Application of a kernel method with stably evaluated Gaussian kernel to problems on irregular domains

2021 ◽  
Author(s):  
Artur Krowiak ◽  
Renata Filipowska
Keyword(s):  
Kernel Method ◽  
Gaussian Kernel ◽  
Irregular Domains

Information structures and uncertainty in an image information system

2021 ◽  
Vol 40 (1) ◽  
pp. 295-317
Author(s):  
Gangqiang Zhang ◽  
Zhaowen Li ◽  
Pengfei Zhang ◽  
Ningxin Xie
Keyword(s):  
Information System ◽  
Kernel Method ◽  
Attribute Reduction ◽  
Gaussian Kernel ◽  
Information Structures ◽  
Image Information ◽  
Effectiveness Analysis ◽  
Uncertainty Measurement ◽  
Properties Of Information ◽  
Information Values

An information system as a database that stands for relationships between objects and attributes is an important mathematical model. An image information system is an information system where each of its information values is an image and its information structures embody internal features of this type of information system. Uncertainty measurement is an effective tool for evaluation. This paper explores measures of uncertainty for an information system by using the proposed information structures. The distance between two objects in an image information system is first given. After that, the fuzzy Tcos-equivalence relation, induced by this system by using Gaussian kernel method, is obtained, where Gaussian kernel is based on this distance. Next, information structures of this system are described by set vectors, dependence between information structures is studied and properties of information structures are given by using inclusion degree, and application for information structures and uncertainty measures of an image information system are investigated by the information structures. Moreover, effectiveness analysis is done to show the feasibility of the proposed measures from the angle of statistics. Finally, an application of the proposed measurement for attribute reduction is given. These results will be helpful for understanding the essence of uncertainty in an image information system.

Time Series Pattern Learning and Forecasting for Long-Term Peak Electricity by Spectral Mixture Gaussian Kernel

2015 ◽  
Vol 781 ◽  
pp. 245-249
Author(s):  
Tuchsanai Ploysuwan ◽  
Prasit Teekaput ◽  
Pramukpong Atsawathawichok
Keyword(s):  
Kernel Method ◽  
Gaussian Kernel ◽  
Percentage Error ◽  
Pattern Learning ◽  
The Past ◽  
Electricity Load ◽  
The Time Domain ◽  
Spectral Mixture ◽  
The Mathematical Model

This paper presents the mathematical model for forecasting of future long-term peak electricity load from January 2014 to December 2024 with totally 132 months from the past knowledge data of training 156 months. The new kernel method is proposed by the combination ofsummed weight spectral mixture Gaussian in the frequency domain and squared exponential in the time domain, which are used as components in the answer of Gaussian Process (GP). Finally, the results show the prediction error mean absolute percentage error (MAPE) by 2.3283%.

scholarly journals Bayesian multi-trait kernel methods improve multi-environment genome based prediction

2021 ◽  
Author(s):  
Osval Antonio Montesinos-López ◽  
José Cricelio Montesinos-López ◽  
Abelardo Montesinos-Lopez ◽  
Juan Manuel Ramírez-Alcaraz ◽  
Jesse Poland ◽  
...  
Keyword(s):  
Kernel Methods ◽  
Genomic Prediction ◽  
Linear Models ◽  
Kernel Method ◽  
Prediction Performance ◽  
Gaussian Kernel ◽  
Phenotypic Traits ◽  
Proposed Model ◽  
The Mean ◽  
Gaussian Polynomial

Abstract When multi-trait data are available, the preferred models are those that are able to account for correlations between phenotypic traits because when the degree of correlation is moderate or large, this increases the genomic prediction accuracy. For this reason, in this paper we explore Bayesian multi-trait kernel methods for genomic prediction and we illustrate the power of these models with three real datasets. The kernels under study were the linear, Gaussian, polynomial and sigmoid kernels; they were compared with the conventional Ridge regression and GBLUP multi-trait models. The results show that, in general, the Gaussian kernel method outperformed conventional Bayesian Ridge and GBLUP multi-trait linear models by 2.2 to 17.45% (datasets 1 to 3) in terms of prediction performance based on the mean square error of prediction. This improvement in terms of prediction performance of the Bayesian multi-trait kernel method can be attributed to the fact that the proposed model is able to capture non-linear patterns more efficiently than linear multi-trait models. However, not all kernels perform well in the datasets used for evaluation, which is why more than one kernel should be evaluated to be able to choose the best kernel.

On the use of Geostationary Lightning Mapper data as proxy for heavy precipitation

2020 ◽  
Author(s):  
Vandoir Bourscheidt ◽  
Maria-Helena Ramos
Keyword(s):  
Kernel Method ◽  
Heavy Precipitation ◽  
Comparison Method ◽  
Convective Precipitation ◽  
Gaussian Kernel ◽  
Climate Change Scenarios ◽  
Spatial And Temporal Scales ◽  
Extreme Precipitation Events ◽  
Precipitation Estimates ◽  
Total Lightning

<p>In view of the likely increase of thunderstorm and extreme precipitation events under climate change scenarios, alternatives to improve the estimates of rainfall and the understanding of the runoff response to extreme events are relevant, especially in areas with low or absent radar or raingauge coverage. Efforts in this direction have resulted, for example, on the Global Precipitation Measurement (GPM) products, which offer potentially useful estimates of precipitation over relatively fine spatial and temporal scales. With the launch of GOES 16 satellite, with its new Geostationary Lightning Mapper (GLM) instrument and improved visible and infrared imagery (with the Advanced Baseline Imager - ABI), new possibilities emerge in the analysis of (severe) convective precipitation and its impact on runoff. In this work, we analyze the relationship between lightning activity and rainfall, with the aim to estimate how total lightning data can be used as proxy of (heavy) precipitation estimates. GLM data is evaluated against weather radar in three different ways: (1) based on a Gaussian Kernel method; (2) using a simple dot-count approach, and (3) using the operational GLM gridded product, built on the ABI fixed grid (2 x 2 km). Two sample strategies are evaluated: a pixel-based comparison and a comparison method that extracts statistics inside polygons (using watersheds). For all cases, both group and flash data from GLM are used. The study area focuses on the southeastern and central-west regions of Brazil, where developments towards enhanced flood nowcasting and warning systems capabilities have been carried out in order to anticipate flash floods and prevent flood damages in the future.</p>

scholarly journals Solving biharmonic problems on irregular domains by stably evaluated Gaussian kernel

2020 ◽  
Vol 7 (1) ◽  
pp. 56-67
Author(s):  
Artur Krowiak
Keyword(s):  
Free Vibration ◽  
Shape Parameter ◽  
Cartesian Product ◽  
High Accuracy ◽  
Thin Plates ◽  
Gaussian Kernel ◽  
Irregular Domains ◽  
Numerical Tests ◽  
Interpolation Problems ◽  
Biharmonic Problems

AbstractThe paper extends recently developed idea of stable evaluation of the Gaussian kernel. Owing to this, the Gaussian radial basis function that is sensitive to the shape parameter can be stably evaluated and applied to interpolation problems as well as to solve differential equations, giving highly accurate results. But it can be done only with grids being the Cartesian product of sets of points, what limits the use of this idea to rectangular domains. In the present paper, by the association of an appropriate transformation with the mentioned method, the latter is applied to solve biharmonic problems on quadrilateral irregular domains. As an example, in the present work this approach is applied to solve bending as well as free vibration problem of thin plates. In the paper some strategies for the implementation of the boundary conditions are also presented and examined due to the accuracy. The numerical tests show high accuracy and usefulness of the method.

scholarly journals Measures of Uncertainty for an Incomplete Set-Valued Information System With the Optimal Selection of Subsystems: Gaussian Kernel Method

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 212022-212035
Author(s):  
Lijun Chen ◽  
Shimin Liao ◽  
Ningxin Xie ◽  
Zhaowen Li ◽  
Gangqiang Zhang ◽  
...  
Keyword(s):  
Information System ◽  
Kernel Method ◽  
Gaussian Kernel ◽  
Optimal Selection ◽  
Selection Of

scholarly journals ESTIMATING WATER LEVEL IN THE URMIA LAKE USING SATELLITE DATA: A MACHINE LEARNING APPROACH

2019 ◽  
Vol XLII-4/W18 ◽  
pp. 219-226
Author(s):  
M. Boueshagh ◽  
M. Hasanlou
Keyword(s):  
Water Level ◽  
Lake Water ◽  
Kernel Method ◽  
Urmia Lake ◽  
Gaussian Kernel ◽  
Support Vector ◽  
Substantial Impact ◽  
Lake Water Level ◽  
Global Environmental Issue ◽  
Rbf Kernel

Abstract. Lakes play a pivotal role in the development of cities and have major impacts on the ecosystem balancing of the area. Remote sensing techniques and advanced modeling methods make it possible to monitor natural phenomena, such as lakes’ water level. The ecosystem of Urmia Lake is one of the most momentous ecosystems in Iran, which is almost close-ended and has become a global environmental issue in recent years. One of the parameters affecting this lake water level is snowfall, which has a key role in the fluctuations of its water level and water resources management. Hence, the purpose of this paper is the Urmia Lake water level estimation during 2000–2006 using observed water level, snow cover, direct precipitation, and evaporation. For this purpose, Support Vector Regression (SVR), which is the most outstanding kernel method (with various kernel types), has been used. Furthermore, four scenarios are considered with different variables as inputs, and the output of all scenarios is the water level of the lake. The results of training and testing data indicate the substantial impact of snow on retrieving the water level of the Urmia Lake at the desired period, and due to the complexity of the data relationships, the Gaussian kernel generally had better results. On the other hand, Quadratic and Cubic kernels did not work well. The fourth scenario, with RBF kernel has the best results [Training: R2 = 97% and RMSE = 0.09 m, Testing: R2 = 96.97% and RMSE = 0.08 m].

scholarly journals Comparison of correlation analysis techniques for irregularly sampled time series

2011 ◽  
Vol 18 (3) ◽  
pp. 389-404 ◽  
Author(s):  
K. Rehfeld ◽  
N. Marwan ◽  
J. Heitzig ◽  
J. Kurths
Keyword(s):  
Time Series ◽  
Kernel Methods ◽  
Large Scale ◽  
Cross Correlation ◽  
Kernel Method ◽  
Linear Interpolation ◽  
Irregular Sampling ◽  
Gaussian Kernel ◽  
Robust Estimator ◽  
Mean Square Errors

Abstract. Geoscientific measurements often provide time series with irregular time sampling, requiring either data reconstruction (interpolation) or sophisticated methods to handle irregular sampling. We compare the linear interpolation technique and different approaches for analyzing the correlation functions and persistence of irregularly sampled time series, as Lomb-Scargle Fourier transformation and kernel-based methods. In a thorough benchmark test we investigate the performance of these techniques. All methods have comparable root mean square errors (RMSEs) for low skewness of the inter-observation time distribution. For high skewness, very irregular data, interpolation bias and RMSE increase strongly. We find a 40 % lower RMSE for the lag-1 autocorrelation function (ACF) for the Gaussian kernel method vs. the linear interpolation scheme,in the analysis of highly irregular time series. For the cross correlation function (CCF) the RMSE is then lower by 60 %. The application of the Lomb-Scargle technique gave results comparable to the kernel methods for the univariate, but poorer results in the bivariate case. Especially the high-frequency components of the signal, where classical methods show a strong bias in ACF and CCF magnitude, are preserved when using the kernel methods. We illustrate the performances of interpolation vs. Gaussian kernel method by applying both to paleo-data from four locations, reflecting late Holocene Asian monsoon variability as derived from speleothem δ18O measurements. Cross correlation results are similar for both methods, which we attribute to the long time scales of the common variability. The persistence time (memory) is strongly overestimated when using the standard, interpolation-based, approach. Hence, the Gaussian kernel is a reliable and more robust estimator with significant advantages compared to other techniques and suitable for large scale application to paleo-data.

Sign in / Sign up

Export Citation Format

Share Document