On Desirable Properties of Example-based Interpolation
【摘要】：正Example-Based Interpolation (EBI) is a powerful method to interpolate function from a set of inputoutput examples. One particular EBI scheme uses Basis Function (BF) over every given example input to model the influence of that example to any arbitrary input. Under this scheme, a weight would be assigned to each example, and the interpolation function would be, for any arbitrary input, the weighted sum of the BF outputs of all the given examples at the input.The function interpolation problem boils down to the design of the weights, one for each example. One particular solution under this interpolating framework has each of these weights expressible as the sum of two terms: a BF term, and a polynomial term. In this paper, we argue that there are three desirable properties the weights so designed should be satisfied, and show two features of the above particular solution with respect to these properties. First, with the polynomial term in its simple form, i.e., being linear, the scheme already has enough degrees of freedom to satisfy all three desirable properties. Second, under the linear form of the polynomial term, the specific least-squares-error solution with respect to the inputs of the given examples does allow all the three desirable properties to be satisfied exactly.