روندزدایی در آمار فضایی با استفاده از رگرسیون بردار پشتیبان

مدل‌بندی و برآوردی کارا از تابع روند در برآورد تغییرنگار و پیش‌گویی داده‌های فضایی از اهمیت بالایی برخوردار است. در این مقاله برای مدل‌بندی تابع روند از روش رگرسیون بردار پشتیبان استفاده شده است. سپس داده‌ها روندزدایی شده و برآورد تغییرنگار و پیش‌گویی انجام می‌شود. بر روی یک مجموعه داده واقعی، نتایج پیش‌گویی حاصل از روش پیشنهادی با روش پیش‌گویی اسپلاین و کریگیدن از طریق اعتبارسنجی متقابل مقایسه شده است. کمینه بودن ریشه دوم میانگین توان‌های دوم خطا  معیار انتخاب روش مناسب پیش‌گویی است. نتایج پیش‌گویی برای چند موقعیت با مقادیر معلوم که بنا به دلایلی از مجموعه داده‌ها کنار گذاشته شده‌اند و برای موقعیت‌های جدید به‌دست آمده‌اند. نتایج بیانگر دقت بالای پیش‌گویی با روش پیشنهادی  نسبت به کریگیدن و اسپلاین است.

trend removal in spatial statistics using support vector regression

stationarity is one of the conditions that must be investigated in the exploratory analysis of spatial data. the existence of a trend in the data is a reason for non-stationarity. as a result، the estimator of the variogram is biased and the prediction will not be accurate enough. until now، various methods have been proposed to remove the trend، including simple linear combination، median polishing، first order difference، etc. in economics، simple linear regression and first differences are the two most popular trendremoval methods. support vector machine (svm) is a supervised learningalgorithm that can be used for both classification and regression problems.support vector regression (svr) is a type of svm used for regression analysis.the goal of svr is to find a function that approximates the relationshipbetween the input variables and a continuous target variable while minimizingthe prediction error. svr can be an effective tool in spatial dataanalysis. in recent years، the use of svr in spatial data analysis has becomewidespread. the purpose of this study is to investigate the detrending ofdata using the svr method and its effect on prediction.material and methodsfirst، the trend in spatial data is tried to be modeled using the svr method.if the relationship between the input variables and the target variable iscomplicated so that a linear model is not suitable for fitting the data، thena nonlinear mapping can be used to transfer the input space to a space withhigher dimensions، then a linear model can be fitted to the data in this spacewith the help of the kernel function. residuals are obtained by removingthe trend from the data. then، a suitable variogram model is fitted to the residuals، and prediction is made based on the universal kriging method. finally،the trend is estimated by the svr method and added to the predictionvalue. in the following، on a real data set، the results of the proposed methodare compared with spline and universal kriging prediction methods throughcross-validation. the minimization of the root-mean-square error (rmse)is considered the criterion for choosing the appropriate forecasting method.the geor and e1071 packages in r software were used for analysis.results and discussionkent and mohammadzadeh (2000) compared the smooth spline as a detrendingmethod and its prediction results on the calcium data (oliveira، 2003)set with the prediction results of the universal kriging method. for this dataset، the trend in the data was modeled by svr and through three kernels:linear، polynomial and gaussian. the results of this study showed that theproposed method has a higher accuracy than the two universal kriging andspline methods. among the applied kernels، the results of the gaussian kernelwere better. the results of this research show that svr can be a suitabletool in spatial data analysis.