Algebraic curve and surface fitting to multidimensional data

We deal with a method of fitting an algebraic curve and surface to multidimensional data without an external criterion. It is often sensible to treat one of the variables as a response variable and the other as an explanatory variable in other words data with an external criterion. The linear regression line or regression curve minimizes the sum of squared derivations in the response variable. In many situations, we do not have a preferred variable that wish to label "response", but would like to summarize the relations of variables. The principal component line minimizes the sum of squared deviations in all of the variables. The PCA can not find nonlinear structures of the data. We present a new method for estimating the algebraic curve or surface that minimizes the sum of squares of perpendicular distances from multidimensional data.