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• Alpha integration encompasses many classic fusion operators. • This paper proposes vector score integration (VSI), a new alpha integration method. • The parameters of VSI are optimized to achieve the minimum probability of error. • VSI was applied to two classification tasks using electroencephalographic signals. • VSI outperformed other fusion methods in both applications. Alpha integration is a family of integrators that encompasses many classic fusion operators (e.g., mean, product, minimum, maximum) as particular cases. This paper proposes vector score integration (VSI), a new alpha integration method for late fusion of multiple classifiers considering the joint effect of all the classes of the multi-class problem. Theoretical derivations to optimize the parameters of VSI for achieving the minimum probability of error are provided. VSI was applied to two classification tasks using electroencephalographic signals. The first task was the automatic stage classification of a neuropsychological test performed by epileptic subjects and the second one was the classification of sleep stages from apnea patients. Four single classifiers (linear and quadratic discriminant analysis, naive Bayes, and random forest) and three competitive fusion methods were estimated for comparison: mean, majority voting, and separated score integration (SSI). SSI is based on alpha integration, but unlike the proposed method, it considers the scores from each class in isolation, not accounting for possible dependencies among scores corresponding to different classes. VSI was able to optimally combine the results from all the single classifiers, in terms of accuracy and kappa coefficient, and outperformed the results of the other fusion methods in both applications. [ABSTRACT FROM AUTHOR]

• A novel non-destructive method for archaeological ceramic provenance classification is presented. • The proposed method implements semi-supervised active learning and optimal fusion by alpha integration. • Features from ultrasound signals based on a linear time variant system are ranked. • Roman Terra Sigillata and Iberian ceramic shards from different deposits are classified. • The experiments simulates real situations of data scarcity and labeling uncertainty. This paper presents a novel application of pattern recognition to the provenance classification of archaeological ceramics. This is a challenging problem for archaeologists, which involves assigning a making location to a fragment of archaeological pottery that was found along with other fragments of pieces made in different distant locations from the find. The pieces look very similar to each other and, often, other contextual information about the use of the pieces cannot be used due to the small size of the fragments. Current standard methods to solve this problem are limited since they are time consuming, require costly equipment, and can lead to the destruction of a part of the pieces. The proposed method overcome those limitations using non-destructive ultrasonic testing and incorporates versatile data analysis through advanced pattern recognition techniques. Those techniques include the following: feature ranking, sample augmentation, semi-supervision based on active learning; and optimal fusion. This latter is based in the concept of alpha integration, which allows optimal fitting of the fusion model parameters. Different provenance classification problems are showcased: provenance classification of terra sigillata ceramic pieces from Aretina, Northern Italy and Sud-Gaul origins; and provenance classification of Iberian ceramic pieces from archaeological sites of Paterna, and Les Jovaes in Valencia, Spain. We demonstrate that the proposed fusion-based method achieves the best results, in terms of balanced classification accuracy and F1 score, compared with competitive methods like linear discriminant analysis, random forest, and support vector machine. Experiments for simulating small sample sizes and uncertainty in labeling of the pieces are included. In addition, the paper provides a design of a practical specialized device that could be used in different applications of archaeological ceramic classification. [ABSTRACT FROM AUTHOR]

Alpha integration methods have been used for integrating stochastic models and fusion in the context of detection (binary classification). Our work proposes separated score integration (SSI), a new method based on alpha integration to perform soft fusion of scores in multiclass classification problems, one of the most common problems in automatic classification. Theoretical derivation is presented to optimize the parameters of this method to achieve the least mean squared error (LMSE) or the minimum probability of error (MPE). The proposed alpha integration method was tested on several sets of simulated and real data. The first set of experiments used synthetic data to replicate a problem of automatic detection and classification of three types of ultrasonic pulses buried in noise (four-class classification). The second set of experiments analyzed two databases (one publicly available and one private) of real polysomnographic records from subjects with sleep disorders. These records were automatically staged in wake, rapid eye movement (REM) sleep, and non-REM sleep (three-class classification). Finally, the third set of experiments was performed on a publicly available database of single-channel real electroencephalographic data that included epileptic patients and healthy controls in five conditions (five-class classification). In all cases, alpha integration performed better than the considered single classifiers and classical fusion techniques. [ABSTRACT FROM AUTHOR]

Abstract Independent Component Analyzers Mixture Models (ICAMM) are versatile and general models for a large variety of probability density functions. In this paper we assume ICAMM to derive new MAP and LMSE estimators. The first one (MAP-ICAMM) is obtained by an iterative gradient algorithm, while the second (LMSE-ICAMM) admits a closed-form solution. Both estimators can be combined by using LMSE-ICAMM to initialize the iterative computation of MAP-ICAMM.The new estimators are applied to the reconstruction of missed channels in EEG multichannel analysis. The experiments demonstrate the superiority of the new estimators with respect to: Spherical Splines, Hermite, Partial Least Squares, Support Vector Regression, and Random Forest Regression. [ABSTRACT FROM AUTHOR]

• Finite training sets lead to classifier error rates above the Bayes error rate. • The training set size required in a practical setting is a relevant information. • Most approaches are purely experimental or consider just two classes. • A theoretical expression for the relative excess over the Bayes error rate is provided. In this paper, a theoretical learning curve is derived for the multi-class Bayes classifier. This curve fits general multivariate parametric models of the class-conditional probability density. The derivation uses a proxy approach based on analyzing the convergence of a statistic which is proportional to the posterior probability of the true class. By doing so, the curve depends only on the training set size and on the dimension of the feature vector; it does not depend on the model parameters. Essentially, the learning curve provides an estimate of the reduction in the excess of the probability of error that can be obtained by increasing the training set size. This makes it attractive in order to deal with the practical problems of defining appropriate training set sizes. [ABSTRACT FROM AUTHOR]

The detection and identification of internal defects in a material require the use of some technology that translates the hidden interior damages into observable signals with different signature-defect correspondences. We apply impact-echo techniques for this purpose. The materials are classified according to their defective status (homogeneous, one defect or multiple defects) and kind of defect (hole or crack, passing through or not). Every specimen is impacted by a hammer, and the spectrum of the propagated wave is recorded. This spectrum is the input data to a Bayesian classifier that is based on the modeling of the conditional probabilities with a mixture of Gaussians. The parameters of the Gaussian mixtures and the class probabilities are estimated using an extended expectation-maximization algorithm. The advantage of our proposal is that it is flexible, since it obtains good results for a wide range of models even under little supervision; e.g., it obtains a harmonic average of precision and recall value of 92.38% given only a 10% supervision ratio. We test the method with real specimens made of aluminum alloy. The results show that the algorithm works very well. This technique could be applied in many industrial problems, such as the optimization of the marble cutting process. [ABSTRACT FROM AUTHOR]

Missing traces in ground penetrating radar (GPR) B-scans (radargrams) may appear because of limited scanning resolution, failures during the acquisition process or the lack of accessibility to some areas under test. Four statistical interpolation methods for recovering these missing traces are compared in this paper: Kriging, Wiener structures, Splines and the expectation assuming an independent component analyzers mixture model (E-ICAMM). Kriging is an adaptation to the spatial context of the linear least mean squared error estimator. Wiener structures improve the linear estimator by including a nonlinear scalar function. Splines are a commonly used method to interpolate GPR traces. This consists of piecewise-defined polynomial curves that are smooth at the connections (or knots) between pieces. E-ICAMM is a new method proposed in this paper. E-ICAMM consists of computing the optimum nonlinear estimator (the conditional mean) assuming a non-Gaussian mixture model for the joint probability density in the observation space. The proposed methods were tested on a set of simulated data and a set of real data, and four performance indicators were computed. Real data were obtained by GPR inspection of two replicas of historical walls. Results show the superiority of E-ICAMM in comparison with the other three methods in the application of reconstructing incomplete B-scans. [ABSTRACT FROM AUTHOR]

Abstract: This paper introduces the application of independent component analysis mixture modelling (ICAMM) in non-destructive testing (NDT). The application consists of discriminating patterns for material quality control from homogeneous and defective materials inspected by impact-echo testing. This problem is modelled as a mixture of independent component analysis (ICA) models, representing a class of defective or homogeneous material by an ICA model whose parameters are learned from the impact-echo signal spectrum. These parameters define a kind of particular signature for the different defects. The proposed procedure is intended to exploit to the maximum the information obtained with the cost efficiency of only a single impact. To illustrate this capability, four levels of classification detail (material condition, kind of defect, defect orientation, and defect dimension) are defined, with the lowest level of detail having up to 12 classes. The results from several 3D finite element models and lab specimens of an aluminium alloy that contain defects of different shapes and sizes in different locations are included. The performance of the classification by ICA mixtures is compared with linear discriminant analysis (LDA) and with multi-layer perceptron (MLP) classification. We demonstrate that the mass spectra from impact-echo testing fit ICAMM, and we also show the feasibility of ICAMM to contribute in NDT applications. [Copyright &y& Elsevier]

Abstract: We present in this communication a procedure to extend ICA mixture models (ICAMM) to the case of having sequential dependence in the feature observation record. We call it sequential ICAMM (SICAMM). We present the algorithm, essentially a sequential Bayes processor, which can be used to sequentially classify the input feature vector among a given set of possible classes. Estimates of the class-transition probabilities are used in conjunction with the classical ICAMM parameters: mixture matrices, centroids and source probability densities. Some simulations are presented to verify the improvement of SICAMM with respect to ICAMM. Moreover a real data case is considered: the computation of hypnograms to help in the diagnosis of sleep disorders. Both simulated and real data analysis suggest the potential interest of including sequential dependence in the implementation of an ICAMM classifier. [Copyright &y& Elsevier]

Abstract: This paper presents a new procedure for learning mixtures of independent component analyzers. The procedure includes non-parametric estimation of the source densities, supervised–unsupervised learning of the model parameters, incorporation of any independent component analysis (ICA) algorithm into the learning of the ICA mixtures, and estimation of residual dependencies after training for correction of the posterior probability of every class to the testing observation vector. We demonstrate the performance of the procedure in the classification of ICA mixtures of two, three, and four classes of synthetic data, and in the classification of defective materials, consisting of 3D finite element models and lab specimens, in non-destructive testing using the impact-echo technique. The application of the proposed posterior probability correction demonstrates an improvement in the classification accuracy. Semi-supervised learning shows that unlabeled data can degrade the performance of the classifier when they do not fit the generative model. Comparative results of the proposed method and standard ICA algorithms for blind source separation in one and multiple ICA data mixtures show the suitability of the non-parametric ICA mixture-based method for data modeling. [Copyright &y& Elsevier]

The method uses ancillary data such as the pixel spectral similarity to enhance the quality of the fine-spatial resolution maps, thus improving the overall accuracy and prediction of the changed pixels. Innovative remote sensing image processing techniques have been progressively studied due to the increasing availability of remote sensing images, powerful techniques of data analysis, and computational power. Sub-pixel processing has emerged as an intense area of research considering the possibility of a pixel to belong to different classes in an image segmentation context. [Extracted from the article]

Abstract: This paper presents a technique for defect detection and material classification based on blind source separation by independent component analysis (ICA) for application in impact-echo testing. The transfer functions between the impact point and the defects in the material are modelled as “sources” for blind source separation. The sensors located on the material surface measure a convolutive mixture of the contribution of each of the defects. From spectral analysis the dominant resonance frequencies, varying from homogeneous to defective material, are selected. These frequencies are processed by instantaneous ICA in order to obtain more information about the defects using bootstrap resampling to analyse the stability of the solution. Results show that source estimates fit well with the theoretical response of the material. In addition, it has been found that the number of defects can be estimated by ICA in simulations and experiments with various defective parallelepiped-shape materials of aluminium alloy series 2000. [Copyright &y& Elsevier]

• A new method for oversampling very scarce training sets. • Based on Generative Adversarial Networks and Markov Random Field models. • Much better performance than SMOTE on simulated and real data experiment. In this work, we propose a new method for oversampling the training set of a classifier, in a scenario of extreme scarcity of training data. It is based on two concepts: Generative Adversarial Networks (GAN) and vector Markov Random Field (vMRF). Thus, the generative block of GAN uses the vMRF model to synthesize surrogates by the Graph Fourier Transform. Then, the discriminative block implements a linear discriminant on features measuring clique similarities between the synthesized and the original instances. Both blocks iterate until the linear discriminant cannot discriminate the synthetic from the original instances. We have assessed the new method, called Generative Adversarial Network Synthesis for Oversampling (GANSO), with both simulated and real data in experiments where the classifier is to be trained with just 3 or 5 instances. The applications consisted of classification of stages of neuropsychological tests using electroencephalographic (EEG) and functional magnetic resonance imaging (fMRI) data and classification of sleep stages using electrocardiographic (ECG) data. We have verified that GANSO can effectively improve the classifier performance, while the benchmark method SMOTE is not appropriate to deal with such a small size of the training set. [ABSTRACT FROM AUTHOR]

Recent works in signal processing on graphs have been driven to estimate the precision matrix and to use it as the graph Laplacian matrix. The normalized elements of the precision matrix are the partial correlation coefficients which measure the pairwise conditional linear dependencies of the graph. However, the non-linear dependencies inherent in any non-Gaussian model cannot be captured. We propose in this paper a generalized partial correlation coefficient which is derived by assuming an underlying multivariate Gaussian Mixture Model of the observations. Exact and approximate methods are proposed to estimate the generalized partial correlation coefficients from estimates of the Gaussian Mixture Model parameters. Thus it may find application in any non-Gaussian scenario where the Laplacian matrix is to be learned from training signals. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze by means of simulations the use of surrogate data algorithms for blind detection of nonlinearities in multiple-echo ultrasonic signals. We assume a blind scheme so that no information about the input (emitted ultrasonic pulse) can be used. The metrics and equations that model some nonlinear situations are carefully reviewed. Also, closed form equations of the third-order metrics from a simplified second-order Volterra kernel are derived. Computer simulations show that the surrogate data technique is a potentially powerful tool for blind detection of nonlinearities in multiple-echo ultrasonic signals if adequate metrics are chosen. They also reveal interesting trade-offs among parameters that model ultrasonic systems and detection percentages. [ABSTRACT FROM AUTHOR]

Many tasks in hyperspectral imaging, such as spectral unmixing and sub-pixel matching, require knowing how many substances or materials are present in the scene captured by a hyperspectral image. In this paper, we present an algorithm that estimates the number of materials in the scene using agglomerative clustering. The algorithm is based on the assumption that a valid clustering of the image has one cluster for each different material. After reducing the dimensionality of the hyperspectral image, the proposed method obtains an initial clustering using K-means. In this stage, cluster densities are estimated using Independent Component Analysis. Based on the K-means result, a model-based agglomerative clustering is performed, which provides a hierarchy of clusterings. Finally, a validation algorithm selects a clustering of the hierarchy; the number of clusters it contains is the estimated number of materials. Besides estimating the number of endmembers, the proposed method can approximately obtain the endmember (or spectrum) of each material by computing the centroid of its corresponding cluster. We have tested the proposed method using several hyperspectral images. The results show that the proposed method obtains approximately the number of materials that these images contain. [ABSTRACT FROM AUTHOR]

We present a new method for fusing scores corresponding to different detectors (two-hypotheses case). It is based on alpha integration, which we have adapted to the detection context. Three optimization methods are presented: least mean square error, maximization of the area under the ROC curve, and minimization of the probability of error. Gradient algorithms are proposed for the three methods. Different experiments with simulated and real data are included. Simulated data consider the twodetector case to illustrate the factors influencing alpha integration and demonstrate the improvements obtained by score fusion with respect to individual detector performance. Two real data cases have been considered. In the first, multimodal biometric data have been processed. This case is representative of scenarios in which the probability of detection is to be maximized for a given probability of false alarm. The second case is the automatic analysis of electroencephalogram and electrocardiogram records with the aim of reproducing the medical expert detections of arousal during sleeping. This case is representative of scenarios in which probability of error is to be minimized. The general superior performance of alpha integration verifies the interest of optimizing the fusing parameters. [ABSTRACT FROM AUTHOR]

The essential step of surrogating algorithms is phase randomizing the Fourier transform while preserving the original spectrum amplitude before computing the inverse Fourier transform. In this paper, we propose a new method which considers the graph Fourier transform. In this manner, much more flexibility is gained to define properties of the original graph signal which are to be preserved in the surrogates. The complex case is considered to allow unconstrained phase randomization in the transformed domain, hence we define a Hermitian Laplacian matrix that models the graph topology, whose eigenvectors form the basis of a complex graph Fourier transform. We have shown that the Hermitian Laplacian matrix may have negative eigenvalues. We also show in the paper that preserving the graph spectrum amplitude implies several invariances that can be controlled by the selected Hermitian Laplacian matrix. The interest of surrogating graph signals has been illustrated in the context of scarcity of instances in classifier training. [ABSTRACT FROM AUTHOR]

Conventional partial correlation coefficients (PCC) were extended to the non-Gaussian case, in particular to independent component analysis (ICA) models of the observed multivariate samples. Thus, the usual methods that define the pairwise connections of a graph from the precision matrix were correspondingly extended. The basic concept involved replacing the implicit linear estimation of conventional PCC with a nonlinear estimation (conditional mean) assuming ICA. Thus, it is better eliminated the correlation between a given pair of nodes induced by the rest of nodes, and hence the specific connectivity weights can be better estimated. Some synthetic and real data examples illustrate the approach in a graph signal processing context. [ABSTRACT FROM AUTHOR]