Reconstructing Patterns from Sample Data

Abstract

Abstract : A Euclidean region is partitioned in an unknown way into a known number of subregions. For a discrete set of points in the region we may observe into which subregion they each fall. The problem is to obtain an estimated reconstruction of the partition based on the observations. Section 1 outlines a probabilistic approach to the problem and defines criteria of goodness for an estimated reconstruction. Section 2 evaluates the performance of nearest-point rules. Section 3 examines the effect of sample-size and compares several arrangements of the data points. Section 4 proposes a modification of nearest-point procedures having a certain optimality property. Section 5 is more or less independent of the earlier sections; it explores several probabilistic partitioning models. (Author)