B-spline Model Selection via Pre-computed Fit Criteria
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Solution Overview
Problem
The iterative selection of parameters for b-spline models, such as the number of knots and polynomial degree, requires significant computer resources due to the large number of combinations that need to be evaluated, making it computationally expensive and inefficient.
Innovation Solution
A computer-readable medium with instructions that facilitate interactive b-spline model selection by defining knot locations, computing fit criterion values, and storing coefficients, allowing users to interactively adjust knot locations and polynomial degrees for efficient model fitting and visualization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If iterative selection of b-spline parameters (number of knots, polynomial degree) is performed to achieve best-fit model selection, then model accuracy is improved, but computational resource consumption increases significantly
Solution Approach 1:
The system pre-computes and stores fit criterion values for multiple combinations of polynomial degrees and numbers of knots before interactive selection. This preliminary computation allows the user to later explore different model configurations without performing expensive iterative fitting operations in real-time, thus resolving the contradiction between achieving accurate model selection and reducing computational resource consumption during interaction.
2Measurement precision
If comprehensive evaluation of multiple knot locations and polynomial degrees is performed, then model selection quality is improved, but computation time increases
Solution Approach 1:
The system performs comprehensive model fitting and stores fit criterion values for various polynomial degrees and knot configurations in advance. This allows the interactive selection process to quickly retrieve and compare pre-computed results without performing time-consuming iterative fitting operations, thereby maintaining high model selection quality while significantly reducing computation time during user interaction.
Solution Approach 2:
The system dynamically adapts the level of computational detail based on user interaction. When the user adjusts knot locations or polynomial degree during interactive exploration, the system efficiently reuses pre-computed fit criterion values where applicable and only performs minimal additional computations, rather than re-evaluating all models from scratch. This dynamic approach maintains model selection quality while minimizing computation time during interactive adjustments.
Data Source
AI summary
A computing device provides graphical interactive b-spline model selection. A presented criterion fit graph includes a number of internal knots line that indicates a number of internal knots value of a determined best fit b-spline model and a polynomial degree curve for each of a set of polynomial degree values. Each polynomial degree curve shows a fit criterion value as a function of the number of internal knot values. A best fit b-spline model graph is presented next to the presented criterion fit graph that includes a knot location line at each of the knot locations of the determined best fit b-spline model and a best fit model curve computed using the coefficients of the determined best fit b-spline model. An indicator that the number of internal knots line is moved to a different number of internal knots value is received. The best fit b-spline model graph is then updated.