Examples of Compactly Supported Functions for Radial Basis Approximations
نویسندگان
چکیده
Radial Basis Functions (RBFs) are widely used in science, engineering and finance for constructing nonlinear models of observed data. Most applications employ activation functions from a relatively small list, including Gaussians, multi-quadrics and thin plate splines. We introduce several new candidate compactly supported RBFs for approximating functions in L (R) via overdetermined least squares. We illustrate their utility on the benchmark Mackey-Glass time series data. We observe that these new RBFs significantly reduce the number of modes required to approximate the data and produce models that have significantly improved condition numbers. Conference: The 2006 International Conference on Machine Learning; Models, Technologies and Applications (MLMTA’06)
منابع مشابه
Collocation Method using Compactly Supported Radial Basis Function for Solving Volterra's Population Model
In this paper, indirect collocation approach based on compactly supported radial basis function (CSRBF) is applied for solving Volterra's population model. The method reduces the solution of this problem to the solution of a system of algebraic equations. Volterra's model is a non-linear integro-differential equation where the integral term represents the effect of toxin. To solve the pr...
متن کاملReal-time 3D Deformations by Means of Compactly Supported Radial Basis Functions
We present an approach to real-time animation of deformable objects. Optimization of algorithms using compactly supported radial basis functions (CSRBF) allows us to generate deformations performed fast enough for such real-time applications as computer games. The algorithm described in detail in this paper uses space mapping technique. Smooth local deformations of animation objects can be defi...
متن کاملCompactly supported radial basis functions : how and why ? by Sheng - Xin
The use of radial basis functions have attracted increasing attention in recent years as an elegant scheme for high-dimensional scattered data approximation, an accepted method for machine learning, one of the foundations of mesh-free methods, an alternative way to construct higher order methods for solving partial differential equations (PDEs), an emerging method for solving PDEs on surfaces, ...
متن کاملConvergence Rates of Compactly Supported Radial Basis Function Regularization
Regularization with radial basis functions is an effective method in many machine learning applications. In recent years classes of radial basis functions with compact support have been proposed in the approximation theory literature and have become more and more popular due to their computational advantages. In this paper we study the statistical properties of the method of regularization with...
متن کاملA New Radial Function
In the field of radial basis functions mathematicians have been endeavouring to find infinitely differentiable and compactly supported radial functions. This kind of functions is extremely important. One of the reasons is that its error bound will converge very fast. However there is hitherto no such function which can be expressed in a simple form. This is a famous question. The purpose of thi...
متن کامل