An Enhanced Squared Exponential Kernel With Manhattan Similarity Measure for High Dimensional Gaussian Process Models

The Gaussian Process (GP) model has become one of the most popular methods and exhibits superior performance among surrogate models in many engineering design applications. However, the standard Gaussian process model is not able to deal with high dimensional applications. The root of the problem comes from the similarity measurements of the GP model that relies on the Euclidean distance, which becomes uninformative in the high-dimensional cases, and causes accuracy and efficiency issues. Limited studies explore this issue. In this study, thereby, we propose an enhanced squared exponential kernel using Manhattan distance that is more effective at preserving the meaningfulness of proximity measures and preferred to be used in the GP model for high-dimensional cases. The experiments show that the proposed approach has obtained a superior performance in high-dimensional problems. Based on the analysis and experimental results of similarity metrics, a guide to choosing the desirable similarity measures which result in the most accurate and efficient results for the Kriging model with respect to different sample sizes and dimension levels is provided in this paper.

Complex mathematical SIR model for spreading of COVID-19 virus with Mittag-Leffler kernel

This paper investigates a new model on coronavirus-19 disease (COVID-19), that is complex fractional SIR epidemic model with a nonstandard nonlinear incidence rate and a recovery, where derivative operator with Mittag-Leffler kernel in the Caputo sense (ABC). The model has two equilibrium points when the basic reproduction number $R_{0} > 1$ R 0 > 1 ; a disease-free equilibrium $E_{0}$ E 0 and a disease endemic equilibrium $E_{1}$ E 1 . The disease-free equilibrium stage is locally and globally asymptotically stable when the basic reproduction number $R_{0} <1$ R 0 < 1 , we show that the endemic equilibrium state is locally asymptotically stable if $R_{0} > 1$ R 0 > 1 . We also prove the existence and uniqueness of the solution for the Atangana–Baleanu SIR model by using a fixed-point method. Since the Atangana–Baleanu fractional derivative gives better precise results to the derivative with exponential kernel because of having fractional order, hence, it is a generalized form of the derivative with exponential kernel. The numerical simulations are explored for various values of the fractional order. Finally, the effect of the ABC fractional-order derivative on suspected and infected individuals carefully is examined and compared with the real data.

Geographically Weighted Regression with Kernel Weighted Function on Poverty Cases in West Java Province

Spatial regression analysis is a form of regression model that considers spatial effects. Geographically weighted regression (GWR) is the spatial regression methods that can be used to deal with the problem of spatial diversity. This method generates local model parameter estimates for each observation location. The application of spatial statistics can be done in all areas such as the problem of poverty. Poverty can be influenced by factors of proximity between regions, so that in determining the poverty factor, the proximity factor of the region cannot be ignored. West Java Province is a province with the largest population, so this study aims to model the poverty data in West Java Province by incorporating spatial effects. The weighting function used for the GWR model is the function of the fixed and adaptive kernels. The analysis results show that the fixed exponential kernel function has the smallest cross validation (CV) value, so the weighting matrix used in the model is determined by the exponential kernel function. The largest value and the smallest AIC value are owned by the GWR model with an exponential kernel function. Based on the results obtained by the the ANOVA table to test GWR's global goodness, the GWR model is more effective than global regression. Therefore, the GWR model is the best model when it used in West Java’s poverty cases. The effect of each explanatory variable on the percentage of poverty varies in each district/city in West Java Province.

Gaussian Process Regression hyperparameter optimization for image time series gap-filling of Earth observation data and crop monitoring

&lt;p&gt;In general, modeling phenological evolution represents a challenging task mainly because of time series gaps and noisy data, coming from different viewing and illumination geometries, cloud cover, seasonal snow and the interval needed to revisit and acquire data for the exact same location. For that reason, the use of reliable gap-filling fitting functions and smoothing filters is frequently required for retrievals at the highest feasible accuracy. Of specific interest to filling gaps in time series is the emergence of machine learning regression algorithms (MLRAs) which can serve as fitting functions. Among the multiple MLRA approaches currently available, the kernel-based methods developed in a Bayesian framework deserve special attention because of both being adaptive and providing associated uncertainty estimates, such as Gaussian Process Regression (GPR).&lt;/p&gt;&lt;p&gt;Recent studies demonstrated the effectiveness of GPR for gap-filling of biophysical parameter time series because the hyperparameters can be optimally set for each time series (one for each pixel in the area) with a single optimization procedure. The entire procedure of learning a GPR model only relies on appropriate selection of the type of kernel and the hyperparameters involved in the estimation of input data covariance. Despite its clear strategic advantage, the most important shortcomings of this technique are the (1) high computational cost and (2) memory requirements of their training, which grows cubically and quadratically with the number of model&amp;#8217;s samples, respectively. This can become problematic in view of processing a large amount of data, such as in Sentinel-2 (S2) time series tiles. Hence, optimization strategies need to be developed on how to speed up the GPR processing while maintaining the superior performance in terms of accuracy.&lt;/p&gt;&lt;p&gt;To mitigate its computational burden and to address such shortcoming and repetitive procedure, we evaluated whether the GPR hyperparameters can be preoptimized over a reduced set of representative pixels and kept fixed over a more extended crop area. We used S2 LAI time series over an agricultural region in Castile and Leon (North-West Spain) and testing different functions for Covariance estimation such as exponential Kernel, Squared exponential kernel and matern kernel with parameter 3/2 or 5/2. The performance of image reconstructions was compared against the standard per-pixel GPR time series training process. Results showed that accuracies were on the same order (12% RMSE degradation) whereas processing time accelerated up to 90 times. Crop phenology indicators were also calculated and compared, revealing similar temporal patterns with differences in start and end of growing season of no more than five days. To the benefit of crop monitoring applications, all the gap-filling and phenology indicators retrieval techniques have been implemented into the &lt;strong&gt;freely downloadable GUI toolbox DATimeS&lt;/strong&gt; (Decomposition and Analysis of Time Series Software - https://artmotoolbox.com/).&lt;/p&gt;

PEMODELAN JUMLAH KASUS DEMAM BERDARAH DENGUE (DBD) DI JAWA TENGAH DENGAN GEOGRAPHICALLY WEIGHTED NEGATIVE BINOMIAL REGRESSION (GWNBR)

Dengue Hemorrhagic Fever (DHF) is one of the diseases with unsual occurrence in Central Java and spread throughout the regency/city. The number sufferers of this disease is still high because the mortality rate is still above the national target. Regarding the less handling of DHF spread, it is necessary to make a plan by identify the factors that allegedly affect that case. Characteristics of data the DHF cases is count data, so this research is carried out using poisson regression. If in poisson regression there is overdispersion, it can be overcome using negative binomial regression. Meanwhile to see the spatial effect, we can use the Geographically Weighted Negative Binomial Regression (GWNBR) method. GWNBR modeling uses a fixed exponential kernel for weighting function. GWNBR is better at modeling the number of DHF cases because it has the smallest AIC value than poisson regression and negative binomial regression. The results of research with poisson regression obtained three variables that have a significant effect on dengue cases. For negative binomial regression, two variables have a significant effect on DHF cases. While the GWNBR method obtained two groups of districts/cities based on significant variables. The variables affecting the number of DHF cases in all districts/cities in Central Java are the percentage of healthy houses, the percentage of clean water quality, and the ratio of medical personnel.Keywords: DHF, GWNBR, Poisson Regression, Binomial Negative Regression, Fixed Exponential Kernel

Analysis of a fractional tumor-immune interaction model with exponential kernel

In this paper, a tumor-immune interaction model has been analyzed via Caputo-Fabrizio fractional derivative operator with exponential kernel. Existence of solution of the model has been established with a fixed-point method and then it demonstrated the uniqueness of solution also. The stability of the model has been analyzed with the help of Hyers-Ulam stability approach and then numerical solution by using the Adam-Basford method. The results are further examined in detail with simulations for different fractional derivative values.