Algebraic Curve Fitting Support Vector Machines

An algebraic curve is defined as the zero set of a multivariate polynomial. We consider the problem of fitting an algebraic curve to a set of vectors given an additional set of vectors labelled as interior or exterior to the curve. The problem of fitting a linear curve in this way is shown to lend itself to a support vector representation, allowing non-linear curves and high dimensional surfaces to be estimated using kernel functions. The approach is attractive due to the stability of solutions obtained, the range of functional forms made possible (including polynomials), and the potential for applying well understood regularisation operators from the theory of Support Vector Machines. 1 Motivation Algebraic curves provide a powerful basis for a range of geometrical analysis problems, including shape recognition and non-iterative shape registration, largely due to the capacity for deriving geometric invariants [5, 3, 6]. Geometric invariants are those properties of an algebraic curv...

• Type: Conference
• Year: 2003
• Where: DICTA
• Authors: Christian J. Walder, Brian C. Lovell, Peter J. Kootsookos
• Keywords: Algebraic Curve, DICTA 2003, DICTA 2007, Linear Curve, Support Vector