gaussian processes, which provide probabilistic predictions (input-dependent error bars), improved accuracy, and virtually no overfitting. Due to their high computational cost, in scenarios with massive data sets, one has to resort to sparse gaussian processes, which strive to achieve similar performance with much smaller computational effort. In this context, we introduce a mixture of NNs with marginalized output weights that can both provide probabilistic predictions and improve on the performance of sparse gaussian processes, at the same computational cost. The effectiveness of this approach is shown experimentally on some representative large data sets.

We present a general inference framework for inter-domain Gaussian Processes (GPs), focusing on its usefulness to build sparse GP models. The state-of-the-art sparse GP model introduced by Snelson and Ghahramani in [1] relies on finding a small, representative pseudo data set of m elements (from the same domain as the n available data elements) which is able to explain existing data well, and then uses it to perform inference. This reduces inference and model selection computation time from O(n^3) to O(m^2n), where m << n. Inter-domain GPs can be used to find a (possibly more compact) representative set of features lying in a different domain, at the same computational cost. Being able to specify a different domain for the representative features allows to incorporate prior knowledge about relevant characteristics of data and detaches the functional form of the covariance and basis functions. We will show how previously existing models fit into this framework and will use it to develop two new sparse GP models. Tests on large, representative regression data sets suggest that significant improvement can be achieved, while retaining computational efficiency.

When training machine classifiers, to replace hard classification targets by emphasized soft versions of them helps to reduce the negative effects of using standard cost functions as approximations to misclassification rates. This emphasis has the same kind of effect as sample editing methods, that have proved to be effective for improving classifiers performance. In this paper, we explore the effectiveness of using emphasized soft targets with generative models, such as Gaussian MixtureModels (GMM), and Gaussian Processes (GP). The interest of using GMMis that they offer advantages such as an easy interpretation and straightforward possibilities to deal with missing values. With respect to GP, if we use soft targets, we do not need to resort to any complex approximation to get a Gaussian Process classifier and, simultaneously, we can obtain the advantages provided by the use of an emphasis. Simulation results support the usefulness of the proposed approach to get better performance and show a low sensitivity to design parameters selection.

Proportionate adaptive filters, such as those based on the improved proportionate normalized least-mean-square (IPNLMS) algorithm, have been proposed for echo cancellation as an interesting alternative to the normalized least-mean-square (NLMS) filter. Proportionate schemes offer improved performance when the echo path is sparse, but are still subject to some compromises regarding their convergence properties and steady-state error. In this paper, we study how combination schemes, where the outputs of two independent adaptive filters are adaptively mixed together, can be used to increase IPNLMS robustness to channels with different degrees of sparsity, as well as to alleviate the rate of convergence versus steady-state misadjustment tradeoff imposed by the selection of the step size. We also introduce a new block-based combination scheme which is specifically designed to further exploit the characteristics of the IPNLMS filter. The advantages of these combined filters are justified theoretically and illustrated in several echo cancellation scenarios.

Adaptive filtering schemes are subject to different tradeoffs regarding their steady-state misadjustment, speed of convergence, and tracking performance. To alleviate these compromises, a new approach has recently been proposed, in which two filters with complementary capabilities adaptively mix their outputs to get an overall filter of improved performance. Following this approach, we propose a new normalized rule for adapting the mixing parameter that controls the combination. The new update rule preserves the good features of the existing scheme and is more robust to changes in the filtering scenario, for instance when the signal-to-noise ratio (SNR) is time varying. The benefits of the normalized scheme are illustrated analytically and with a number of experiments in both stationary and tracking situations.

Progressively emphasizing samples that are difficult to classify correctly is the base for the recognized high performance of real Adaboost (RA) ensembles. The corresponding emphasis function can be written as a product of a factor that measures the quadratic error and a factor related to the proximity to the classification border; this fact opens the door to explore the potential advantages provided by using adjustable combined forms of these factors. In this paper, we introduce a principled procedure to select the combination parameter each time a new learner is added to the ensemble, just by maximizing the associated edge parameter, calling the resulting method the dynamically adapted weighted emphasis RA (DW-RA). A number of application examples illustrates the performance improvements obtained by DW-RA.

This paper proposes a new cost function for supervised training of neural networks in binary classification applications. This cost function aims at reducing the probability of classification error by reducing the overlap between distributions of the soft output for each class. The non parametric Parzen window method, with Gaussian kernels, is used to estimate the distributions from the training data set. The cost function has been implemented in a GRBF neural network and has been tested in a motion detection application from low resolution infrared images, showing some advantages with respect to the conventional mean squared error cost function and also with respect to the support vector machine, a reference binary classifier.

Adaptive blind equalization plays an essential role in modern communication systems. We propose to improve the performance of constant modulus algorithm (CMA) based equalizers by using an adaptive convex combination of two CMA filters with a large and small step size, respectively, in order to simultaneously obtain fast convergence with low misadjustment during stationary periods. Some experiments show the effectiveness of the new algorithm and suggest that it is a reasonable alternative to blind equalizers that commute between the CMA and the (decision-directed) least mean square filter

In many real-life applications it is important to know how to deal with missing data (incomplete feature vectors). The ability of handling missing data has become a fundamental requirement for pattern classification because inappropriate treatment of missing data may cause large errors or false results on classification. A novel effective neural network is proposed to handle missing values in incomplete patterns with multitask learning (MTL). In our approach, a MTL neural network learns in parallel the classification task and the different tasks associated to incomplete features. During the MTL process, missing values are estimated or imputed. Missing data imputation is guided and oriented by the classification task, i.e., imputed values are those that contribute to improve the learning. We prove the robustness of this MTL neural network for handling missing values in classification problems from UCI database.

Nonlinear system identification based on support vector machines (SVM) has been usually addressed by means of the standard SVM regression (SVR), which can be seen as an implicit nonlinear autoregressive and moving average (ARMA) model in some reproducing kernel Hilbert space (RKHS). The proposal of this letter is twofold. First, the explicit consideration of an ARMA model in an RKHS (SVM-ARMA2K) is proposed. We show that stating the ARMA equations in an RKHS leads to solving the regularized normal equations in that RKHS, in terms of the autocorrelation and cross correlation of the (nonlinearly) transformed input and output discrete time processes. Second, a general class of SVM-based system identification nonlinear models is presented, based on the use of composite Mercer's kernels. This general class can improve model flexibility by emphasizing the input-output cross information (SVM-ARMA4K), which leads to straightforward and natural combinations of implicit and explicit ARMA models (SVR-ARMA2K and SVR-ARMA4K). Capabilities of these different SVM-based system identification schemes are illustrated with two benchmark problems.

Combination approaches can improve the performance of adaptive schemes. In this paper, we study the steady-state performance of an adaptive convex combination of transversal filters and show its universality in the sense that the combination performs, in steady-state, at least as well as its best component. We specialize the results to a convex combination of LMS filters using energy conservation arguments.

The recent interest in combining neural networks has produced a variety of techniques. This paper deals with boosting methods, in particular, real AdaBoost schemes built up with radial basis function networks. Real Adaboost emphasis function can be divided into two different terms, the first only focus on the quadratic error of each pattern and the second only takes into account its "proximity" to the boundary. Incorporating to this fixed emphasis function an additional degree of freedom, that allows us to weight these two terms, and also to select the radial basis functions centroids according to the emphasized regions, we show performance improvements: an error rate reduction, a faster convergence, and overfitting robustness.

An adaptive, convex linear combination of the outputs of a standard least mean square (LMS) equalizer and a sigmoidal equalizer is proposed. This procedure results in improving the speed of the LMS equalizer while retaining the low steady-state error of the sigmoidal filter. Appropriate adaption schemes for both of the filters and for the combination parameters are established. Simulations of practical communication applications demonstrate the effectiveness of this adaptive combination.

Decision theory shows that the optimal decision is a function of the posterior class probabilities. More specifically, in binary classification, the optimal decision is based on the comparison of the posterior probabilities with some threshold. Therefore, the most accurate estimates of the posterior probabilities are required near these decision thresholds. This paper discusses the design of objective functions that provide more accurate estimates of the probability values, taking into account the characteristics of each decision problem. We propose learning algorithms based on the stochastic gradient minimization of these loss functions. We show that the performance of the classifier is improved when these algorithms behave like sample selectors: samples near the decision boundary are the most relevant during learning.

We present a new approach to nonparametric spectral estimation on the basis of the support vector method (SVM). A reweighted least squares error formulation avoids the computational limitations of quadratic programming. The application to a synthetic example and to a digital communication problem shows the robustness of the SVM spectral analysis algorithm.

In this paper, we propose a general technique for solving support vector classifiers (SVCs) for an arbitrary loss function, relying on the application of an iterative reweighted least squares (IRWLS) procedure. We further show that three properties of the SVC solution can be written as conditions over the loss function. This technique allows the implementation of the empirical risk minimization (ERM) inductive principle on large margin classifiers obtaining, at the same time, very compact (in terms of number of support vectors) solutions. The improvements obtained by changing the SVC loss function are illustrated with synthetic and real data examples.

The broadcast scheduling problem (BSP) arises in frame design for packet radio networks (PRNs). The frame structure determines the main communication parameters: communication delay and throughput. The BSP is a combinatorial optimization problem which is known to be NP-hard. To solve it, we propose an algorithm with two main steps which naturally arise from the problem structure: the first one tackles the hardest contraints and the second one carries out the throughput optimization. This algorithm combines a Hopfield neural network for the constraints satisfaction and a genetic algorithm for achieving a maximal throughput. The algorithm performance is compared with that of existing algorithms in several benchmark cases; in all of them, our algorithm finds the optimum frame length and outperforms previous algorithms in the resulting throughput.

We propose a genetic algorithm for the design of palettes for the color quantization of images in applications of compression and transmission through noisy channels. Our algorithm includes specific genetic operators and a noisy channel version of the widespread generalized Lloyd algorithm (GLA) to optimise the search. Besides it operates in the YUV space using a weighted distortion measure adequate to the characteristics of eye perception. Simulation tests proved the benefit of our approach compared to previous methods either in computational requirements or in the quality of the quantized images.

In the context of classification problems, the paper analyzes the general structure of the strict sense Bayesian (SSB) cost functions, those having a unique minimum when the soft decisions are equal to the posterior class probabilities. We show that any SSB cost is essentially the sum of a generalized measure of entropy, which does not depend on the targets, and an error component. Symmetric cost functions are analyzed in detail. Our results provide a further insight on the behavior of this family of objective functions and are the starting point for the exploration of novel algorithms. Two applications are proposed. First, the use of asymmetric SSB cost functions for posterior probability estimation in non-maximum a posteriori (MAP) decision problems. Second, a novel entropy minimization principle for hybrid learning: use labeled data to minimize the cost function, and unlabeled data to minimize the corresponding entropy measure.

An iterative block training method for support vector classifiers (SVCs) based on weighted least squares (WLS) optimization is presented. The algorithm, which minimizes structural risk in the primal space, is applicable to both linear and nonlinear machines. In some nonlinear cases, it is necessary to previously find a projection of data onto an intermediate-dimensional space by means of either principal component analysis or clustering techniques. The proposed approach yields very compact machines, the complexity reduction with respect to the SVC solution is especially notable in problems with highly overlapped classes. Furthermore, the formulation in terms of WLS minimization makes the development of adaptive SVCs straightforward, opening up new fields of application for this type of model, mainly online processing of large amounts of (static/stationary) data, as well as online update in nonstationary scenarios (adaptive solutions). The performance of this new type of algorithm is analyzed by means of several simulations.

The attractive possibility of applying layerwise block training algorithms to multilayer perceptrons MLP, which offers initial advantages in computational effort, is refined in this article by means of introducing a sensitivity correction factor in the formulation. This results in a clear performance advantage, which we verify in several applications. The reasons for this advantage are discussed and related to implicit relations with second-order techniques, natural gradient formulations through Fisher's information matrix, and sample selection. Extensions to recurrent networks and other research lines are suggested at the close of the article.

A new algorithm, the joint network and data density estimation (JNDDE), is proposed to estimate the 'a posteriori' probabilities of the targets with neural networks in multiple classes problems. It is based on the estimation of conditional density functions for each class with some restrictions or constraints imposed by the classifier structure and the use Bayes rule to force the a posteriori probabilities at the output of the network, known here as a implicit set. The method is applied to train perceptrons by means of Gaussian mixture inputs, as a particular example for the generalized Softmax perceptron (GSP) network. The method has the advantage of providing a clear distinction between the network architecture and the model of the data constraints, giving network parameters or weights on one side and data over parameters on the other. MLE stochastic gradient based rules are obtained for JNDDE. This algorithm can be applied to hybrid labeled and unlabeled learning in a natural fashion.

In time series problems, where time ordering is a crucial issue, the use of partial likelihood estimation (PLE) represents a specially suitable method for the estimation of parameters in the model. We propose a general supervised neural network algorithm, joint network and data density estimation (JNDDE), that employs PLE to approximate conditional probability density functions for multi-class classification problems. The logistic regression analysis is generalized to multiple class problems with a softmax regression neural network used to model the a posteriori probabilities such that they are approximated by the network outputs. Constraints to the network architecture, as well as to the model of data, are imposed, resulting in both a flexible network architecture and distribution modeling. We consider application of JNDDE to channel equalization and present simulation results.

The problem of designing cost functions to estimate a posteriori probabilities in multiclass problems is addressed in this paper. We establish necessary and sufficient conditions that these costs must satisfy in one-class one-output networks whose outputs are consistent with probability laws. We focus our attention on a particular subset of the corresponding cost functions; those which verify two usually interesting properties: symmetry and separability (well-known cost functions, such as the quadratic cost or the cross entropy are particular cases in this subset). Finally, we present a universal stochastic gradient learning rule for single-layer networks, in the sense of minimizing a general version of these cost functions for a wide family of nonlinear activation functions.

This paper explores the possibility of constructing RBF classifiers which, somewhat like support vector machines, use a reduced number of samples as centroids, by means of selecting samples in a direct way. Because sample selection is viewed as a hard computational problem, this selection is done after a previous vector quantization: this way obtaining also other similar machines using centroids selected from those that are learned in a supervised manner. Several forms of designing these machines are considered, in particular with respect to sample selection; as well as some different criteria to train them. Simulation results for well-known classification problems show very good performance of the corresponding designs, improving that of support vector machines and reducing substantially their number of units. This shows that our interest in selecting samples (or centroids) in an efficient manner is justified. Many new research avenues appear from these experiments and discussions, as suggested in our conclusions.

This paper deals with the compensation for the nonlinear distortion introduced by power-efficient amplifiers on linear modulation by means of equalization. We propose a new equalizer based on a reduced-complexity network called the generalized cerebellar model arithmetic computer (GMAC) GCMAC. The GCMAC-based equalizer is compared with other well-known structures such as the Volterra filter and the multi-layer perceptron. Extensive computer simulations have been carried out. The obtained results show the effectiveness of the proposed structure to compensate for strong nonlinearities.

The cerebellar model articulation controller (CMAC) is a simple and fast neural-network based on local approximations. However, its rigid structure reduces its accuracy of approximation and speed of convergence with heterogeneous inputs. In this paper, we propose a generalized CMAC (GCMAC) network that considers different degrees of generalization for each input. Its representation abilities are analyzed, and a set of local relationships that the output function must satisfy are derived. An adaptive growing method of the network is also presented. The validity of our approach and methods are shown by some simulated examples.

Sequence extrapolation is a classical problem in signal processing. The application of the expectation-maximization (EM) algorithm to estimate the signal autocorrelation in Wiener extrapolation allows us to view previous techniques as particular cases, to modify them, and to introduce new ones offering better performance with a moderate increase in computational load.

This correspondence presents a new two-stage adaptive vector quantizer of LSF parameters in LPC speech coding. The first codebook is adapted by a partition-delete operation, whereas the code-vectors of the second codebook remain unchanged. The objective and subjective evaluations show that the proposed scheme offers transparent quantization with 22 b/frame.>

This paper describes a method to incorporate linear constraints into an adaptive beamformer based on cyclostationary signal properties, previously proposed by the authors (see Proc. ICASSP'93, vol.IV, p. 284-287, Minneapolis, MN, April, 1993). The constraints allow an efficient exploitation of the spatial information available from the environment. This knowledge is used to prevent the beamformer from being captured by interferences showing the same cyclostationary properties as the desired signal and to control the sidelobe level of the radiation pattern.>

An optimal least-mean-square (LMS) algorithm is presented to be used with a lookup-table plus transversal filter adaptive echo canceller that has independent steps for the non-overlapped and overlapped parts of the transversal structure. Its advantage over previous schemes and algorithms used with this family of structures is presented. A suboptimal switched step version is discussed. Some simulation examples illustrate the performances of these schemes.>

The authors explore the possibility of introducing a novel family of algorithms for data blind equalization based on minimizing phase error cost functions. A simple discussion of the difficulties involved and how to avoid them serves to introduce the family. Then, the authors discuss the general and particular characteristics of these schemes, and show the performance of two representative particular cases by means of simulation examples. Finally, they propose some basic ideas on reducing the limitation of these phase constraining algorithms.>

The drawbacks of using the adaptive delay filter for plant identification are discussed. These drawbacks are due to regression and gain estimation errors and the filter's limitations under colored excitation hypotheses. After proposing simple solutions for both drawbacks, the authors show how the limitations can be solved by using different known techniques, such as dynamic programming or by applying adaptively thresholded gradient-type algorithms. The direct use of the latter algorithms is also presented as an alternative. Some simulation results illustrate the behaviour of the proposed modifications and extensions.>

The authors present a novel formulation of harmonic extrapolation based on a deconvolution interpretation of the frequency problem that allows techniques and algorithms that have been successfully used in spiky deconvolution to be used. A gradient-type method is proposed that, combined with the application of a threshold to reduce progressively the band of the signal, shows the advantages of having low computational cost, the possibility of using different windows, and better estimations if the period of the signal is known. Finally, a comparison is made of with the result for the MUSIC algorithm in a series of simulations to show the performance of the method.>

A generalization of the RLS algorithm is presented. The objective measure to be minimized is composed of the sum of arbitrarily weighted kth powers of the observed error (RLK algorithm). The authors formulate general recursive algorithm in the context of noisy transversal plant identification. An approximate analysis of its performance based on the convergence of the mean and covariance matrix of the adaptive filter coefficients is carried out. This analysis evidences the importance of the choice of the order k under the knowledge of the plant noise statistics. The coherence of some computer simulation results for two different algorithms (k=2, 4) and plant noise statistics (binary and Laplacian) with the theoretical analysis is shown.>

We present a general family of frequency adaptive algorithms; it is based on the minimization of the gradient of the k-th absolute power of the overall frequency error. We use a context of plant identification to develop the adaptive equations, to establish their averaged versions and to find the convergence conditions. A general discussion of performance is also given. Finally, we verify the obtained results for the first four algorithms by means of some computer simulations.

High-order Yule-Walker equations are a, theoretically, correct tool for the computation of the AR parameters of an ARMA process. Unfortunatelly, in practical applications, working with sample data, one frequently obtain unreliable results. The high variance (in contrast with the small bias) exhibited by the corresponding AR parameter estimates is the main reason of having such a performance. Here, we propose a class of high-order Yule-Walker estimates that allow variance control in an easy form. The proposed methods, although simple to apply, are the result of a rather elaborated analysis, which also gives, as intermediate results, new insights into the practical problems of the high-order Yule-Walker equations. Although we have concentrated on ARMA processes of the AR plus white noise type, the results could be probably extended to more general cases.

In this paper a new speech coding method will be presented, its base being the multipulse model of speech production. A closeness relationship between natural utterances and synthetic ones can be defined in terms of the speech signal itself: at some intervals, the coding error-that is to say the difference between natural and synthetic signals- is set to a particular value in order to meet pre-stablished signal-to-noise ratio criteria, whereas at some other intervals equality of the envelopes of both signals is the only constrain of the synthesis process. Thus defining the closeness constrains, the optimum multipulse sequence can be found through the minimization of the sum of the absolute values of its samples.

In this paper, we propose a simplification of the model introduced by B.S. Atal and M.R. Schroeder for a code-excited linear predictor. Our scheme is based on a two-step search of the optimum code-word. In the first step, a sub-set in the code-book is selected by using a simple distance measure and taking into account the selections already made for the previous frames of speech. In the second step, the original model of Atal and Schroeder, including perceptual weighting, is applied to the sub-set in order to make the final selection of the optimum code-word. The proposed scheme reduces the computational load involved in the original one, and our preliminar results indicate that the quality of the synthetic speech is fairly good.

Two methods to model a signal as the output of an all-pole linear filter driven by a sparse spike sequence are presented. These techniques can also be used to compute the filter coefficients when the input signal is assumed to be composed by pulses with a certain width. The linear system coefficients are obtained by minimizing the mean absolute value of the error for a forward-backward predictor. The advantages, in this particular case, of L1minimization over the well known least-squares optimization are shown.

A simple nonlinear structure together with a LMS-type algorithm to update its parameters are considered and applied to nonlinear echo cancellation of data signals. The nonlinear filter is one with functionally separated memory and nonlinearity. This makes it suitable to compensate the unavoidable nonlinear transfer of the monolithic digital-analog converter (DAC) in the echo cancelling scheme and, in general, to handle nonlinearly distorted signals.

This paper provides a first structured view of using the L1-norm minimization of error when computing the parameters corresponding to spectral estimation models, discussing its interest and advantage/disadvantage balance compared with the standard L2-norm minimization procedures. Some examples illustrate this comparison.

The channel noise effects on linear delta modulation (LDM) systems have not yet been adequately analyzed. This paper presents a new and general formulation of these effects, based on the theoretical work by Wolf [1]. A comparative discussion of our formulas with previous results is also included. Finally, the application of our methods and the validity of our comments are illustrated by some numerical examples.