Polynomial Coordinate Compression for Noise-Stable Data Encoding
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Solution Overview
Problem
Existing techniques for compressing non-numerical data, such as scanned documents and photographs, face challenges due to instability in the face of noise and distortion, leading to ineffective polynomial evaluation.
Innovation Solution
The Stable Approximate Vanishing Ideal (SAVI) technique processes data points to determine stable polynomials for each class of interest, using an iterative process involving initialization, projection, subtraction, singular value decomposition, and partitioning engines to generate approximately-zero polynomials for compression.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of substance
If existing compression techniques are applied to non-numerical data, then data compression is achieved, but stability in the face of noise and distortion deteriorates
Solution Approach 1:
The patent transforms non-numerical data into numerical coordinates and applies polynomial evaluations with specific degree parameters. By changing the parameter of polynomial degree and selecting coordinates that satisfy vanishing ideal conditions, the system achieves both compression and stability against noise and distortion.
Solution Approach 2:
The patent replaces traditional mechanical or direct compression methods with a mathematical field-based approach using polynomials and coordinate geometry. This substitution allows the system to handle noise and distortion through algebraic relationships rather than direct physical compression, improving reliability.
2Productivity
If polynomials are used to represent data classes, then data compression efficiency is improved, but complexity of determining stable polynomials increases
Solution Approach 1:
The patent segments the polynomial determination process into distinct functional engines: initialization engine, projection engine, subtraction engine, and partitioning engine. Each engine handles a specific aspect of the process, making the overall complex task manageable and systematic while maintaining compression efficiency.
Solution Approach 2:
The patent employs an iterative dynamic process where polynomials are refined through multiple passes. The system dynamically adjusts polynomial coefficients and selects from candidate polynomials based on performance criteria, allowing the process to adapt and converge on optimal solutions without requiring static pre-computation.
3Measurement precision
If iterative polynomial refinement is performed, then accuracy of data representation is improved, but processing time increases
Solution Approach 1:
The patent performs preliminary actions by pre-initializing polynomial candidates and pre-computing coordinate transformations before the main iterative refinement process. This preliminary setup reduces the computational burden during iteration, allowing higher accuracy to be achieved with reduced processing time.
Solution Approach 2:
The patent implements convergence criteria that allow the iterative process to skip unnecessary iterations once sufficient accuracy is achieved. The system rushes through the refinement process by terminating early when polynomials satisfy vanishing ideal conditions within acceptable tolerances, balancing accuracy with processing time efficiency.
Data Source
AI summary
A method for compressing a plurality of coordinates includes obtaining a plurality of approximately-zero polynomials of dimension dim for a plurality of coordinate parameters. The method further includes selecting dim+1 non-approximately-zero polynomials, and providing a compressed data set that includes the approximately-zero polynomials, the dim+1 non-approximately-zero polynomials, and evaluations of the selected dim+1 non-approximately-zero polynomials based on the coordinates.