Generalized Cross Validation Research Articles

An adaptive parameter-free seismic data denoising approach by combining general cross-validation thresholding and pixel connectivity in synchrosqueezed domain

High signal-to-noise ratio (SNR) seismic waveform data are conductive to various studies in seismology. Seismic denoising aims to enhance SNR by eliminating additive noise through signal processing while preserving important features of the seismic signal. Conventional parametric seismic denoising methods often require selecting appropriate parameters to achieve optimal results, which may be limiting when dealing with various types and scales of seismic data. Here, we develop an adaptive parameter-free denoising method by combining general cross-validation (GCV) thresholding and pixel connectivity in synchrosqueezed (SS) domain. In this denoising framework, the synchrosqueezed continuous wavelet transform (SS-CWT) is first applied to obtain a high-resolution time–frequency representation. Then, the GCV approach, which allows for choosing the (nearly) optimal threshold without relying on any prior knowledge about the noise level, is employed to attenuate most of the low-energy noise. After that, the relatively isolated high-energy residual noise remaining in the SS-CWT spectrum is removed using pixel connectivity thresholding. Finally, the inverse SS-CWT is applied to the thresholded spectrum to obtain the denoised seismic record. As the thresholds for GCV and pixel connectivity are derived from the spectrum characteristics of the data being analyzed, the proposed denoising approach is highly adaptive and parameter-free. We demonstrate the effectiveness and versatility of the proposed denoising framework using synthetic data and real seismic data from diverse monitoring scenarios, including land, ocean, and emerging distributed acoustic sensing (DAS). The results indicate that the method is a stable and efficient tool for seismic data denoising.Graphical

Association Between Climatic Factors and Varicella Incidence in Wuxi, East China, 2010-2019: Surveillance Study.

Varicella is a common infectious disease and a growing public health concern in China, with increasing outbreaks in Wuxi. Analyzing the correlation between climate factors and varicella incidence in Wuxi is crucial for guiding public health prevention efforts. This study examines the impact of meteorological variables on varicella incidence in Wuxi, eastern China, from 2010 to 2019, offering insights for public health interventions. We collected daily meteorological data and varicella case records from January 1, 2010, to December 31, 2019, in Wuxi, China. Generalized cross-validation identified optimal lag days by selecting those with the lowest score. The relationship between meteorological factors and varicella incidence was analyzed using Poisson generalized additive models and segmented linear regression. Subgroup analyses were conducted by gender and age. The study encompassed 64,086 varicella cases. Varicella incidence in Wuxi city displayed a bimodal annual pattern, with peak occurrences from November to January of the following year and lower peaks from May to June. Several meteorological factors influencing varicella risk were identified. A decrease of 1°C when temperatures were ≤20°C corresponded to a 1.99% increase in varicella risk (95% CI 1.57-2.42, P<.001). Additionally, a decrease of 1°C below 22.38°C in ground temperature was associated with a 1.36% increase in varicella risk (95% CI 0.96-1.75, P<.001). Each 1 mm increase in precipitation above 4.88 mm was associated with a 1.62% increase in varicella incidence (95% CI 0.93-2.30, P<.001). A 1% rise in relative humidity above 57.18% increased varicella risk by 2.05% (95% CI 1.26-2.84, P<.001). An increase in air pressure of 1 hPa below 1011.277 hPa was associated with a 1.75% rise in varicella risk (95% CI 0.75-2.77, P<.001). As wind speed and evaporation increased, varicella risk decreased linearly with a 16-day lag. Varicella risk was higher with sunshine durations exceeding 1.825 hours, with a 14-day lag, increasing by 1.30% for each additional hour of sunshine (95% CI 0.62-2.00, P=.006). Subgroup analyses revealed that teenagers and children under 17 years of age faced higher varicella risks associated with temperature, average ground temperature, precipitation, relative humidity, and air pressure. Adults aged 18-64 years experienced increased risk with longer sunshine durations. Additionally, males showed higher varicella risks related to ground temperature and air pressure compared with females. However, no significant gender differences were observed regarding varicella risks associated with temperature (male: P<.001; female P<.001), precipitation (male: P=.001; female: P=.06), and sunshine duration (male: P=.53; female: P=.04). Our preliminary findings highlight the interplay between varicella outbreaks in Wuxi city and meteorological factors. These insights provide valuable support for developing policies aimed at reducing varicella risks through informed public health measures.

Evaluation of the Performance of Kernel Non-parametric Regression and Ordinary Least Squares Regression

Researchers need to understand the differences between parametric and nonparametric regression models and how they work with available information about the relationship between response and explanatory variables and the distribution of random errors. This paper proposes a new nonparametric regression function for the kernel and employs it with the Nadaraya-Watson kernel estimator method and the Gaussian kernel function. The proposed kernel function (AMS) is then compared to the Gaussian kernel and the traditional parametric method, the ordinary least squares method (OLS). The objective of this study is to examine the effectiveness of nonparametric regression and identify the best-performing model when employing the Nadaraya-Watson kernel estimator method with the proposed kernel function (AMS), the Gaussian kernel, and the ordinary least squares (OLS) method. Additionally, it determines which method yields the most accurate results when analyzing nonparametric regression models and provides valuable insights for practitioners looking to apply these techniques in real-world scenarios. However, criteria such as generalized cross-validation (GCV), mean square error (MSE), and coefficient determination are used to select the most efficient estimated model. Simulated data was used to evaluate the performance and efficiency of estimators using different sample sizes. The results favorable the simulation illustrate that the Nadaraya-Watson kernel estimator using the proposed kernel function (AMS) exhibited favorable and superior performance compared to other methods. The coefficients of determination indicate that the highest values attained were 98%, 99%, and 99%. The proposed function (AMS) yielded the lowest MSE and GCV values across all samples. Therefore, this suggests that the model can generate precise predictions and enhance the performance of the focused data.

Corrected generalized cross-validation for finite ensembles of penalized estimators

Abstract Generalized cross-validation (GCV) is a widely used method for estimating the squared out-of-sample prediction risk that employs scalar degrees of freedom adjustment (in a multiplicative sense) to the squared training error. In this paper, we examine the consistency of GCV for estimating the prediction risk of arbitrary ensembles of penalized least-squares estimators. We show that GCV is inconsistent for any finite ensemble of size greater than one. Towards repairing this shortcoming, we identify a correction that involves an additional scalar correction (in an additive sense) based on degrees of freedom adjusted training errors from each ensemble component. The proposed estimator (termed CGCV) maintains the computational advantages of GCV and requires neither sample splitting, model refitting, or out-of-bag risk estimation. The estimator stems from a finer inspection of the ensemble risk decomposition and two intermediate risk estimators for the components in this decomposition. We provide a non-asymptotic analysis of the CGCV and the two intermediate risk estimators for ensembles of convex penalized estimators under Gaussian features and a linear response model. Furthermore, in the special case of ridge regression, we extend the analysis to general feature and response distributions using random matrix theory, which establishes model-free uniform consistency of CGCV.

Escalation of Human Resource Quality in National Health Resilience Through Estimating Multilevel Model Parameters with the Restricted Maximum Likelihood Approach to The 2019 UTBK Average

Multilevel modeling or Hierarchical Linear Modeling (HLM) is a statistical approach specifically used to analyze data with a two-level structure. This approach allows an understanding of the contribution of factors at both the individual and group levels to the response variable. One method commonly used in HLM is Restricted Maximum Likelihood (REML). REML is a parameter estimation method that is often applied in statistical models, especially linear models that incorporate random components. This allows more efficient parameter assessment compared to conventional estimation methods. In this research, multilevel model parameter estimation analysis was carried out using the limited maximum likelihood approach. The aim is to determine the multilevel linear regression model on the average UTBK score for health cluster study programs in 2019. This involves selecting the optimal node point based on the minimum Generalized Cross Validation (GCV) and identifying the factors that influence it. Predictor variables considered include interest and capacity of study programs at university level (Level-1), as well as the average UNBK and HDI scores at provincial level (Level-2). The findings of this research indicate that the most appropriate multilevel regression model is formed with three nodes with a minimum GCV value at Level-1 of 864.6593 and at Level-2 of 3.1816. At Level-1, the influencing factor is the interest variable and at Level-2 is the average provincial UNBK score in 2019 and the Human Development Index (HDI).

MODELING DHF IN CENTRAL JAVA USING HYBRID NONPARAMETRIC SPLINE TRUNCATED-FOURIER SERIES APPROACH

Regression analysis aims to determine the relationship and influence of predictor variables on response variables through regression curve. The problem with nonparametric regression research so far is that it only uses one approach, causing the estimation results to be biased, even though each data sub-pattern has its own suitability depending on the approach method used. Therefore, the hybrid method emerged as a development of nonparametric regression. Hybrid models are models that combine approach methods, with the hope of increasing accuracy in modeling analysis. This research was carried out using two non-parametric approaches, namely Spline Truncated and Fourier Series. Dengue Hemorrhagic Fever (DHF) is a disease caused by the dengue virus. DHF is endemic and occurs throughout the year, especially during the rainy season because mosquitoes reproduce optimally. The aim of this research is to estimate the Hybrid Nonparametric Spline Truncated -Fourier Series model and apply the estimation results to data on DHF cases in Central Java. The data used to apply the hybrid nonparametric Spline Truncated-Fourier series regression model is DHF in the city/districts of Central Java. Estimation smoothing parameters uses the GCV (Generalized Cross Validation) method. The best model is selected based on largest R-Square and the smallest MSE. Modeling the disease of DHF cases in Central Java using the Spline Truncated-Fourier Series hybrid estimator produced the best model from the Spline Truncated model with two knot points for each predictor and the Fourier Series model with value of 9. Based on the results obtained, it can be compared that the Truncated Spline-Fourier Series hybrid model is better than the Spline Truncated model, this can be seen from the largest R-square, namely 99.94% and the smallest MSE.

Selection of optimal knot point and best geographic weighted on geographically weighted spline nonparametric regression model

This study proposes the development of a nonparametric regression model combined with geographically weighted regression. The regression model considers geographical factors and has a data pattern that does not follow a parametric form to overcome the problem of spatial heterogeneity and unknown regression functions. This study aims to model provincial food security index data in Indonesia with the GWSNR model, so finding the optimal knot point and the best geographic weighting is necessary. We propose the selection of optimal knot points using the Cross Validation (CV) and Generalized Cross Validation (GCV) methods. The optimal knot point will control the accuracy of the regression curve as we also consider the MSE value in showing the ability of the model. In addition, we determine the best geographic weighting and test the significance of the model parameters. We demonstrate the GWSNR model on food security index data. The best GWSNR model uses the Gaussian kernel weighting function and selects the optimal knot point as one-knot point based on the lowest CV and GCV values. Simultaneous and partial parameter test results show that there are 10 area classifications with different effects on each group of classification results. Some of the highlights of the proposed approach are:•The method is the development of a nonparametric regression model with geographic weighting, which combines nonparametric and spatial regression in modeling the national food security index.•There are three-knot points tested in nonparametric truncated spline regression and three geographic weightings in spatial regression. Then the optimal knot point and best bandwidth are determined using Cross Validation and Generalized Cross Validation.•This article will determine regional groupings in Indonesia in 2022 based on significant predictors in modeling the national food security index numbers.

Stunting Prevalence Modeling Using Nonparametric Regression of Quadratic Splines

The nonparametric regression approach is used when the shape of the regression curve between the response variable and the predictor variable is assumed to be of unknown shape. The advantages of nonparametric regression have high flexibility. A nonparametric regression approach that is often used is truncated spline which has an excellent ability to handle data whose behavior changes at certain sub-sub intervals. The purpose of this study is to obtain the best model of multivariable nonparametric regression with linear and quadratic truncated spline approaches using the Generalized Cross Validation (GCV) and Unbiased Risk (UBR) methods and to find out the factors that influence the prevalence of stunting in Indonesia in 2021. The data used were the prevalence of stunting as a response variable and the predictor variable used was the percentage of infants receiving exclusive breastfeeding for 6 months, the percentage of households that have proper sanitation, the percentage of toddlers who get Early Initiation of Breastfeeding (IMD), the percentage of poor people, and the percentage of pregnant women at risk of SEZ. The results showed that the best quadratic truncated spline nonparametric regression model in modeling stunting prevalence was quadraic truncated spline using the GCV method with three knot points. This model has a minimum GCV value of 7.29 with an MSE value of 1.82 and a R2 value of 94.07%.

Modeling of Economic Growth Rate in West Nusa Tenggara Province with Longitudinal Kernel Nonparametric Regression

Economic growth can indicate the success of economic development in people's lives, so it is essential to study the relationship between economic growth and factors that affect economic growth. Regression analysis is one of the most widely used statistical data analysis methods to determine the relationship pattern between the independent and dependent variables. Three methods can be used to estimate the regression curve, one of which is nonparametric regression. Economic growth data is one form of longitudinal data, with observations of independent subjects, with each subject being observed repeatedly over different periods. Kernel nonparametric regression model applications can be used for longitudinal data. This research aims to estimate the curve and get the best regression model. In this research, the smoothing technique chosen to estimate the nonparametric regression model for longitudinal data is the kernel triangle estimator, which can be obtained by minimizing the square of error using Weighted Least Squares (WLS) and selecting the optimum bandwidth using the Generalized Cross Validation (GCV) method. This study uses the economic growth rate in West Nusa Tenggara as the dependent variable and the human development index, population density, general allocation funds, local revenue, and labor force participation as independent variables. The result showed that the model is less accurate because of the low value of the coefficient for determination and the high value of the mean absolute percentage error (MAPE). This can be caused by the selection of bandwidth intervals that are too small.

MODELLING CRIME RATES IN INDONESIA USING TRUNCATED SPLINE ESTIMATOR

Criminal acts are actions that violate the law and can arise from various factors such as emotions, psychological pressure, and others. Crime rate is a number that indicate the level of crime vulnerability in a certain area at a certain time. Higher crime rates correspond to increased vulnerability in an area, and vice versa. Among various forms of criminal acts, the number of criminal acts and narcotics crimes in Indonesia tends to increase in 2020 and 2021. The aim of the research is to identify the characteristics of crime rate data based on the number of decency and narcotics incidents in Indonesia using a nonparametric regression approach. This research uses a nonparametric regression method spline truncated and linear regression as comparison. It was found that West Papua Province has the highest crime rate, based on a comparison between linear regression model and truncated spline nonparametric regression model, it can be concluded that the best model is the truncated spline nonparametric regression model with a Generalized Cross Validation (GCV) of 2468.487 and a coefficient of determination of 0 .7389091, indicating that approximately 73% of the variability of the dependent variable can be explained by the independent variables included in the model.

APPLICATION OF NONPARAMETRIC REGRESSION SPLINE TRUNCATED FOR MODELING THE HEIGHT OF YEOP CHAGI KICKS OF TAEKWONDO ATHLETES IN SAMARINDA CITY

Nonparametric regression is a model approach method that is used when the shape of the regression curve between the response variable and the predictor variable is assumed to have an unknown shape or pattern. One of the estimators in the nonparametric regression approach is the truncated spline which has the ability to handle data whose behavior changes at certain sub intervals. The purpose of this study was to obtain the estimated value of the parameters of the nonparametric regression model with a truncated spline approach at one knot point, two knot points, and three knot points for kick height data of yeop chagi taekwondo athletes in Samarinda City. The results showed that the truncated spline nonparametric regression model was the best in modeling high kick height data for yeop chagi taekwondo athletes in Samarinda City with three knot points. This model has the minimum Generalized Cross Validation (GCV) value of 7.94 with an R2 value of 94.72% and a Mean Square Error (MSE) value of 2.62. Based on the results of the model parameter significance test, it was concluded that the factors that influence the kick height of the yeop chagi taekwondo athlete in Samarinda City are flexibility, leg power, leg length, and waist circumference.

Estimation curve of multivariate adaptive biresponse fuzzy clustering means regression splines approach to stunting and wasting cases in Southeast Sulawesi

This article offers a new method of clustering data. This method is constructed by combining the multivariate adaptive regression spline biresponse continuous model (MARSBC) with the fuzzy clustering means (FCM) approach, called the multivariate adaptive biresponse fuzzy clustering means regression splines (MABFCMRS) model. This method uses patterns obtained from the MARSBC model to separate data into specific groups. Observing unobserved heterogeneity that has not been obtained from previous models. Unlike the classic fuzzy clustering methods that use euclid distances to determine the weight of the object, this method uses the total square of the massed residual distance generated by the MARSBC model. Theoretical studies were conducted to obtain predictions for the MABFCMRS model parameters. Furthermore, this method was applied to stunting and wasting cases in southeastern Sulawesi province. The results of the research show that in the case of stunting modeling and wasting in southeast Sulawesi province, the best clusters were obtained based on the criteria of partition coefficient (PC) and modification of PC (MPC). This research is able to show that the clustering process using the MABFCMRS model has been able to improve generalized cross-validation (GCV) values and determination coefficients.•This paper presents a new, effective method for clustering data based on unobserved heterogeneity.•This is applicable to sizable samples with 3 to 20 predictors.

High-Dimensional Multivariate Linear Regression with Weighted Nuclear Norm Regularization

We consider a low-rank matrix estimation problem when the data is assumed to be generated from the multivariate linear regression model. To induce the low-rank coefficient matrix, we employ the weighted nuclear norm (WNN) penalty defined as the weighted sum of the singular values of the matrix. The weights are set in a nondecreasing order, which yields the non-convexity of the WNN objective function in the parameter space. Although the objective function has been widely applied, studies on the estimation properties of its resulting estimator are limited. We propose an efficient algorithm under the framework of the alternative directional method of multipliers (ADMM) to estimate the coefficient matrix. The estimator from the suggested algorithm converges to a stationary point of an augmented Lagrangian function. Under the orthogonal design setting, the effects of the weights for estimating the singular values of the ground-truth coefficient matrix are derived. Under the Gaussian design setting, a minimax convergence rate on the estimation error is derived. We also propose a generalized cross-validation (GCV) criterion for selecting the tuning parameter and an iterative algorithm for updating the weights. Simulations and a real data analysis demonstrate the competitive performance of our new method. Supplementary materials for this article are available online.

The performance of mixed truncated spline-local linear nonparametric regression model for longitudinal data

A mixed estimator nonparametric regression (MENR) model is an additive model that involves a combination of two estimators or more in multivariable nonparametric regression. The model is used when there are differences in data patterns among predictor variables. This study proposes the development of the MENR model on longitudinal data namely a mixed truncated spline-local linear nonparametric regression (MTSLLNR) model. A modified weighted least square (WLS) method through two-stage estimation is used to estimate the regression function in the proposed model. To illustrate the performance of the MTSLLNR model, a simulation study with a sample size variation of subjects and time points is provided. Additionally, the MTSLLNR model is also applied to model the poverty gap index data. Both simulated and real data results suggest that the proposed model has consistency findings and good performance in longitudinal data modeling. Some highlights of the proposed method are:•The method combines two estimators of local linear and truncated spline to accommodate the differences in data patterns in the nonparametric regression for longitudinal data.•Selection of optimal knots and bandwidth using the generalized cross-validation (GCV) method.•The consistency findings and general performance of the method is shown by simulation and real data application.

Wavelet denoising based on comprehensive index optimization and improved L2 regularization for load identification

Load identification, as an inverse problem, is still one of the challenges in the field of vibration engineering. In this paper, a comprehensive load identification method combining entropy weight Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) noise reduction evaluation algorithm and improved L2 regularization method is proposed to improve the load identification accuracy from the following two perspectives. Firstly, the entropy weight TOPSIS method is used to evaluate the wavelet denoising scheme comprehensively, and the optimal denoising scheme is found to reduce the noise interference in the process of inverse problem solving. Secondly, we introduce a new regularization filter function, and search for the regularization parameters by Generalized Cross-Validation (GCV) criterion and one-dimensional optimization algorithm to improve the ill-posedness of the inverse problem. Finally, the simulation and experimental verification of single-source load identification are carried out with the scaled crankcase model, while the accuracy is compared with the Tikhonov regularization method. The results show that the integrated algorithm proposed in this paper can improve the accuracy of load identification while overcoming the inadequacy of inverse problem. Unlike previous studies, the comprehensive evaluation method of denoising effect introduced in this paper provides a way to judge the denoising effect in practical engineering, and the experimental model is closer to practical engineering structures, which shows potential engineering application value.

MODELING OPEN UNEMPLOYMENT RATE IN KALIMANTAN ISLAND USING NONPARAMETRIC REGRESSION WITH FOURIER SERIES ESTIMATOR

Nonparametric regression is a regression approach that is used to determine the relationship between the response variable and the predictor variable if the shape of the regression curve is unknown. One of the popular estimators used in nonparametric regression is the Fourier series estimator. Fourier series nonparametric regression is generally used when the pattern of the investigated data is unknown and there is a tendency for the pattern to repeat. The purpose of this study is to estimate nonparametric regression using the Fourier series approach and to find out the factors that influence the open unemployment rate on the island of Borneo in 2021. The criteria for the goodness of the model used Generalized Cross Validation (GCV) and the coefficient of determination ( ). Based on the results, it was found that the best nonparametric regression model for the Fourier series was the model with 5 oscillations which indicated a minimum GCV of 10.47 and an of 74.22%. Furthermore, based on the results of parameter significance testing either simultaneously or partially, it shows that all predictor variables have a significant effect on the open unemployment rate. The predictor variables include the labor force participation rate, the average length of schooling, the percentage of poor people, economic growth rate, and total population.

Nonparametric Additive Models for Billion Observations

The nonparametric additive model (NAM) is a widely used nonparametric regression method. Nevertheless, due to the high computational burden, classic statistical techniques for fitting NAMs are not well-equipped to handle massive data with billions of observations. To address this challenge, we develop a scalable element-wise subset selection method, referred to as Core-NAM, for fitting penalized regression spline based NAMs. Specifically, we first propose an approximation of the penalized least squares estimation, based on which we develop an efficient variant of generalized cross-validation (GCV) to select the smoothing parameter and approximate the Bayesian confidence intervals for statistical inference. Theoretically, we show that the proposed estimator approximately minimizes an upper bound of the estimation mean squared error. Moreover, we provide a non-asymptotic approximation guarantee for the proposed estimator and establish the asymptotic optimality of the proposed variant of GCV. Extensive simulations demonstrate the superior accuracy and efficiency of the Core-NAM method. We also apply the proposed method to a total column ozone dataset containing nearly one billion observations, and the results indicate a speed-up by almost a thousand times with comparable performance compared to the full data approach. Supplementary materials for this article are available online.

CROSS STYLE IMAGE SYNTHESIS THROUGH SEMI COUPLED DICTIONARY LEARNING AND GENERALIZED CROSS VALIDATION ALGORITHM

In various Computer vision applications for better visualization, interpretation and better recognition, we frequently want to change an image in one style into another one which is a large research area of compressive sensing. Algorithms on compressed sensing are in demand to create better reconstruction of the images while taking less computational time and requiring less storage capacity. In the present work attempts are put in the same direction and brought an algorithm which includes semi coupled dictionary learning (SCDL) model of compressed sensing with Singular Value Decomposition (SVD) based Generalized Cross Validation (GCV) algorithm. Using this algorithm one can find the different value of regularization parameters for different sizes of images and that helps to get better reconstruction of the images with ease while doing experiments on cross style image synthesis problems.

PEMODELAN REGRESI NONPARAMETRIK SPLINE TRUNCATED KASUS KEJADIAN DIARE DI PROVINSI BALI

Nonparametric regression is a flexible approach used to determine the relationship between the predictor variable and the response variable is unknown. One method that can be used to estimate nonparametric regression models is the truncated spline. The truncated spline is an effective method to estimate nonparametric regression models due to its ability to adapt to the data's characteristics through knots. Truncated spline estimates its parameters with the maximum likelihood estimator (MLE) method and finds the optimal knot points with the minimum generalized cross validation (GCV) value. This study used the truncated spline to model diarrhea cases in Bali Province, examining five variables that could affect incidence. The optimal knot points were 2-1-3-3-2 with a minimum GCV value of 67572,38. The study found that the number of clean drinking water facilities, food management places that meet health requirements, public places that meet health requirements, population density, and access to proper sanitation facilities had a significant effect on diarrhea incidence. The coefficient of determination for this model is 98,87%.

Application of Regularization Methods in the Sky Map Reconstruction of the Tianlai Cylinder Pathfinder Array

The Tianlai cylinder pathfinder is a radio interferometer array to test 21 cm intensity mapping techniques in the post-reionization era. It works in passive drift scan mode to survey the sky visible in the northern hemisphere. To deal with the large instantaneous field of view and the spherical sky, we decompose the drift scan data into m-modes, which are linearly related to the sky intensity. The sky map is reconstructed by solving the linear interferometer equations. Due to incomplete uv coverage of the interferometer baselines, this inverse problem is usually ill-posed, and regularization method is needed for its solution. In this paper, we use simulation to investigate two frequently used regularization methods, the Truncated Singular Value Decomposition (TSVD), and the Tikhonov regularization techniques. Choosing the regularization parameter is very important for its application. We employ the generalized cross validation method and the L-curve method to determine the optimal value. We compare the resulting maps obtained with the different regularization methods, and for the different parameters derived using the different criteria. While both methods can yield good maps for a range of regularization parameters, in the Tikhonov method the suppression of noisy modes are more gradually applied, produce more smooth maps which avoids some visual artefacts in the maps generated with the TSVD method.