Linear Regression via Parallel Summation for Big Data
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Solution Overview
Problem
Existing methods for generating linear regressions are computationally demanding due to the need for matrix inversion and repeated iterations, making them inefficient for real-time data analysis in big data environments.
Innovation Solution
A computer-implemented technique that generates linear regressions without matrix inversion or multiple iterations by computing summations derived from zero first derivatives in parallel, allowing for rapid comparison and visualization of datasets.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional linear regression methods using matrix inversion and multiple iterations are used, then measurement precision is improved, but productivity deteriorates due to computational demands
Solution Approach 1:
The patent transforms the traditional linear regression approach by changing the computational parameters from matrix inversion operations to closed-form summation calculations. This parameter change allows the system to maintain regression accuracy while dramatically reducing computational complexity and processing time, directly resolving the contradiction between measurement precision and productivity
2Measurement precision
If pre-computing linear regressions is performed on large datasets, then measurement precision is improved, but loss of time increases due to large processing costs
Solution Approach 1:
The patent extracts the computationally intensive matrix inversion step from the linear regression process and replaces it with direct summation calculations. This extraction eliminates the time-consuming iterative operations while preserving the essential regression functionality, thereby reducing loss of time without sacrificing measurement precision
3Manufacturing precision
If matrix inversion and multiple iterations are used for linear regression, then manufacturing precision is improved, but device complexity increases
Solution Approach 1:
The patent substitutes the complex mechanical-like iterative matrix inversion process with a simpler closed-form mathematical solution based on summations. This substitution replaces a multi-step iterative computational mechanism with a direct calculation approach, reducing device complexity while maintaining manufacturing precision in the regression results
Data Source
AI summary
A data processing method comprises receiving a request to analyze a relationship between an explanatory element and a response element and obtaining, in response to the request, data associated with the explanatory element and the response element. The method further comprises determining coefficients for an equation and storing the coefficients in digital computer memory by: computing, using a plurality of processes in parallel and for each of the coefficients, summations derived from a zero first derivative of the equation with respect to each of the coefficients, computing a value for each of the coefficients using the summations, determining, in response to the computing, a vector of response element values in the digital computer memory using the value of each of the coefficients and values representing the explanatory element as input, and causing displaying a trend graph of the relationship.