Recursive CSP Algorithm for Real-Time Statistical Computation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing algorithms for computing Corrected Sums of Products (CSP) and Corrected Sums of Squares (CSS) in data analysis are inefficient and lack real-time updatable capabilities, leading to inaccuracies in variance, standard deviation, and correlation coefficient computations.
Innovation Solution
A new CSP computation algorithm is developed using successive differences and weight coefficients, allowing for recursive and real-time updatable computations through matrix factorization, improving accuracy and efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional CSP algorithms are used, then computation can be performed, but accuracy is insufficient and real-time updates are not supported
Solution Approach 1:
The patent segments the computation process into distinct phases: data loading, CSSP computation, and result analysis. This segmentation allows each phase to be optimized independently, improving both accuracy and efficiency. The CSSP computation is further segmented into iterative updates that can be performed in real-time as new data arrives.
Solution Approach 2:
The patent implements dynamic computation capabilities where the CSSP values can be updated in real-time as new data points are added. The system transitions from static batch processing to dynamic incremental updates, allowing the computation to adapt continuously to changing data streams while maintaining accuracy through proper mathematical formulations.
2Productivity
If real-time updatable computation is implemented, then processing speed improves, but algorithm complexity increases
Solution Approach 1:
The patent performs preliminary computations of mean and initial CSSP values before the main analysis phase. This preliminary action establishes a foundation that simplifies subsequent real-time updates, as the incremental computations can build upon these pre-calculated values rather than starting from scratch each time.
Solution Approach 2:
The computation system is designed to be self-updating, where new data points automatically trigger incremental updates to the CSSP values without requiring external intervention or complex re-computation. The algorithm serves itself by maintaining running totals and updating statistics as data flows in, reducing the need for complex external control mechanisms.
3Measurement precision
If accurate CSSP computation is performed, then data analysis precision improves, but computation time increases
Solution Approach 1:
The patent implements continuous computation where the CSSP values are updated incrementally as each new data point arrives, rather than performing discrete batch computations. This continuity eliminates idle time between data processing operations and maintains precision throughout the entire data stream, ensuring that analysis precision is not compromised by time constraints.
Data Source
AI summary
This invention proposed a new algorithm. By multiply the proposed weight coefficients of this invention, CSP and CSS can be computed without computing for the mean(s) of the data. After the proposed weight coefficients of this invention undergo factorization, it can promote a new recursive and real time updatable computation method. To test the accuracy of the new invention, the StRD data were separately tested using SAS ver 9.0, SPSS ver15.0 and EXCEL 2007 for comparison. The results showed that the accuracy of the results of the proposed invention exceeds the level of accuracy of SAS ver9.0, SPSS ver15.0 and EXCEL 2007. Aside from an accurate computation, this new invented algorithm can also produce efficient computations.