Modeling by Fitting a Union of Polynomial Functions to Data in an Errors-in-Variables Context

We present a model construction method based on a local fitting of polynomial functions to noisy data and building the entire model as a union of regions explained by such polynomial functions. Local fitting is shown to reduce to solving a polynomial eigenvalue problem where the matrix coefficients are data covariance and approximated noise covariance matrices that capture distortion effects by noise. By defining the asymmetric distance between two points as the projection of one onto the function fitted to the neighborhood of the other, we use a best weighted cut method to find a proper partitioning of the entire set of data into feasible regions. Finally, the partitions are refined using a modified version of a k-planes algorithm.