A Fast k Nearest Neighbor Finding Algorithm Based on the Ordered Partition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multidimensional divide-and-conquer
Communications of the ACM
A new philosophy for model selection and performance estimation of data-based approximate mappings
Mathematical and Computer Modelling: An International Journal
| Hi-index | 0.98 |
We establish the mathematical basis for building the MC-HARP data-processing environment. The MC-HARP strategy determines the functional structure and parameters of a mathematical model simultaneously. A Monte Carlo (MC) strategy combined with the concept of Hierarchical Adaptive Random Partitioning (HARP) and fuzzy subdomains determines the multivariate parallel distributed mapping. The HARP algorithm is based on a divide-and-conquer strategy that partitions the input space into measurable connected subdomains and builds a local approximation for the mapping task. Fuzziness promotes continuity of the mapping constructed by HARP and smooths the mismatching of the local approximations in the neighboring subdomains. The Monte Carlo superposition of a sample of random partitions reduces the localized disturbances among the fuzzy subdomains, controls the global smoothness of the mean average mapping, and improves the generalization of the approximation. We illustrate the procedure by applying it to a two-dimensional surface fitting problem.