Gaussian Process Models of Spatial Aggregation Algorithms

Multi-level spatial aggregates are important for data mining in a variety of scientific and engineering applications, from analysis of weather data (aggregating temperature and pressure data into ridges and fronts) to performance analysis of wireless systems (aggregating simulation results into configuration space regions exhibiting particular performance characteristics). In many of these applications, data collection is expensive and time consuming, so effort must be focused on gathering samples at locations that will be most important for the analysis. This requires that we be able to functionally model a data mining algorithm in order to assess the impact of potential samples on the mining of suitable spatial aggregates. This paper describes a novel Gaussian process approach to modeling multi-layer spatial aggregation algorithms, and demonstrates the ability of the resulting models to capture the essential underlying qualitative behaviors of the algorithms. By helping cast classical spatial aggregation algorithms in a rigorous quantitative framework, the Gaussian process models support diverse uses such as directed sampling, characterizing the sensitivity of a mining algorithm to particular parameters, and understanding how variations in input data fields percolate up through a spatial aggregation hierarchy.