Accession Number : ADA272660


Title :   Measure Fields for Function Approximation


Descriptive Note : Memo rept.,


Corporate Author : MASSACHUSETTS INST OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB


Personal Author(s) : Marroquin, Jose L


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a272660.pdf


Report Date : Jun 1993


Pagination or Media Count : 22


Abstract : The computation of a piecewise smooth function that approximates a finite set of data points may be decomposed into two decoupled tasks: first, the computation of the locally smooth models, and hence, the segmentation of the data into classes that consist on the sets of points best approximated by each model, and second, the computation of the normalized discriminant functions for each induced class (which may be interpreted as relative probabilities). The approximating function may then be computed as the optimal estimator with respect to this measure field. For the first step, we propose a scheme that involves both robust regression and spatial localization using Gaussian windows. The discriminant functions are obtained by fitting Gaussian mixture models for the data distribution in the boundary of each class. We give an efficient procedure for effecting both computations, and for the determination of the optimal number of components. Examples of the application of this scheme to image filtering, surface reconstruction and time series prediction are presented as well.


Descriptors :   *STATISTICAL DATA , *APPROXIMATION(MATHEMATICS) , *ARTIFICIAL INTELLIGENCE , *DISTRIBUTION FUNCTIONS , NEURAL NETS , COMPUTATIONS , ALGEBRA , TIME , IMAGES , DETERMINATION , FILTRATION , CLASSIFICATION , WINDOWS , BOUNDARIES , SURFACES , MIXTURES , PREDICTIONS , MODELS


Subject Categories : Statistics and Probability
      Cybernetics


Distribution Statement : APPROVED FOR PUBLIC RELEASE