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The problem (or scenario) involving qualitative or imprecise information is not solvable by classical set theory. To overcome the shortcoming of classical set theory, Zadeh (Inf Control 8(3):338–356, 26) introduced the concept of fuzzy sets that generalizes the concept of classical sets. Fuzzy set theory allows modelling and handling of imprecise information in an effective way. As a special class of fuzzy sets, fuzzy numbers (FN) which are very much important in decision making was introduced by Dubois and Prade (Int J Syst Sci 9:631–626, 12). The available methods for solving multi-criteria decision making problems (MCDM) are problem dependent in nature due to the partial ordering on the class of FN. Total ordering on the class of FN by countable number of real-valued parameters was achieved by Wang and Wang (Fuzzy Sets Syst 243:131–141, 21). A complete ranking on the class of trapezoidal fuzzy numbers (TrFNs) using finite number of score functions is achieved in this paper. In this paper, a new ranking procedure (complete) on the class of TrFNs using the concepts of mid-point, radius, left and right fuzziness of TrFN is proposed and further we introduce a method for solving fuzzy multi-criteria decision making (Fuzzy MCDM) problem. Finally, comparisons of our proposed method with familiar existing methods are listed.

Bearing signals are often contaminated by in-band interferences and random noise. Oscillatory Behavior-based Signal Decomposition (OBSD) is a new technique which decomposes a signal according to its oscillatory behavior, rather than frequency or scale. Due to the low oscillatory transients of bearing fault-induced signals, the OBSD can be used to effectively extract bearing fault signatures from a blurred signal. However, the quality of the result highly relies on the selection of method-related parameters. Such parameters are often subjectively selected and a systematic approach has not been reported in the literature. As such, this paper proposes a systematic approach to automatic selection of OBSD parameters for reliable extraction of bearing fault signatures. The OBSD utilizes the idea of Morphological Component Analysis (MCA) that optimally projects the original signal to low oscillatory wavelets and high oscillatory wavelets established via the Tunable Q-factor Wavelet Transform (TQWT). In this paper, the effects of the selection of each parameter on the performance of the OBSD for bearing fault signature extraction are investigated. It is found that some method-related parameters can be fixed at certain values due to the nature of bearing fault-induced impulses. To adaptively tune the remaining parameters, index-guided parameter selection algorithms are proposed. A Convergence Index (CI) is proposed and a CI-guided self-tuning algorithm is developed to tune the convergence-related parameters, namely, penalty factor and number of iterations. Furthermore, a Smoothness Index (SI) is employed to measure the effectiveness of the extracted low oscillatory component (i.e. bearing fault signature). It is shown that a minimum SI implies an optimal result with respect to the adjustment of relevant parameters. Thus, two SI-guided automatic parameter selection algorithms are also developed to specify two other parameters, i.e., Q-factor of high-oscillatory wavelets and regularization parameter. Based on the index-guided parameter selection algorithms, an automatic parameter selection method is then proposed for the application of OBSD to bearing fault signature extraction. The proposed method is then validated with simulated signals and experimental data.

In this paper an immuno-inspired algorithm is proposed to generate sequences of data close to the ideal white noise. The motivation to propose the algorithm is that in many cases there is a necessity to generate white noises with a small number of samples, and the pseudo-random generators may fail to perform this task. The proposed algorithm is based on the maximization of the whiteness criterion, clearly defined in this paper, and is different from other immuno-inspired algorithms because it presents an automatic regulation of the suppression threshold, that is an important control variable of the algorithm. This feature allows the proposed algorithm to reach good results, even for different sizes of candidate solutions. To test the proposed algorithm, the results obtained from it are compared to the results obtained from a known pseudo-random generator and it is shown that the solutions obtained with the proposed algorithm are better, for time and frequency domain, if the number of samples required is limited. It is also shown that the proposed algorithm consumes a time comparable to the pseudo-random generator to reach solutions that are better than the ones obtained with that kind of algorithm.

Super-resolution (SR) has become more vital, because of its capability to generate high-quality ultra-high definition (UHD) high-resolution (HR) images from low-resolution (LR) input images. Conventional SR methods entail high computational complexity, which makes them difficult to be implemented for up-scaling of full-high-definition input images into UHD-resolution images. Nevertheless, our previous super-interpolation (SI) method showed a good compromise between Peak-Signal-to-Noise Ratio (PSNR) performances and computational complexity. However, since SI only utilizes simple linear mappings, it may fail to precisely reconstruct HR patches with complex texture. In this paper, we present a novel SR method, which inherits the large-to-small patch conversion scheme from SI but uses global regression based on local linear mappings (GLM). Thus, our new SR method is called GLM-SI. In GLM-SI, each LR input patch is divided into 25 overlapped subpatches. Next, based on the local properties of these subpatches, 25 different local linear mappings are applied to the current LR input patch to generate 25 HR patch candidates, which are then regressed into one final HR patch using a global regressor. The local linear mappings are learned cluster-wise in our off-line training phase. The main contribution of this paper is as follows: Previously, linear-mapping-based conventional SR methods, including SI only used one simple yet coarse linear mapping to each patch to reconstruct its HR version. On the contrary, for each LR input patch, our GLM-SI is the first to apply a combination of multiple local linear mappings, where each local linear mapping is found according to local properties of the current LR patch. Therefore, it can better approximate nonlinear LR-to-HR mappings for HR patches with complex texture. Experiment results show that the proposed GLM-SI method outperforms most of the state-of-the-art methods, and shows comparable PSNR performance with much lower computational complexity when compared with a super-resolution method based on convolutional neural nets (SRCNN15). Compared with the previous SI method that is limited with a scale factor of 2, GLM-SI shows superior performance with average 0.79 dB higher in PSNR, and can be used for scale factors of 3 or higher.

Orthogonal moments play an important role in image analysis and other similar applications. However, existing orthogonal moments are restricted to integer order, and little investigation of non-integer order orthogonal moments has been conducted to date. In this paper, a general framework of real-order orthogonal moments, also known as fractional-order orthogonal moments, is proposed. In this general framework, fractional-order orthogonal moments can be defined in Cartesian and polar coordinate systems. Shifted Legendre polynomials are implemented in this paper to investigate the properties of fractional-order orthogonal moments. A series of experiments are performed, which demonstrate that fractional-order orthogonal moments are not only capable of region-of-interest (ROI) feature extraction but also have potential for image reconstruction and face recognition and have high noise robustness in invariant image recognition.

In the framework of regression trees, this paper provides a recursive partitioning methodology to deal with a non-standard response variable. Specifically, either multivalued numerical or modal response of the type histogram will be considered. These data are known as symbolic data, which special cases are classical data, imprecise data, conjunctive data as well as fuzzy data. In spite of pre-processing data in order to deal with standard regression tree methodology, this paper provides, as main contribution, a definition of the impurity measure and of the splitting criterion allowing for building the regression tree for multivalued numerical response variable. We analyze and evaluate the performance of our proposal, using simulated data as well as a real-world case studies.

Clustering is an important field for making data meaningful at various applications such as processing satellite images, extracting information from financial data or even processing data in social sciences. This paper presents a new clustering approach called Gaussian Density Distance (GDD) clustering algorithm based on distance and density properties of sample space. The novel part of the method is to find best possible clusters without any prior information and parameters. Another novel part of the algorithm is that it forms clusters very close to human clustering perception when executed on two dimensional data. GDD has some similarities with today's most popular clustering algorithms; however, it uses both Gaussian kernel and distances to form clusters according to data density and shape. Since GDD does not require any special parameters prior to run, resulting clusters do not change at different runs. During the study, an experimental framework is designed for analysis of the proposed clustering algorithm and its evaluation, based on clustering performance for some characteristic data sets. The algorithm is extensively tested using several synthetic data sets and some of the selected results are presented in the paper. Comparative study outcomes produced by other well-known clustering algorithms are also discussed in the paper. (C) 2016 Elsevier Ltd. All rights reserved.

This paper focuses on sensitivity analysis of intuitionistic fuzzy solid transportation problem (IFSTP). In real-world situation, IFSTP seems to be more realistic than solid transportation problem (STP) as available information is uncertain. Due to degeneracy of IFSTP or that of STP, Type I sensitivity analysis seems to be impractical. Hence , in this paper, a new algorithm is proposed to determine the Type II sensitivity ranges to overcome this problem. A numerical example is illustrated to demonstrate the feasibility of the proposed algorithm and the efficiency of recommended method over existing method.

The Cramer-Rao bound (CRB) offers a lower bound on the variances of unbiased estimates of parameters, e.g., directions of arrival (DOA) in array processing. While there exist landmark papers on the study of the CRB in the context of array processing, the closed-form expressions available in the literature are not easy to use in the context of sparse arrays (such as minimum redundancy arrays (MRAs), nested arrays, or coprime arrays) for which the number of identifiable sources D exceeds the number of sensors N. Under such situations, the existing literature does not spell out the conditions under which the Fisher information matrix is nonsingular, or the condition under which specific closed-form expressions for the CRB remain valid. This paper derives a new expression for the CRB to fill this gap. The conditions for validity of this expression are expressed as the rank condition of a matrix defined based on the difference coarray. The rank condition and the closed-form expression lead to a number of new insights. For example, it is possible to prove the previously known experimental observation that, when there are more sources than sensors, the CRB stagnates to a constant value as the SNR tends to infinity. It is also possible to precisely specify the relation between the number of sensors and the number of uncorrelated sources such that these conditions are valid. In particular, for nested arrays, coprime arrays, and MRAs, the new expressions remain valid for D = O ( N 2 ) , the precise detail depending on the specific array geometry.

Compressed sensing (CS) is a new field used for signal acquisition and design of sensor that made a large drooping in the cost of acquiring sparse signals. In this paper, new algorithms are developed to improve the performance of the greedy algorithms. In this paper, a new greedy pursuit algorithm, SS-MSMP (Split Signal for Multiple Support of Matching Pursuit), is introduced and theoretical analyses are given. The SS-MSMP is suggested for sparse data acquisition, in order to reconstruct analog and efficient signals via a small set of general measurements. This paper proposes a new fast method which depends on a study of the behavior of the support indices through picking the best estimation of the corrosion between residual and measurement matrix. The term multiple supports originates from an algorithm; in each iteration, the best support indices are picked based on maximum quality created by discovering correlation for a particular length of support. We depend on this new algorithm upon our previous derivative of halting condition that we produce for Least Support Orthogonal Matching Pursuit (LS-OMP) for clear and noisy signal. For better reconstructed results, SS-MSMP algorithm provides the recovery of support set for long signals such as signals used in WBAN. Numerical experiments demonstrate that the new suggested algorithm performs well compared to existing algorithms in terms of many factors used for reconstruction performance.

In MMMF, ratings matrix with multiple discrete values is treated by specially extending hinge loss function to suit multiple levels.We view this process as analogous to extending two-class classifier to a unified multi-class classifier.Alternatively, multi-class classifier can be built by arranging multiple two- class classifiers in a hierarchical manner.In this paper, we investigate this aspect for collaborative filtering and propose an efficient and novel framework of multiple bi-level MMMFs.We compare our method with nine well-known algorithms on two benchmark datasets and show that our method outperforms these methods on NMAE measure. Maximum Margin Matrix Factorization (MMMF) has been a successful learning method in collaborative filtering research. For a partially observed ordinal rating matrix, the focus is on determining low-norm latent factor matrices U (of users) and V (of items) so as to simultaneously approximate the observed entries under some loss measure and predict the unobserved entries. When the rating matrix contains only two levels (1), rows of V can be viewed as points in k-dimensional space and rows of U as decision hyperplanes in this space separating +1 entries from 1 entries. When hinge/smooth hinge loss is the loss function, the hyperplanes act as maximum-margin separator. In MMMF, rating matrix with multiple discrete values is treated by specially extending hinge loss function to suit multiple levels. We view this process as analogous to extending two-class classifier to a unified multi-class classifier. Alternatively, multi-class classifier can be built by arranging multiple two-class classifiers in a hierarchical manner. In this paper, we investigate this aspect for collaborative filtering and propose an efficient and novel framework of multiple bi-level MMMFs. There is substantial saving in computational overhead. We compare our method with nine well-known algorithms on two benchmark datasets and show that our method outperforms these methods on NMAE measure. We also show that our method yields latent factors of lower ranks and the trade-off between empirical and generalization error is low.

Mismatch removal is a key step in many computer vision problems. In this paper, we handle the mismatch removal problem by adopting shape interaction matrix (SIM). Given the homogeneous coordinates of the two corresponding point sets, we first compute the SIMs of the two point sets. Then, we detect the mismatches by picking out the most different entries between the two SIMs. Even under strong affine transformations, outliers, noises, and burstiness, our method can still work well. Actually, this paper is the first non-iterative mismatch removal method that achieves affine invariance. Extensive results on synthetic 2D points matching data sets and real image matching data sets verify the effectiveness, efficiency, and robustness of our method in removing mismatches. Moreover, when applied to partial-duplicate image search, our method reaches higher retrieval precisions with shorter time cost compared with the state-of-the-art geometric verification methods.

This is Part II of a series of two papers where we address sequential estimation of wide-sense stationary autoregressive moving average (ARMA) state processes by particle filtering. In Part I, we considered a state-space model where the state was an ARMA process of known order and where the parameters of the process could be known or unknown. In this paper, we extend our work from Part I by considering the same type of models, with the added complexity that the ARMA processes are now of unknown order. Instead of working on a scheme that first tracks the state by operating with different assumed models, and then selects the best model by using a predefined criterion, we present a method that directly estimates the state without the need of knowing the model order. We derive the transition density of the state for unknown ARMA model order, and propose a particle filter based on that density and the empirical Bayesian methodology. We demonstrate the performance of the proposed method with computer simulations and compare it with the methods from Part I.

A giant leap has been made in the past couple of decades with the introduction of kernel-based learning as a mainstay for designing effective nonlinear computational learning algorithms. In view of the geometric interpretation of conditional expectation and the ubiquity of multiscale characteristics in highly complex nonlinear dynamic systems [1] – [3] , this paper presents a new orthogonal projection operator wavelet kernel, aiming at developing an efficient computational learning approach for nonlinear dynamical system identification. In the framework of multiresolution analysis, the proposed projection operator wavelet kernel can fulfill the multiscale, multidimensional learning to estimate complex dependencies. The special advantage of the projection operator wavelet kernel developed in this paper lies in the fact that it has a closed-form expression, which greatly facilitates its application in kernel learning. To the best of our knowledge, it is the first closed-form orthogonal projection wavelet kernel reported in the literature. It provides a link between grid-based wavelets and mesh-free kernel-based methods. Simulation studies for identifying the parallel models of two benchmark nonlinear dynamical systems confirm its superiority in model accuracy and sparsity.

This paper proposes a new strategy to promote the robustness of structure from motion algorithm from uncalibrated video sequences. First, an augmented affine factorization algorithm is formulated to circumvent the difficulty in image registration with noise and outliers contaminated data. Then, an alternative weighted factorization scheme is designed to handle the missing data and measurement uncertainties in the tracking matrix. Finally, a robust strategy for structure and motion recovery is proposed to deal with outliers and large measurement noise. This paper makes the following main contributions: 1) An augmented factorization algorithm is proposed to circumvent the difficult image registration problem of previous affine factorization, and the approach is applicable to both rigid and nonrigid scenarios; 2) by employing the fact that image reprojection residuals are largely proportional to the error magnitude in the tracking data, a simple outliers detection approach is proposed; and 3) a robust factorization strategy is developed based on the distribution of the reprojection residuals. Furthermore, the proposed approach can be easily extended to nonrigid scenarios. Experiments using synthetic and real image data demonstrate the robustness and efficiency of the proposed approach over previous algorithms.

This paper proposes an estimator of mutual information for both discrete and continuous variables and applies it to the Chow-Liu algorithm to find a forest that expresses probabilistic relations among them. The state-of-the-art assumes that the continuous variables are Gaussian and that the graphical model under discrete and continuous variables is ANOVA. Consequently, it is difficult to obtain the maximum likelihood of three connected variables such that the center is Gaussian and the other two are discrete, and thus, the state-of-the-art restricts the class to the forest such that there is no Gaussian node between discrete variables. The proposed method executes in a general setting without any assumptions, preparing several meshes, computing the mutual information values, and selecting the maximum value. We prove that the number of meshes to be prepared is at most O ( log 2 ź n ) and that the estimated mutual information is no larger than zero if and only if the variables are independent for large n. Finally, we apply the proposed method to the problems of gene differential analysis and relation discovery between gene expression and SNPs (single nucleotide polymorphisms). In particular, for the latter experiment, we demonstrate that the proposed method successfully captures the relation among them but that the state-of-the-art fails because of the merits and demerits of the proposed and existing methods. A novel mutual information estimator for both discrete and continuous variables is proposed.The estimator takes a positive value for large n if and only if the two variables are independent.The estimation completes within a quasi-polynomial time of sample size.This paper demonstrates that it finds relations among the gene expressions and SNP values.

In this paper, a novel model-based compressive sampling (CS) technique for natural images is proposed. Our algorithm integrates a universal hidden Markov tree (uHMT) model, which captures the relation among the sparse wavelet coefficients of images, into both sampling and recovery steps of CS. At the sampling step, we employ the uHMT model to devise a nonuniformly sparse measurement matrix $\boldsymbol{\Phi }_{\text{uHMT}}$ . In contrast to the conventional CS sampling matrices, such as dense Gaussian, Bernoulli or uniformly sparse matrices that are oblivious to the signal model and the correlation among the signal coefficients, the proposed $\boldsymbol{\Phi }_{\text{uHMT}}$ is designed based on the signal model and samples the coarser wavelet coefficients with higher probabilities and more sparse wavelet coefficients with lower probabilities. At the recovery step, we integrate the uHMT model into two state-of-the-art Bayesian CS recovery schemes. Our simulation results confirm the superiority of our proposed HMT model-based nonuniform compressive sampling and recovery , referred to as uHMT-NCS , over other model-based CS techniques that solely consider the signal model at the recovery step. This paper is distinguished from other model-based CS schemes in that we take a novel approach to simultaneously integrating the signal model into both CS sampling and recovery steps. We show that such integration greatly increases the performance of the CS recovery, which is equivalent to reducing the required number of samples for a given reconstruction quality.

In this paper, we address the problem of robustly recovering several instances of a curve model from a single noisy data set with outliers. Using M-estimators revisited in a Lagrangian formalism, we derive an algorithm that we call Simultaneous Multiple Robust Fitting (SMRF), which extends the classical Iterative Reweighted Least Squares algorithm (IRLS). Compared to the IRLS, it features an extra probability ratio, which is classical in clustering algorithms, in the expression of the weights. Potential numerical issues are tackled by banning zero probabilities in the computation of the weights and by introducing a Gaussian prior on curves coefficients. Applications to camera calibration and lane-markings tracking show the effectiveness of the SMRF algorithm, which outperforms classical Gaussian mixture model algorithms in the presence of outliers.

Recently, based on negentropy of squared envelope (SE) and of squared envelope spectrum (SES), extensions of spectral kurtosis, the infograms including the SE infogram and the SES infogram, were proposed to detect impulsive and cyclostationary transients. Moreover, they have abilities to detect transients in the cases, where impulsive noises exist or relaxation times of repetitive transients are lower than their repetition rate. Nevertheless, the infograms are fast filtering algorithms and cannot achieve optimal filtering for bearing fault feature identification. This paper aims to extend the infograms to novel Bayesian inference based optimal wavelet filtering for bearing fault feature identification. The innovations of this paper are summarized as follows. Firstly, a state space model of wavelet parameters is presented. Here, wavelet parameters are the states of the state space model. Monotonically increasing guess negentropy measurements are constructed. Secondly, either the SE infogram or the SES infogram is employed to initialize the state space model. Then, considering Gaussian disturbance on wavelet parameters, wavelet parameters are assumed to follow a joint Gaussian distribution. Thirdly, spherical cubature integration based Bayesian inference is introduced to iteratively establish posterior wavelet parameters distributions. At last, optimal wavelet parameters are determined from the posterior wavelet parameters distributions so as to conduct optimal wavelet filtering. Two instance studies including simulated and experimental bearing fault data were investigated to illustrate how the proposed Bayesian inference method works. The results show that the proposed Bayesian inference method is convergent and provides more fault signatures than the infogram.

The task of designing estimators that are able to track time-varying distributions has found promising applications in many real-life problems.Existing approaches resort to sliding windows that track changes by discarding old observations. In this paper, we report a novel estimator referred to as the Stochastic Discretized Weak Estimator (SDWE), that is based on the principles of discretized Learning Automata (LA). In brief, the estimator is able to estimate the parameters of a time varying binomial distribution using finite memory. The estimator tracks changes in the distribution by operating a controlled random walk in a discretized probability space. The steps of the estimator are discretized so that the updates are done in jumps, and thus the convergence speed is increased. Further, the state transitions are both state-dependent and randomized. As far as we know, such a scheme is both novel and pioneering. The results which have first been proven for binomial distributions have subsequently been extended for the multinomial case, using which they can be applied to any univariate distribution using a histogram-based scheme. The most outstanding and pioneering contribution of our work is that of achieving multinomial estimation without relying on a set of binomial estimators, and where the underlying strategy is truly randomized. Interestingly, the estimator possesses a low computational complexity that is independent of the number of parameters of the multinomial distribution. The generalization of these results for other distributions has also been alluded to. The paper briefly reports conclusive experimental results that prove the ability of the SDWE to cope with non-stationary environments with high adaptation and accuracy. HighlightsWe present finite-memory estimation techniques for non-stationary environments.These new techniques use the principles of discretized Learning Automata.The results have been tested for many time-varying problems and applications.

Purpose Effective and robust motion estimation with sub-pixel accuracy is essential in many image processing and computer vision applications. Due to its computational efficiency and robustness in the presence of intensity changes as well as geometric distortions, phase correlation in the Fourier domain provides an attractive solution for global motion estimation and image registration. The paper aims to discuss these issues. Design/methodology/approach In this paper, relevant sub-pixel strategies are categorized into three classes, namely, single-side peak interpolation, dual-side peak interpolation and curve fitting. The well-known images “Barbara” and “Pentagon” were used to evaluate the performance of eight typical methods, in which Gaussian noise was attached in the synthetic data. Findings For eight such typical methods, the tests using synthetic data have suggested that considering dual-side peaks in interpolation or fitting helps to produce better results. In addition, dual-side interpolation outperforms curve fitting methods in dealing with noisy samples. Overall, Gaussian-based dual-side interpolation seems the best in the experiments. Originality/value Based on the comparisons of eight typical methods, the authors can have a better understanding of the phase correlation for motion estimation. The evaluation can provide useful guidance in this context.

This paper proposed an optimized algorithm which combines density clustering of parameter selection with feature-based classification for hot region prediction. First, all the residues are classified by SVM to remove non-hot spot residues, then density clustering of parameter selection is used to find hot regions. In the density clustering, this paper studies how to select input parameters. There are two parameters radius and density in density-based incremental clustering. We firstly fix density and enumerate radius to find a pair of parameters which leads to maximum number of clusters, and then we fix radius and enumerate density to find another pair of parameters which leads to maximum number of clusters. Experiment results show that the proposed method using both two pairs of parameters provides better prediction performance than the other method, and compare these two predictive results, the result by fixing radius and enumerating density have slightly higher prediction accuracy than that by fixing density and enumerating radius.

The previous studies have shown that optimizing the driving velocity profiles and route selection based on the availability of the traffic lights' operation information in a traffic network can significantly reduce the individual and cumulative energy consumption of on-road vehicles for the urban driving. In this paper, we propose an accurate and precise stochastic online estimation method of the parameters of the traffic lights operating at a piecewise constant period. In this paper, we first model the traffic lights with a semi-hidden Markov model (SHMM) and then develop the period measurement model governed by a unique noise model specific to the indirect traffic light period measurements. The proposed method solves the estimation problem in two stages: in the first stage, we determine the sequence of the Markovian states maximizing the probability given the measurements and the SHMM parameters; then, in the second stage, we update the period and state duration estimates based on the Bayesian tracking given the corresponding latest measurements. The simulation and real vehicle data results prove that the proposed method can accurately estimate the switching times and the period of the piecewise fixed-period traffic lights.

International audience; This paper first provides statistical properties of wavelet operators when the observation model can be seen as the product of a deterministic piece-wise regular function (signal) and a stationary random field (noise). This multiplicative observation model is analyzed in two standard frameworks by considering either (1) a direct wavelet transform of the model or (2) a log-transform of the model prior to wavelet decomposition. The paper shows that, in Framework (1), wavelet coefficients of the time series are affected by intricate correlation structures which blur signal singularities. Framework (2) is shown to be associated with a multiplicative (or geometric) wavelet transform and the multiplicative interactions between wavelets and the model highlight both sparsity of signal changes near singularities (dominant coefficients) and decorre-lation of speckle wavelet coefficients. The paper then derives that, for time series of synthetic aperture radar data, geometric wavelets represent a more intuitive and relevant framework for the analysis of smooth earth fields observed in the presence of speckle. From this analysis, the paper proposes a fast-and-concise geometric wavelet based method for joint change detection and regularization of synthetic aperture radar image time series. In this method, geometric wavelet details are first computed with respect to the temporal axis in order to derive generalized-ratio change-images from the time series. The changes are then enhanced and speckle is attenuated by using spatial block sigmoid shrinkage. Finally, a regularized time series is reconstructed from the sigmoid shrunken change-images. Some applications highlight relevancy of the method for the analysis of SENTINEL-1A and TerraSAR-X image time series over Chamonix-Mont-Blanc.

This paper proposes a new registration algorithm using bidirectional distance with bounded rotation angle to deal with 2D isotropic scaling point set registration problem. In the paper, a new isotropic registration problem based on the bidirectional distance is presented, which is described as a least square registration model with bounded rotation angle. To solve this problem, the proposed algorithm builds up the correspondence and computes the transformation repeatedly, which is similar to the iterative closest point (ICP) algorithm. A closed-form solution of the transformation is obtained in the given interval at each iterative step. The proposed algorithm monotonically converges to a local minimum from any given initial value. Therefore, to obtain the desired results, the boundary of rotation angle and initial value are estimated by the principle component analysis. A series of experiments are conducted to demonstrate that the proposed method is much more robust when compared with the state-of-the-art point set registration methods.

Recently, the paper 2 introduced a method for model order estimation based on penalizing adaptively the likelihood (PAL). In this paper, we use the PAL based order estimation method for a nonlinear sinusoidal model and study its asymptotic statistical properties. We prove that the estimator of the model order using the PAL rule is consistent. Simulation examples are presented to illustrate the performance of the PAL method for small sample sizes and to compare it with that of three information criterion-based methods. In this paper, we use the PAL based order estimation method for estimating the number of components of a superimposed nonlinear sinusoidal model.We have proved that the estimator of the model order using the PAL rule is large sample consistent.Simulation examples are presented to illustrate the performance of the PAL method for small sample sizes and to compare it with three standard methods, namely, the usual AIC, the usual BIC and the asymptotic MAP rule.The PAL rule can also be extended for estimating the number of components for similar nested superimposed nonlinear 1-d and 2-d signal models.

This paper proposes a prior near-ignorance model for regression based on a set of Gaussian Processes (GP). GPs are natural prior distributions for Bayesian regression. They offer a great modeling flexibility and have found widespread application in many regression problems. However, a GP requires the prior elicitation of its mean function, which represents our prior belief about the shape of the regression function, and of the covariance between any two function values.In the absence of prior information, it may be difficult to fully specify these infinite dimensional parameters. In this work, by modeling the prior mean of the GP as a linear combination of a set of basis functions and assuming as prior for the combination coefficients a set of conjugate distributions obtained as limits of truncate exponential priors, we have been able to model prior ignorance about the mean of the GP. The resulting model satisfies translation invariance, learning and, under some constraints, convergence, which are desirable properties for a prior near-ignorance model. Moreover, it is shown in this paper how this model can be extended to allow for a weaker specification of the GP covariance between function values, by letting each basis function to vary in a set of functions.Application to hypothesis testing has shown how the use of this model induces the capability of automatically detecting when a reliable decision cannot be made based on the available data. We derive new near-ignorance models for Bayesian nonparametric regression.It uses Gaussian processes with mean obtained combining explicit basis functions.A set of limit exponential priors is assumed for the combination coefficients.We prove prior ignorance, translation invariance and learning properties of the model.We show the merits of this approach on an application to hypothesis testing.

We propose a graph-based mode-seeking method to fit multi-structural data.The proposed method combines mode-seeking with preference analysis.The proposed method exploits the global structure of graphs by random walks.Experiments show the proposed method is superior to some other fitting methods. In this paper, we propose a novel graph-based mode-seeking fitting method to fit and segment multiple-structure data. Mode-seeking is a simple and effective data analysis technique for clustering and filtering. However, conventional mode-seeking based fitting methods are very sensitive to the proportion of good/bad hypotheses, while most of sampling techniques may generate a large proportion of bad hypotheses. In this paper, we show that the proposed graph-based mode-seeking method has significant superiority for geometric model fitting. We intrinsically combine mode seeking with preference analysis. This enables mode seeking to be beneficial for reducing the influence of bad hypotheses since bad hypotheses usually have larger residual values than good ones. In addition, the proposed method exploits the global structure of graphs by random walks to alleviate the sensitivity to unbalanced data. Experimental results on both synthetic data and real images demonstrate that the proposed method outperforms several other competing fitting methods especially for complex data.

This paper treats the estimation of a flat fading Rayleigh channel with Jakes' Doppler spectrum model and slow fading variations. A common method is to use a Kalman filter (KF) based on an auto-regressive model of order p (AR(p)). The parameters of the AR model can be simply tuned by using the correlation matching (CM) criterion. However, the major drawback of this method is that high orders are required to approach the Bayesian Cramer–Rao lower bound. The choice of p together with the tuning of the model parameters is thus critical, and a tradeoff must be found between the numerical complexity and the performance. The reasonable tradeoff arising from setting p = 2 has received much attention in the literature. However, the methods proposed for tuning the model parameters are either based on an extensive grid-search analysis or experimental results, which limits their applicability. A general solution for any scenario is simply missing for p = 2 and this paper aims at filling this gap. We propose using a Minimization of Asymptotic Variance (MAV) criterion, for which a general closed-form formula has been derived for the optimal tuning of the model and the mean square error. This provides deeper insight into the behavior of the KF with respect to the channel state (Doppler frequency and signal to noise ratio). Moreover, the paper interprets the proposed solution, especially the dependence of the shape of the optimal AR(2) spectrum on the channel state. Analytic and numerical comparisons with first- and second-order algorithms in the literature are also performed. Simulation results show that the proposed AR(2)-MAV model performs better than the literature and similarly to AR(p)-CM models with p ≥ 15 .

In this paper, we investigated the application of artificial neural networks with composite architectures into the prediction of local control (LC) of lung cancer patients after radiotherapy. The motivation of this paper was to take advantage of the temporal associations among longitudinal (sequential) data to improve the predictive performance of outcome models under the circumstance of limited sample sizes. Two composite architectures: 1) a 1-D convolutional + fully connected and 2) a locally connected + fully connected architectures were implemented for this purpose. Compared with the fully connected architecture [multilayer perceptron (MLP)], our composite architectures yielded better predictive performance of LC in lung cancer patients who received radiotherapy. Specifically, in a cohort of 98 patients (29 patients failed locally), the composite architecture of 1-D convolutional layers and fully connected layers achieved an area under receiver operating characteristic curve (AUC) of 0.83 [95% confidence interval (CI): 0.807–0.841] with 18 features (14 features are longitudinal data). Whereas, the composite architecture of locally connected layers and fully connected layers achieved an AUC of 0.80 (95% CI: 0.775–0.811). Both outperformed an MLP in the prediction performance with the same set of features, which achieved an AUC of 0.78 (95% CI: 0.751–0.790); ( ${P}$ -values for differences in AUC using the DeLong tests were ${1.609 \times 10^{-14}}$ and ${1.407 \times 10^{-4}}$ , respectively).

Several lifetime distributions have played an important role to fit survival data. However, for some of these models, the computation of maximum likelihood estimators is quite difficult due to presence of flat regions in the search space, among other factors. Several well-known derivative-based optimization tools are unsuitable for obtaining such estimates. To circumvent this problem, we introduce the AdequacyModel computational library version 2.0.0 for the R statistical environment with two major contributions: a general optimization technique based on the Particle Swarm Optimization (PSO) method (with a minor modification of the original algorithm) and a set of statistical measures for assessment of the adequacy of the fitted model. This library is very useful for researchers in probability and statistics and has been cited in various papers in these areas. It serves as the basis for the Newdistns library (version 2.1) published in an impact journal in the area of computational statistics, see https://CRAN.R-project.org/package=Newdistns. It is also the basis of the Wrapped library (version 2.0), see https://CRAN.R-project.org/package=Wrapped. A third package making use of the AdequacyModel library can be found in https://CRAN.Rproject.org/package=sglg. In addition, the proposed library has proved to be very useful for maximizing log-likelihood functions with complex search regions. The library provides a greater control of the optimization process by introducing a stop criterion based on a minimum number of iterations and the variance of a given proportion of optimal values. We emphasize that the new library can be used not only in statistics but in physics and mathematics as proved in several examples throughout the paper.

Precision point positioning (PPP) is widely used in maritime navigation and other scenarios because it does not require a reference station. In PPP, the satellite clock bias (SCB) cannot be eliminated by differential, thus leading to an increase in positioning error. The prediction accuracy of SCB has become one of the key factors restricting positioning accuracy. Although International GNSS Service (IGS) provides the ultra-rapid ephemeris prediction part (IGU-P), its quality and real-time performance can not meet the practical application. In order to improve the accuracy of PPP, this paper proposes to use the Prophet model to predict SCB. Specifically, SCB sequence is read from the observation part in the ultra-rapid ephemeris (IGU-O) released by IGS. Next, the SCB sequence between adjacent epochs are subtracted to obtain the corresponding SCB single difference sequence. Then using the Prophet model to predict SCB single difference sequence. Finally, the prediction result is substituted into the PPP positioning observation equation to obtain the positioning result. This paper uses the final ephemeris (IGF) published by IGS as a benchmark and compares the experimental results with IGU-P. For the selected four satellites, compared with the results of the IGU-P, the accuracy of SCB prediction of the model in this paper is improved by about 50.3%, 61.7%, 60.4%, and 48.8%. In terms of PPP positioning results, we use Real-time kinematic (RTK) measurements as a benchmark in this paper. Positioning accuracy has increased by 26%, 35%, and 19% in the N, E, and U directions, respectively. The results show that the Prophet model can improve the performance of PPP.

This paper studies instance-dependent Positive and Unlabeled (PU) classification, where whether a positive example will be labeled (indicated by s) is not only related to the class label y, but also depends on the observation x. Therefore, the labeling probability on positive examples is not uniform as previous works assumed, but is biased to some simple or critical data points. To depict the above dependency relationship, a graphical model is built in this paper which further leads to a maximization problem on the induced likelihood function regarding P(s,y|x). By utilizing the well-known EM and Adam optimization techniques, the labeling probability of any positive example P(s=1|y=1,x) as well as the classifier induced by P(y|x) can be acquired. Theoretically, we prove that the critical solution always exists, and is locally unique for linear model if some sufficient conditions are met. Moreover, we upper bound the generalization error for both linear logistic and non-linear network instantiations of our algorithm. Empirically, we compare our method with state-of-the-art instance-independent and instance-dependent PU algorithms on a wide range of synthetic, benchmark and real-world datasets, and the experimental results firmly demonstrate the advantage of the proposed method over the existing PU approaches.

This paper addresses the design of adaptive subspace matched filter (ASMF) detectors in the presence of a mismatch in the steering vector. These detectors are coined as adaptive in reference to the step of utilizing an estimate of the clutter covariance matrix using training data of signal-free observations. To estimate the clutter covariance matrix, we employ regularized covariance estimators that, by construction, force the eigenvalues of the covariance estimates to be greater than a positive scalar $\rho $ . While this feature is likely to increase the bias of the covariance estimate, it presents the advantage of improving its conditioning, thus making the regularization suitable for handling high-dimensional regimes. In this paper, we consider the setting of the regularization parameter and the threshold for ASMF detectors in both Gaussian and compound Gaussian clutters. In order to allow for a proper selection of these parameters, it is essential to analyze the false alarm and detection probabilities. For tractability, such a task is carried out under the asymptotic regime in which the number of observations and their dimensions grow simultaneously large, thereby allowing us to leverage existing results from random matrix theory. Simulation results are provided in order to illustrate the relevance of the proposed design strategy and to compare the performances of the proposed ASMF detectors versus adaptive normalized matched filter (ANMF) detectors under mismatch scenarios.

Atanassov (Intuitionistic fuzzy set, Fuzzy Sets and Systems 20 (1986) 87–96) proposed the intuitionistic fuzzy set (A-IFS) that is a generalization of Zadeh's fuzzy set. The essential elements of an A-IFS are intuitionistic fuzzy values (IFVs), each of which is depicted by a membership degree and a non-membership degree. The existing literature only gives the explanation of the meaning and the aggregation operators of IFVs, which is very hard and non-visualized for us to comprehend. To overcome the above shortcomings, this paper puts forward the diagram method to analyze the structures of the basic aggregation operations of IFVs. In addition, this paper utilizes the diagram method which is similar to joint probability distribution to describe the components of aggregation operations of IFVs, and each IFV depicts a 3-dimensional vector which is regarded as the marginal distributions of the joint probability distribution.

This paper proposes a computationally efficient optimization algorithm for segmenting colour satellite images.CS algorithm incorporating Mantegna's and McCulloch's method for modeling levy flight is presented.PSO, DPSO, ABC and CS algorithms are compared with the proposed algorithm.All these optimization algorithms are exploited using three different objective functions.Performance assessment metrics demonstrated the improvement in the efficiency of the proposed algorithm. Satellite image segmentation is challenging due to the presence of weakly correlated and ambiguous multiple regions of interest. Several bio-inspired algorithms were developed to generate optimum threshold values for segmenting such images efficiently. Their exhaustive search nature makes them computationally expensive when extended to multilevel thresholding. In this paper, we propose a computationally efficient image segmentation algorithm, called CSMcCulloch, incorporating McCulloch's method for l e ? v y flight generation in Cuckoo Search (CS) algorithm. We have also investigated the impact of Mantegna's method for l e ? v y flight generation in CS algorithm (CSMantegna) by comparing it with the conventional CS algorithm which uses the simplified version of the same. CSMantegna algorithm resulted in improved segmentation quality with an expense of computational time. The performance of the proposed CSMcCulloch algorithm is compared with other bio-inspired algorithms such as Particle Swarm Optimization (PSO) algorithm, Darwinian Particle Swarm Optimization (DPSO) algorithm, Artificial Bee Colony (ABC) algorithm, Cuckoo Search (CS) algorithm and CSMantegna algorithm using Otsu's method, Kapur entropy and Tsallis entropy as objective functions. Experimental results were validated by measuring PSNR, MSE, FSIM and CPU running time for all the cases investigated. The proposed CSMcCulloch algorithm evolved to be most promising, and computationally efficient for segmenting satellite images. Convergence rate analysis also reveals that the proposed algorithm outperforms others in attaining stable global optimum thresholds. The experiments results encourages related researches in computer vision, remote sensing and image processing applications.

International audience; Multiple measurements using various data acquisition systems are generally required to substancially enhance measurement accuracy , reliability and holisticity of freeform shapes. The obtained multiple measurement data of the shape are transformed and fused into a common coordinate system within a registration technique involving coarse and fine alignments. Standardized methods have been established for fine registration such as Iterative Closest Points (ICP) and its variants. For coarse registration , no conventional method has been adopted yet despite a significant number of techniques which have been developed in the literature to supply an automatic rough matching between data sets. The work presented in this paper proposes an improvement of registration techniques by the consideration of new discrete curvature parameters. Two main issues are addressed in this paper : the coarse registration and the fine registration. For coarse registration , two novel automated methods based on the exploitation of discrete curvatures are presented : an enhanced Hough Transformation (HT) and an improved Ransac Transformation. The use of curvature features in both methods aims to reduce computational cost. For fine registration , a new variant of ICP method is proposed in order to reduce registration error using curvature parameters. A specific distance considering the curvature similarity is combined with Euclidean distance to define the distance criterion used for correspondences searching. Additionally , the objective function is improved by combining the point-to-point (P-P) minimization and the point-to-plane (P-Pl) minimization with automatic weights. The algorithms are applied on simulated and real data performed by a computed tomography (CT) system. The obtained results reveal the benefit of the proposed improved curvature-based registration methods .-2

This paper addresses the problem of joint detection, tracking and classification (JDTC) of multiple maneuvering targets in clutter. The multiple model cardinality balanced multi-target multi-Bernoulli (MM-CBMeMBer) filter is a promising algorithm for tracking an unknown and time-varying number of multiple maneuvering targets by utilizing a fixed set of models to match the possible motions of targets, while it exploits only the kinematic information. In this paper, the MM-CBMeMBer filter is extended to incorporate the class information and the class-dependent kinematic model sets. By following the rules of Bayesian theory and Random Finite Set (RFS), the extended multi-Bernoulli distribution is propagated recursively through prediction and update. The Sequential Monte Carlo (SMC) method is adopted to implement the proposed filter. At last, the performance of the proposed filter is examined via simulations.

In data stream clustering studies, majority of methods are traditional hard clustering, the literatures of fuzzy clustering in clustering are few. In this paper, the fuzzy clustering algorithm is used to research data stream clustering, and the clustering results can truly reflect the actual relationship between objects and classes. It overcomes the either-or shortcoming of hard clustering. This paper presents a new method to detect concept drift. The membership degree of fuzzy clustering is used to calculate the information entropy of data, and according to the entropy to detect concept drift. The experimental results show that the detection of concept drift based on the entropy theory is effective and sensitive.

Due to the huge computation complexity of Dezert–Smarandache Theory (DSmT), its applications especially for multi-source (more than two sources) complex fusion problems have been limited. To get high similar approximate reasoning results with Proportional Conflict Redistribution 6 (PCR6) rule in DSmT framework (DSmT +PCR6) and remain less computation complexity, an Evidence Clustering DSmT approximate reasoning method for more than two sources is proposed. Firstly, the focal elements of multi evidences are clustered to two sets by their mass assignments respectively. Secondly, the convex approximate fusion results are obtained by the new DSmT approximate formula for more than two sources. Thirdly, the final approximate fusion results by the method in this paper are obtained by the normalization step. Analysis of computation complexity show that the method in this paper cost much less computation complexity than DSmT +PCR6. The simulation experiments show that the method in this paper can get very similar approximate fusion results and need much less computing time than DSmT +PCR6, especially, when the numbers of sources and focal elements are large, the superiorities of the method are remarkable.

Discrete fractional Fourier transform (DFrFT) is a powerful signal processing tool. This paper proposes a method for DFrFT-based image retrieval via Fisher discriminant and 1-NN classification rule. First, this paper proposes to extend the conventional discrete Fourier transform (DFT) descriptors to the DFrFT descriptors to be used for representing the edges of images. The DFrFT descriptors extracted from the training images are employed to construct a dictionary, for which the corresponding optimal rotational angles of the DFrFTs are required to be determined. This dictionary design problem is formulated as an optimization problem, where the Fisher discriminant is the objective function to be minimized. This optimization problem is nonconvex (Guan et al. in IEEE Trans Image Process 20(7):2030---2048, 2011; Ho et al. in IEEE Trans Signal Process 58(8):4436---4441, 2010). Furthermore, both the intraclass separation and interclass separation of the DFrFT descriptors are independent of the rotational angles if these separations are defined in terms of the 2-norm operator. To tackle these difficulties, the 1-norm operator is employed. However, this reformulated optimization problem is nonsmooth. To solve this problem, the nondifferentiable points of the objective function are found. Then, the stationary points between any two consecutive nondifferentiable points are identified. The objective function values are evaluated at these nondifferentiable points and these stationary points. The smallest L objective function values are picked up and the corresponding rotational angles are determined, which are then used to construct the dictionary. Here, L is the total number of the rotational angles of the DFrFTs used to construct the dictionary. Finally, an 1-NN classification rule is applied to perform the image retrieval. Application examples and experimental results show that our proposed method outperforms the conventional DFT approach.

The paper introduces the multi-level interval-valued fuzzy concept lattices in an interval-valued fuzzy formal context. It introduces the notion of multi-level attribute reductions in an interval-valued fuzzy formal context and investigates related properties. In addition, the paper formulates a corresponding attribute reduction method by constructing a discernibility matrix and its associated Boolean function. The paper also proposes the multi-level granule representation in interval-valued fuzzy formal contexts.

The support vector ordinal regression (SVOR) method is derived from support vector machine and developed to tackle the ordinal regression problems. However, it ignores the distribution characteristics of the data. In this paper, we propose a novel method to handle the ordinal regression problems. This method is referred to as minimum class variance support vector ordinal regression (MCVSVOR). In contrast with SVOR, MCVSVOR explicitly takes into account the distribution of the categories and achieves better generalization performance. Moreover, the problem of MCVSVOR can be transformed into one of SVOR. Thus, the existing software of SVOR can be used to solve the problem of MCVSVOR. In the paper, we first discuss the linear case of MCVSVOR and then develop the nonlinear MCVSVOR through using the kernelization trick. The comprehensive experiment results show that the proposed method is effective and can achieve better generalization performance in contrast with SVOR.

This paper considers parameter identification problems for multivariable Hammerstein controlled autoregressive moving average (CARMA) systems. We transform a multivariable Hammerstein CARMA system into a new identification model which contains a set of bilinear parameter vectors, i.e., two sets of parameter vectors. To solve the difficulty of estimating the two sets of parameter vectors, this paper constructs two different forms of the identification model in each of which the output is linear about one set of parameter vectors, and presents an extended stochastic gradient algorithm to interactively estimate the two sets of parameter vectors by using the hierarchical identification principle. The proposed hierarchical identification algorithm has a higher computational efficiency than the over-parametrization model based stochastic gradient algorithm. The simulation results indicate that the proposed algorithm is effective, and an example of modeling a photovoltaic array system with the multivariable Hammerstein model is given.

This paper introduces a new scheme for encrypting images with few details based on wavelet fusion..The fusion is a pre-processing step to change the homogeneity of flat areas in the images having a few details. RC6 or chaotic Baker map encryption are then performed on the fused image.Encryption with chaotic Baker map is just a permutation algorithm that cannot perform well on flat areas of the images, because the permutation yields approximately the same intensities. So, circular shifts on pixels are performed on the fused image prior to chaotic encryption to remove flat areas or reduce the degree of homogeneity.The robustness of the suggested image ciphering schemes is tested in the presence of noise before decryption. Simulation results demonstrated that the suggested image ciphering schemes provide a secure and effective way for encrypting images with few details. This paper introduces a new scheme for encrypting images with a few details based on wavelet fusion. In this scheme, the image with a few details to be encrypted is fused with another image that is rich in details utilizing the Discrete Wavelet Transform (DWT) prior to encryption. The fusion is a pre-processing step to change the homogeneity of flat areas in the images having a few details. RC6 or chaotic Baker map encryption are then performed on the fused image. Encryption with chaotic Baker map is just a permutation algorithm that cannot perform well on flat areas of the images, because the permutation yields approximately the same intensities. So, circular shifts on pixels are performed on the fused image prior to chaotic encryption to remove flat areas or reduce the degree of homogeneity. Chaotic encryption is then performed in the wavelet domain to increase the degree of diffusion. Several metrics are used in this paper for performance evaluation of the suggested ciphering schemes like visual inspection, histogram test, encryption quality analysis, and diffusion analysis. The robustness of the suggested image ciphering schemes is tested in the presence of noise before decryption. Simulation results demonstrated that the suggested image ciphering schemes provide a secure and effective way for encrypting images with few details.

One of the key issues in removing random-valued impulse noise from digital images using switching filters is the impulse noise detection. Impulse noise is a random, spiked variation in the brightness of the image. In this paper, a new impulse noise detection algorithm is presented that is based on Noise ratio Estimation and a combination of K-means clustering and Non-Local Means based filter (NEK-NLM). Luo-statistic is employed as a non-local means based estimator. The novelty of this work lies in the introduction of a pre-processing step of noise ratio estimation before noise detection, this estimation allows us to select suitable parameters for the noise detection algorithm. In noise filtering stage, nonlocal-means estimator is applied for restoring noisy pixels to their actual values. Using real world datasets, this paper shows that the impulse noise can be removed effectively. Extensive comparison of simulation results with the already published results show that the proposed method outperforms most of the existing impulse noise removal techniques both in terms of noise detection and image restoration.

This paper is to critically examines Pollock's critical-link semantics with variable degrees of justification. Some possibly counterintuitive consequences of Pollock's definition of degrees of justification are identified and a modified definition is proposed which avoids these consequences. Then the new solution is applied to the case of so-called presumptive defeat. A second contribution of the paper is to show how the modified semantics can be applied to the ASPIC(+) framework: first the ASPIC(+) framework is modified to allow for variable degrees of justification and then the modified way to compute these degrees is applied in a new notion of an argument graph.

This paper addresses the issue of estimating the parameters of nonlinear models using heteroscedastic data. A weighted least squares problem formulation where the sum of the Mahalanobis distance for all measurements is minimized, forms the framework of this paper. Determining the Mahalanobis distance requires the gradient of the cost function with respect to the noisy measurements which can be computationally expensive and infeasible for model which are discontinuous. A derivative free approach to determine the Mahalanobis distance as an error metric is proposed using the Unscented Transformation. The advantages of using the proposed approach include: a black box approach to evaluate the gradient weighted objective function precluding the need for analytical gradients and an improved estimation of the covariance. Numerical results for various applications such as triangulation using radar measurements, ellipse, and super ellipse fitting demonstrate the benefits of the proposed approach. Heteroscedastic data resulting from real X-ray images are also used to illustrate the potential of the proposed approach. HighlightsDerivative free approach of solving gradient weighted least squares problems.Improved approximation of the geometric distance for curve fitting.Improved performance of proposed technique demonstrated on three benchmarks.Monte Carlo used to benchmark the reduction in bias in estimated parameters.Relevant to model fitting problems with heteroscedastic data.

The paper presents approximate inversion of fuzzy model with parametrized consequences.The method inverts an existing model.The method uses Ridders algorithm.The paper formulates a theorem for quicker inversion. Fuzzy models are known for their ability of precise data approximation. They can be used in automatic control as controllers. One of the techniques is based on inversion of fuzzy models. Fuzzy models can be inverted exactly or approximately. The exact inversion requires special features of fuzzy models. The approximate methods can be applied to a wider class of fuzzy models. The paper presents an approximate inversion of a fuzzy model with parametrized consequences. This fuzzy model cannot be inverted exactly. The presented approach inverts an existing fuzzy model with respect to any input. The inversion procedure uses the Ridders algorithm. The inversion is fast and does not require a separate training for each inverse input. The convergence of this approach is faster than linear. The paper formulates a theorem that shortens a search interval and may help to accelerate an inversion. The paper is accompanied by numerical examples.

Accurate ore grade estimation is crucial to mineral resources evaluation and exploration. In this paper, we consider the borehole data collected from the Solwara 1 deposit, where the hydrothermal sulfide ore body is quite complicated with incomplete ore grade values. To solve this estimation problem, the relevance vector machine (RVM) and the expected squared distance (ESD) algorithm are incorporated into one regression model. Moreover, we improve the ESD algorithm by weighting the attributes of the data set and propose the weighted expected squared distance (WESD). In this paper, we uncover the symbiosis characteristics among different elements of the deposits by statistical analysis, which leads to estimating certain metal based on the data of other elements instead of on geographical position. The proposed WESD-RVM features high sparsity and accuracy, as well as the capability of handling incomplete data. Effectiveness of the proposed model is demonstrated by comparing with other estimating algorithms, such as inverse distance weighted method and Kriging algorithm which utilize only geographical spatial coordinates for inputs; extreme learning machine, which is unable to deal with incomplete data; and ordinary ESD based RVM regression model without entropy weighted distance. The experimental results show that the proposed WESD-RVM outperforms other methods with considerable predictive and generalizing ability.