A parallel finite element surface fitting algorithm for data mining

A major task in data mining is to develop automatic techniques to process and to detect patterns in very large data sets. Multivariate regression techniques form the core of many data mining applications. A common assumption is that the multivariate data is well approximated by an additive model involving only first and second order interaction terms. In this case high-dimensional nonparametric regression is reduced to the determination of a couple set of first and second order interaction terms, that is the determination of a coupled set of curves and surfaces. Thin plate splines provide a very good method to determine an approximating surface. Obtaining standard thin plate splines requires the solution of a dense linear system of equations of order n, where n is the number of observations. For data mining applications the number of observations is often in the millions, so standard thin plate splines may not be practical. We have developed a finite element approximation of a spline that can handle data sizes with millions of records. The resolution of the finite element method can independently be chosen from the number of observations. The observation data can be read from a secondary storage once, and does not need to be stored in memory. In this paper, we discuss the parallel implementation of this method in an MPI environment.