Bezier functions, which are Bezier curves constrained to behave like functions, are excellent for representing smooth and continuous function of high degree, over the entire range of the independent variable. They provide excellent solutions to systems of linear, nonlinear, ordinary and partial differential equations. In this paper we examine their usefulness for data approximation as a prelude to their use in solving the inverse problem. Bezier function and B-splines, which are related, have mostly been used in geometrical modeling. There are not many examples of their use in data analysis. In this paper, organized and unorganized data are used to illustrate the effectiveness of Bezier functions for data approximation, reduction, mining, transformation, and prediction. Two criteria are used for the overall data fitting process. A simple incremental strategy identifies the order of the function using the minimum of the sum of the absolute error over all data. For a given order of the function, the least squared error over all data identifies the Bezier function through a non iterative algebraic relation. The entire data can then be represented by the coefficients of the Bezier function. Alternately, the data can also be reduced to a polynomial based on a parameter varying between 0 and 1. The Bezier function is global over all of the data so that all data points, including interpolated data, have the same properties. Three important properties are explicit is using Bezier functions for data analysis. The mean of the original data and the approximate data are the same. Large orders of polynomials can be used without local distortion. The independent and dependent variables can be decoupled by the Bezier representation. The data fitting process can also filter noisy data to recover principal data behavior.

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