Parallel Goodness-of-Fit Testing for Spatial Process Models
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Solution Overview
Problem
Existing methods for testing the goodness-of-fit of spatial process models to spatial point datasets are resource-intensive, requiring the generation of large amounts of simulated data and consuming significant processing resources.
Innovation Solution
An apparatus and method that utilize a network of processors to perform a goodness-of-fit test by generating a KD tree from the observed spatial point dataset, dividing the region into quadrats, and distributing iterations of nearest neighbor processing across multiple execution threads, allowing for parallel processing and reduced resource consumption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional goodness-of-fit testing methods are used for spatial process models, then comprehensive model validation is achieved, but processing resource consumption increases significantly
Solution Approach 1:
The patent divides the spatial study region into multiple non-overlapping quadrats (spatial segments). Each processor handles a specific quadrat independently, computing nearest neighbor statistics only for points within that quadrat. This segmentation reduces the computational burden on each processor from O(n log n) to O(n/k log n), where k is the number of quadrats, thereby reducing overall processing resource consumption while maintaining validation accuracy through aggregation of results from all quadrats.
Solution Approach 2:
The patent introduces parallel processing across multiple processors and execution threads as an additional computational dimension. By distributing iterations of nearest neighbor processing across multiple execution threads of a single processor or across multiple processors, the system transforms a single-threaded sequential computation into a multi-threaded parallel computation, effectively reducing processing time and resource consumption while maintaining the same validation thoroughness.
2Measurement precision
If large amounts of simulated spatial point data are generated for goodness-of-fit testing, then model fit assessment accuracy is improved, but processing time increases
Solution Approach 1:
By segmenting the spatial region into quadrats and distributing simulated data generation and nearest neighbor processing across multiple processors handling different quadrats simultaneously, the patent reduces the total processing time. Each processor generates and processes simulated points for its assigned quadrat in parallel, maintaining the statistical accuracy required for goodness-of-fit assessment while significantly reducing the sequential processing time that would be required without parallelization.
Solution Approach 2:
The patent performs preliminary organization of observed spatial point data by constructing a KD-tree before the goodness-of-fit testing iterations begin. This preliminary action optimizes the data structure for efficient nearest neighbor queries, reducing the computational complexity of each iteration. By preparing the data structure in advance, subsequent iterations of simulated data generation and nearest neighbor processing can proceed more quickly, reducing overall processing time while maintaining assessment accuracy.
3Measurement precision
If nearest neighbor processing is performed on large spatial datasets, then accurate spatial pattern analysis is achieved, but computational complexity increases
Solution Approach 1:
The patent reduces computational complexity by dividing the spatial dataset into smaller subsets (quadrats) that can be processed independently by different processors. Instead of performing nearest neighbor searches across the entire dataset on a single processor, each processor performs searches only within its assigned quadrat, reducing the search space and computational complexity from O(n log n) to O(n/k log n) per processor, where k is the number of quadrats/processors.
Solution Approach 2:
The patent performs preliminary construction of a KD-tree data structure from the observed spatial point data before the iterative goodness-of-fit testing begins. This preliminary action organizes the spatial data in a way that optimizes nearest neighbor queries, reducing the computational complexity of each subsequent iteration. The KD-tree structure enables efficient spatial partitioning and search, reducing the complexity of nearest neighbor processing while maintaining accurate spatial pattern analysis.
Data Source
AI summary
An apparatus includes processor(s) to: receive a request to test goodness-of-fit of a spatial process model; generate a KD tree from observed spatial point dataset including locations within a region at which instances of an event occurred; derive, from the observed spatial point dataset, multiple quadrats into which the region is divided; receive, from multiple processors, current levels of availability of processing resources including quantities of currently available execution threads; select, based on the quantity of currently available execution threads, a subset of the multiple processors to perform multiple iterations of a portion of the test in parallel; provide, to each processor of the subset, the KD tree, the spatial process model, and the multiple quadrats; receive, from each processor of the subset, per-quadrat data portions indicative of results of an iteration; derive a goodness-of-fit statistic from the per-quadrat data portions; and transmit an indication of goodness-of-fit to another device.