Data Fitting Based On Clustering Algorithm

As an important method of data processing,data fitting is widely used in many fields such as engineering,medicine,statistics and so on.When choose the appropriate fitting method,the precision will be higher.The traditional fitting method is the least square method,which is based on the sum of squares of deviations.After that,a linear system is established and then solved.However,when faced with complex shape or a large amount of data in the actual process,the processing of data is often non-linear which is not so simple to solve the problem of linear equations.Then,when the experimental data or sampling data points are numerous,sometimes there are outliers,thus affecting the curve and surface fitting precision.The pretreatment of outliers is also the first problem to improve the accuracy of curve and surface fitting.In the above two main issues,this paper has done the following work:Firstly,the least squares curve and surface fitting analysis is carried out for non-linear data by using R language.As multivariate linear model in statistics,the polynomial model is established.Then,the coefficient estimation value is obtained.By calculating the coefficient of determination,the errors of the curve and surface fitting by different polynomials is compared.Secondly,the principle of the moving least square method,the weight function and the compact supported domain are described in detail.By plotting the curve and surface fitting graph,the moving least squares fitting is compared with the least squares fitting.Through two concrete examples,the influence of weight function with different degree on the fitting and the influence of the linear basis function and the quadratic basis function on the fitting are compared.Finally,as the fitting data points could be very large and the outlier easily took place in curve and surface fitting,statistical clustering algorithm was proposed for outlier detection and pretreatment of nodal data.After that,the moving least square method(MLS)was utilized for the curve and surface fitting.In this paper,clustering algorithm is applied to the method of moving least by using R language.Through some examples,we pretreat the data by outlier detection,then fitting the data.It is proved that the method of outlier detection is feasibile by comparing the maximum absolute error,minimum absolute error and mean square error for the both fitting cases.