A Derivation of the Algebraic Curve for Multi-dimensional Data using the Least-squares Distance

We propose a method for finding the algebraic curve that fits multi-dimensional data. An algebraic curve in n dimensional space is generally defined by n-1 polynomial expressions. The proposed method finds the n-1 polynomial expressions of the algebraic curve for n dimensional data. The sum of the squares' distances from the data point to the nearest point on the curve is minimum.