SciCombinator

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Concept: Kriging

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Spatial interpolation method is the basis of soil heavy metal pollution assessment and remediation. The existing evaluation index for interpolation accuracy did not combine with actual situation. The selection of interpolation methods needs to be based on specific research purposes and research object characteristics. In this paper, As pollution in soils of Beijing was taken as an example. The prediction accuracy of ordinary kriging (OK) and inverse distance weighted (IDW) were evaluated based on the cross validation results and spatial distribution characteristics of influencing factors. The results showed that, under the condition of specific spatial correlation, the cross validation results of OK and IDW for every soil point and the prediction accuracy of spatial distribution trend are similar. But the prediction accuracy of OK for the maximum and minimum is less than IDW, while the number of high pollution areas identified by OK are less than IDW. It is difficult to identify the high pollution areas fully by OK, which shows that the smoothing effect of OK is obvious. In addition, with increasing of the spatial correlation of As concentration, the cross validation error of OK and IDW decreases, and the high pollution area identified by OK is approaching the result of IDW, which can identify the high pollution areas more comprehensively. However, because the semivariogram constructed by OK interpolation method is more subjective and requires larger number of soil samples, IDW is more suitable for spatial prediction of heavy metal pollution in soils.

Concepts: Regression analysis, Evaluation, Maxima and minima, Heavy metal music, Interpolation, Kriging, Multivariate interpolation, Geostatistics

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A spike train kernel provides an effective way of decoding information represented by a spike train. Some spike train kernels have been extended to multineuron spike trains, which are simultaneously recorded spike trains obtained from multiple neurons. However, most of these multineuron extensions were carried out in a kernel-specific manner. In this paper, a general framework is proposed for extending any single-neuron spike train kernel to multineuron spike trains, based on the R-convolution kernel. Special subclasses of the proposed R-convolution linear combination kernel are explored. These subclasses have a smaller number of parameters and make optimization tractable when the size of data is limited. The proposed kernel was evaluated using Gaussian process regression for multineuron spike trains recorded from an animal brain. It was compared with the sum kernel and the population Spikernel, which are existing ways of decoding multineuron spike trains using kernels. The results showed that the proposed approach performs better than these kernels and also other commonly used neural decoding methods.

Concepts: Nervous system, Neuron, Brain, Vector space, Linear algebra, Interpolation, Kriging

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Gaussian process regression (GPR) provides a means to generate flexible personalized models of time series of patient vital signs. These models can perform useful clinical inference in ways that population-based models cannot. A challenge for the use of personalized models is that they must be amenable to a wide range of parameterizations, to accommodate the plausible physiology of any patient in the population. Additionally, optimal performance is typically achieved when models are regularized in light of the knowledge of the physiology of the individual patient. In this paper, we describe a method to build GP models with varying complexity (via covariance kernels) and regularization (via fixed priors over hyperparameters) on a patient-specific level, for the purpose of robust vital-sign forecasting. To this end, our results present evidence in support of two main hypotheses: 1) the use of patient-specific models can outperform population-based models for useful clinical tasks, such as vital-sign forecasting; and 2) the optimal values of (hyper)parameters of these models are best determined by sophisticated methods of optimization, due to high correlation between dimensions of the search space. The resulting models are sufficiently robust to inform clinicians of a patient’s vital-sign trajectory and warn of imminent deterioration.

Concepts: Regression analysis, Vital signs, Statistical inference, Optimization, Optimal control, Interpolation, Kriging, Gaussian process

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A comparative study was made of three methods of interpolation - inverse distance weighting (IDW), spline and ordinary kriging - after optimization of their characteristic parameters. These interpolation methods were used to represent the electric field levels for three emission frequencies (774kHz, 900kHz, and 1107kHz) and for the electrical stimulation quotient, QE, characteristic of complex electromagnetic environments. Measurements were made with a spectrum analyser in a village in the vicinity of medium-wave radio broadcasting antennas. The accuracy of the models was quantified by comparing their predictions with levels measured at the control points not used to generate the models. The results showed that optimizing the characteristic parameters of each interpolation method allows any of them to be used. However, the best results in terms of the regression coefficient between each model’s predictions and the actual control point field measurements were for the IDW method.

Concepts: Regression analysis, Mathematics, Radio, Curve fitting, Interpolation, Kriging, Multivariate interpolation, AM broadcasting

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The appropriate spatial interpolation methods must be selected to analyze the spatial distributions of Potentially Toxic Elements (PTEs), which is a precondition for evaluating PTE pollution. The accuracy and effect of different spatial interpolation methods, which include inverse distance weighting interpolation (IDW) (power = 1, 2, 3), radial basis function interpolation (RBF) (basis function: thin-plate spline (TPS), spline with tension (ST), completely regularized spline (CRS), multiquadric (MQ) and inverse multiquadric (IMQ)) and ordinary kriging interpolation (OK) (semivariogram model: spherical, exponential, gaussian and linear), were compared using 166 unevenly distributed soil PTE samples (As, Pb, Cu and Zn) in the Suxian District, Chenzhou City, Hunan Province as the study subject. The reasons for the accuracy differences of the interpolation methods and the uncertainties of the interpolation results are discussed, then several suggestions for improving the interpolation accuracy are proposed, and the direction of pollution control is determined. The results of this study are as follows: (i) RBF-ST and OK (exponential) are the optimal interpolation methods for As and Cu, and the optimal interpolation method for Pb and Zn is RBF-IMQ. (ii) The interpolation uncertainty is positively correlated with the PTE concentration, and higher uncertainties are primarily distributed around mines, which is related to the strong spatial variability of PTE concentrations caused by human interference. (iii) The interpolation accuracy can be improved by increasing the sample size around the mines, introducing auxiliary variables in the case of incomplete sampling and adopting the partition prediction method. (iv) It is necessary to strengthen the prevention and control of As and Pb pollution, particularly in the central and northern areas. The results of this study can provide an effective reference for the optimization of interpolation methods and parameters for unevenly distributed soil PTE data in mining areas.

Concepts: Interpolation, Hunan, Kriging, Multivariate interpolation, Geostatistics, Radial basis function, Chenzhou, Variogram

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This paper considers two important problems for autonomous robot navigation in a dynamic environment, where the goal is to predict pedestrian motion and control a robot with the prediction for safe navigation. While there are several methods for predicting the motion of a pedestrian and controlling a robot to avoid incoming pedestrians, it is still difficult to safely navigate in a dynamic environment due to challenges, such as the varying quality and complexity of training data with unwanted noises. This paper addresses these challenges simultaneously by proposing a robust kernel subspace learning algorithm based on the recent advances in nuclear-norm and l 1 -norm minimization. We model the motion of a pedestrian and the robot controller using Gaussian processes. The proposed method efficiently approximates a kernel matrix used in Gaussian process regression by learning low-rank structured matrix (with symmetric positive semi-definiteness) to find an orthogonal basis, which eliminates the effects of erroneous and inconsistent data. Based on structured kernel subspace learning, we propose a robust motion model and motion controller for safe navigation in dynamic environments. We evaluate the proposed robust kernel learning in various tasks, including regression, motion prediction, and motion control problems, and demonstrate that the proposed learning-based systems are robust against outliers and outperform existing regression and navigation methods.

Concepts: Scientific method, Regression analysis, Prediction, Control theory, Machine learning, Normal distribution, Interpolation, Kriging

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Received Signal Strength Indicator (RSSI) localization using fingerprint has become a prevailing approach for indoor localization. However, the fingerprint-collecting work is repetitive and time-consuming. After the original fingerprint radio map is built, it is laborious to upgrade the radio map. In this paper, we describe a Fingerprint Renovation System (FRS) based on crowdsourcing, which avoids the use of manual labour to obtain the up-to-date fingerprint status. Extended Kalman Filter (EKF) and Gaussian Process Regression (GPR) in FRS are combined to calculate the current state based on the original fingerprinting radio map. In this system, a method of subset acquisition also makes an immediate impression to reduce the huge computation caused by too many reference points (RPs). Meanwhile, adjusted cosine similarity (ACS) is employed in the online phase to solve the issue of outliers produced by cosine similarity. Both experiments and analytical simulation in a real Wireless Fidelity (Wi-Fi) environment indicate the usefulness of our system to significant performance improvements. The results show that FRS improves the accuracy by 19.6% in the surveyed area compared to the radio map un-renovated. Moreover, the proposed subset algorithm can bring less computation.

Concepts: Signal processing, Normal distribution, Kalman filter, Bluetooth, Filtering problem, Interpolation, Kriging, Wi-Fi

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To genetically analyse growth traits in genetically improved farmed tilapia (GIFT), the body weight (BWE) and main morphological traits, including body length (BL), body depth (BD), body width (BWI), head length (HL) and length of the caudal peduncle (CPL), were measured six times in growth duration on 1451 fish from 45 mixed families of full and half sibs. A random regression model (RRM) was used to model genetic changes of the growth traits with days of age and estimate the heritability for any growth point and genetic correlations between pairwise growth points. Using the covariance function based on optimal RRMs, the heritabilities were estimated to be from 0.102 to 0.662 for BWE, 0.157 to 0.591 for BL, 0.047 to 0.621 for BD, 0.018 to 0.577 for BWI, 0.075 to 0.597 for HL and 0.032 to 0.610 for CPL between 60 and 140 days of age. All genetic correlations exceeded 0.5 between pairwise growth points. Moreover, the traits at initial days of age showed less correlation with those at later days of age. With phenotypes observed repeatedly, the model choice showed that the optimal RRMs could more precisely predict breeding values at a specific growth time than repeatability models or multiple trait animal models, which enhanced the efficiency of selection for the BWE and main morphological traits.

Concepts: Regression analysis, Genetics, Evolution, Statistics, Prediction, Prediction interval, Oreochromis, Kriging

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The aim of this study was to investigate how to improve predictions from Gaussian Process models by optimising the model hyperparameters.

Concepts: Regression analysis, Statistical terminology, Business process modeling, Interpolation, Kriging

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Soil heavy metals exhibit significant spatiotemporal variability and are strongly correlated with other soil heavy metals. Thus, other heavy metals can be used to improve the accuracy of predictions when performing spatiotemporal predictions of soil heavy metals within a given area. In this study, we propose the spatiotemporal cokriging (STCK) method to enable the use of historical sampling points and co-variables in the spatial prediction of soil heavy metals. Moreover, experimental spatiotemporal (ST) semivariogram and ST cross-semivariogram computational methods, a fitting strategy to the ST semivariogram and ST cross-semivariogram models based on the Bilonick model, and the STCK interpolation algorithm are introduced; these methods are based on spatiotemporal kriging (STK) and cokriging (CK). The data used in this study consist of measurements of soil heavy metals from 2010 to 2014 in Wuhan City, China. The results show that the behavior of predictions of the concentrations of heavy metals in soils is physically more realistic, and the prediction uncertainties are slightly smaller, when STCK is used with greater numbers of co-variables and neighboring points.

Concepts: Scientific method, Regression analysis, Model, Heavy metal music, Tungsten, Wuhan, Kriging