Search results for "Linear reconstruction"
showing 2 items of 2 documents
Multiresolution based on weighted averages of the hat function I: Linear reconstruction techniques
1998
In this paper we analyze a particular example of the general framework developed in [A. Harten, {\it SIAM J. Numer. Anal}., 33 (1996) pp. 1205--1256], the case in which the discretization operator is obtained by taking local averages with respect to the hat function. We consider a class of reconstruction procedures which are appropriate for this multiresolution setting and describe the associated prediction operators that allow us to climb up the ladder from coarse to finer levels of resolution. In Part I we use data-independent (linear) reconstruction techniques as our approximation tool. We show how to obtain multiresolution transforms in bounded domains and analyze their stability with r…
On using prototype reduction schemes to optimize locally linear reconstruction methods
2012
Authors version of an article published in the journal: Pattern Recognition. Also available from the publisher at: http://dx.doi.org/10.1016/j.patcog.2011.06.021 This paper concerns the use of prototype reduction schemes (PRS) to optimize the computations involved in typical k-nearest neighbor (k-NN) rules. These rules have been successfully used for decades in statistical pattern recognition (PR) [1,15] applications and are particularly effective for density estimation, classification, and regression because of the known error bounds that they possess. For a given data point of unknown identity, the k-NN possesses the phenomenon that it combines the information about the samples from a pri…