Spatial modeling is an integral component of most geographic information systems (GISs). However, conventional GIS modeling techniques can require substantial processing time and storage space and have limited statistical and machine learning functionality. To address these limitations, many have parallelized spatial models using multiple coding libraries and have applied those models in a multiprocessor environment. Few, however, have recognized the inefficiencies associated with the underlying spatial modeling framework used to implement such analyses. In this paper, we identify a common inefficiency in processing spatial models and demonstrate a novel approach to address it using lazy evaluation techniques. Furthermore, we introduce a new coding library that integrates Accord.NET and ALGLIB numeric libraries and uses lazy evaluation to facilitate a wide range of spatial, statistical, and machine learning procedures within a new GIS modeling framework called function modeling. Results from simulations show a 64.3% reduction in processing time and an 84.4% reduction in storage space attributable to function modeling. In an applied case study, this translated to a reduction in processing time from 2247 h to 488 h and a reduction is storage space from 152 terabytes to 913 gigabytes.

Discriminant analysis, referred to as maximum likelihood classification within popular remote sensing software packages, is a common supervised technique used by analysts. Polytomous logistic regression (PLR), also referred to as multinomial logistic regression, is an alternative classification approach that is less restrictive, more flexible, and easy to interpret. To assess the utility of PLR in image classification, we compared the results of 15 classifications using independent validation datasets, estimates of kappa and error, and a non-parametric analysis of variance derived from visually interpreted observations, Landsat Enhanced Thematic Mapper plus imagery, PLR, and traditional maximum likelihood classifications algorithms.