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This paper proposes a neural network architecture for solving systems of non-linear equations. A back propagation algorithm is applied to solve the problem, using an adaptive learning rate procedure, based on the minimization of the mean squared error function defined by the system, as well as the network activation function, which can be linear or non-linear. The results obtained are compared with some of the standard global optimization techniques that are used for solving non-linear equations systems. The method was tested with some well-known and difficult applications (such as Gauss–Legendre 2-point formula for numerical integration, chemical equilibrium application, kinematic application, neuropsychology application, combustion application and interval arithmetic benchmark) in order to evaluate the performance of the new approach. Empirical results reveal that the proposed method is characterized by fast convergence and is able to deal with high-dimensional equations systems. [ABSTRACT FROM PUBLISHER]

This paper presents an MLP-type neural network with some fixed connections and a backpropagation-type training algorithm that identifies the full set of solutions of a complete system of nonlinear algebraic equations with n equations and n unknowns. The proposed structure is based on a backpropagation-type algorithm with bias units in output neurons layer. Its novelty and innovation with respect to similar structures is the use of the hyperbolic tangent output function associated with an interesting feature, the use of adaptive learning rate for the neurons of the second hidden layer, a feature that adds a high degree of flexibility and parameter tuning during the network training stage. The paper presents the theoretical aspects for this approach as well as a set of experimental results that justify the necessity of such an architecture and evaluate its performance. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the evolving field of medical imaging and machine learning (ML), this paper introduces a novel framework for evaluating synthetic pulmonary imaging aiming to assess synthetic data quality and applicability. Our study concentrates on synthetic X-ray chest images, crucial for diagnosing respiratory diseases. We employ SPINE (Synthetic Pulmonary Imaging Evaluation) framework, a threefold synthetic images evaluation method including expert domain assessment, statistical data analysis and adversarial evaluation. In order to replicate and validate our methodology, we followed an End-to-End data and model management process which begins with a dataset of Normal and Pneumonia chest X-rays, generating synthetic images using Generative Adversarial Networks (GANs) and training a baseline classifier, essential in the adversarial evaluation axis, testing synthetic images against real data assessing their predictive value. The critical outcome of our approach is the post-market analysis of synthetic images. This innovative method evaluates synthetic images using clinical, statistical, and scientific criteria independently from traditional generation performance metrics. This independent evaluation provides deep insights into the clinical and research effectiveness of the synthetic data. By ensuring these images mirror real data's statistical properties and maintain clinical accuracy, our framework establishes a new standard for the ethical and reliable use of synthetic data in medical imaging and research., (© 2024 The Authors.)

The article emphasizes the critical importance of language generation today, particularly focusing on three key aspects: Multitasking, Multilinguality, and Multimodality, which are pivotal for the Natural Language Generation community. It delves into the activities conducted within the Multi3Generation COST Action (CA18231) and discusses current trends and future perspectives in language generation., Competing Interests: No competing interests were disclosed., (Copyright: © 2024 Lloret E et al.)

Alzheimer's disease (AD) is the main cause of dementia and Mild cognitive impairment (MCI) is a prodromal stage of AD whose early detection is considered crucial as it can contribute in slowing the progression of AD. In our study we attempted to classify a subject into AD, MCI, or Healthy Control (HC) groups with the use of electroencephalogram (EEG) data. Due to the time-series nature of EEG we exper-imented with the powerful recurrent neural network (RNN) classifiers and more specifically with models including basic or bidirectional Long Short-Term Memory (LSTM) modules. The EEG signals from 17 channels were preprocessed using a 0.1-32 Hz band-pass filter and then segmented into 2-second epochs during which, the subject had closed eyes. Finally, on each segment Fast Fourier Transform (FFT) was applied. To evaluate our models we studied four different classification problems: problem 1: separating subject into three classes (HC, MCI, AD) and problems 2-4: pairwise classifications AD vs. MCI, AD vs. HC and MCI vs. HC. For each problem we employed two different cross-validation approaches ( a) by segment and (b) by patient. In the first one, segments from a subject EEG may exist in both training and validations set, while in the second one, all the EEG segments of a subject can only exist in either the training or the validation set. In the AD-MCI-HC classification we achieved an accuracy of 99% by segment cross-validation, which was an improvement to earlier studies that utilized recurrent neural network models. In the pairwise classification problems we achieved over 90% accuracy by segment and over 80% by subject.

The optimal linear Karhunen-Loeve transform (KLT) attains the minimum reconstruction error for a fixed number of transform coefficients assuming that these coefficients do not contain noise. In any real coding system, however, the representation of the coefficients using a finite number of bits requires the presence of quantizers. We formulate the optimal linear transform using a data model that incorporates the quantization noise. Our solution does not correspond to an orthogonal transform and in fact, it achieves a smaller mean squared error (MSE) compared to the KLT, in the noisy case. Like the KLT, our solution depends on the statistics of the input signal, but it also depends on the bit-rate used for each coefficient. Especially for images, based on our optimality theory, we propose a simple modification of the discrete cosine transform (DCT). Our coding experiments show a peak signal-to noise ratio (SNR) performance improvement over JPEG of the order of 0.2 dB with an overhead less than 0.01 b/pixel.

In a typical linear data compression system the representation variables resulting from the coding operation are assumed totally reliable and therefore the solution in the mean-squared-error sense is an orthogonal projector to the so-called principal component subspace. When the representation variables are contaminated by additive noise which is uncorrelated with the signal, the problem is called noisy principal component analysis (NPCA) and the optimal MSE solution is not a trivial extension of PCA. We first show that the problem is not well defined unless we impose explicit or implicit constraints on either the coding or the decoding operator. Second, orthogonality is not a property of the optimal solution under most constraints. Third, the signal components may or may not be reconstructed depending on the noise level. As the noise power increases, we observe rank reduction in the optimal solution under most reasonable constraints. In these cases it appears that it is preferable to omit the smaller signal components rather than attempting to reconstruct them. This phenomenon has similarities with classical information theoretical results, notably the water-filling analogy, found in parallel additive Gaussian noise channels. Finally, we show that standard Hebbian-type PCA learning algorithms are not optimally robust to noise, and propose a new Hebbian-type learning algorithm which is optimally robust in the NPCA sense.

The most widely used signal in clinical practice is the ECG. ECG conveys information regarding the electrical function of the heart, by altering the shape of its constituent waves, namely the P, QRS, and T waves. Thus, the required tasks of ECG processing are the reliable recognition of these waves, and the accurate measurement of clinically important parameters measured from the temporal distribution of the ECG constituent waves. In this paper, we shall review some current trends on ECG pattern recognition. In particular, we shall review non-linear transformations of the ECG, the use of principal component analysis (linear and non-linear), ways to map the transformed data into n-dimensional spaces, and the use of neural networks (NN) based techniques for ECG pattern recognition and classification. The problems we shall deal with are the QRS/PVC recognition and classification, the recognition of ischemic beats and episodes, and the detection of atrial fibrillation. Finally, a generalised approach to the classification problems in n-dimensional spaces will be presented using among others NN, radial basis function networks (RBFN) and non-linear principal component analysis (NLPCA) techniques. The performance measures of the sensitivity and specificity of these algorithms will also be presented using as training and testing data sets from the MIT-BIH and the European ST-T databases.

The linear threshold element (LTE), or perceptron, is a linear classifier with limited capabilities due to the problems arising when the input pattern set is linearly nonseparable. Assuming that the patterns are presented in a sequential fashion, we derive a theory for the detection of linear nonseparability as soon as it appears in the pattern set. This theory is based on the precise determination of the solution region in the weight space with the help of a special set of vectors. For this region, called the solution cone, we present a recursive computation procedure which allows immediate detection of nonseparability. The separability-violating patterns may be skipped so that, at the end, we derive a totally separable subset of the original pattern set along with its solution cone. The intriguing aspect of this algorithm is that it can be directly cast into a simple neural-network implementation. In this model the synaptic weights are committed (they are updated only once, and the only change that may happen after that is their destruction). This bears resemblance to the behavior of biological neural networks, and it is a feature unlike those of most other artificial neural techniques. Finally, by combining many such neural models we develop a learning procedure capable of separating convex classes.

This paper is developed in two parts. First, the authors formulate the solution to the general reduced-rank linear approximation problem relaxing the invertibility assumption of the input autocorrelation matrix used by previous authors. The authors' treatment unifies linear regression, Wiener filtering, full rank approximation, auto-association networks, SVD and principal component analysis (PCA) as special cases. The authors' analysis also shows that two-layer linear neural networks with reduced number of hidden units, trained with the least-squares error criterion, produce weights that correspond to the generalized singular value decomposition of the input-teacher cross-correlation matrix and the input data matrix. As a corollary the linear two-layer backpropagation model with reduced hidden layer extracts an arbitrary linear combination of the generalized singular vector components. Second, the authors investigate artificial neural network models for the solution of the related generalized eigenvalue problem. By introducing and utilizing the extended concept of deflation (originally proposed for the standard eigenvalue problem) the authors are able to find that a sequential version of linear BP can extract the exact generalized eigenvector components. The advantage of this approach is that it's easier to update the model structure by adding one more unit or pruning one or more units when the application requires it. An alternative approach for extracting the exact components is to use a set of lateral connections among the hidden units trained in such a way as to enforce orthogonality among the upper- and lower-layer weights. The authors call this the lateral orthogonalization network (LON) and show via theoretical analysis-and verify via simulation-that the network extracts the desired components. The advantage of the LON-based model is that it can be applied in a parallel fashion so that the components are extracted concurrently. Finally, the authors show the application of their results to the solution of the identification problem of systems whose excitation has a non-invertible autocorrelation matrix. Previous identification methods usually rely on the invertibility assumption of the input autocorrelation, therefore they can not be applied to this case.