Multi-Agent Generalized Eigenvector Computation for Big Data
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Solution Overview
Problem
Existing systems for determining generalized eigenvectors of large matrices are computationally expensive and inefficient, especially in big data settings, and often introduce bias in parallelized implementations.
Innovation Solution
A system that models the determination of generalized eigenvectors as a multi-agent interaction, utilizing parallel processing hardware like GPUs or TPUs to efficiently compute top-k eigenvectors using multi-agent engines, which are assigned to determine respective eigenvectors and update estimates in a parallelized manner, minimizing bias and reducing computational complexity to O(dk) from O(d3) or O(d2k) complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If existing systems determine generalized eigenvectors using traditional algorithms, then accuracy is maintained, but computational complexity is O(d3) or O(d2k) which is prohibitively expensive for big data
Solution Approach 1:
The patent segments the computation of generalized eigenvectors into multiple independent agent processes, where each agent computes a portion of the eigenvector decomposition. This allows parallel processing of the computation tasks, reducing the overall computational complexity from O(d3) to O(dk) by dividing the work across multiple processing units and iterations.
Solution Approach 2:
The patent employs iterative refinement where agents dynamically update their estimates of eigenvectors through multiple stages. The system transitions from static traditional algorithms to dynamic iterative computations that converge to accurate results, allowing the computational approach to adapt and improve with each iteration while maintaining parallel execution.
2Productivity
If parallelized implementation is used to improve efficiency, then productivity increases, but bias is introduced in the computations
Solution Approach 1:
The patent implements feedback mechanisms where agents exchange information and coordinate their computations to correct biases introduced by parallel processing. Through iterative communication and adjustment of estimates, the system eliminates computational bias while maintaining the speed benefits of parallelization, ensuring accurate results are achieved across multiple processing stages.
3Measurement precision
If exact values for matrices A and B are computed in big data settings, then precision is improved, but computational resources become prohibitively expensive
Solution Approach 1:
The patent applies partial action by computing only the necessary portions of matrix decompositions through iterative refinement rather than computing exact values upfront. Agents perform computations incrementally, calculating only what is needed for each iteration, which significantly reduces computational resource usage while still achieving accurate eigenvector estimates for big data applications.
Data Source
AI summary
Methods, systems, and apparatus, including computer programs encoded on computer storage media, for determining generalized eigenvectors that characterize a data set.