Stable Approximate Vanishing Ideal for Noisy Data Classification
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Solution Overview
Problem
Existing data classification techniques, such as Approximate Vanishing Ideal (AVI), are unstable and perform poorly in the presence of noise, particularly when dealing with non-numerical data like scanned documents, leading to inaccurate classification of alphanumeric characters due to distortion or extraneous pixels.
Innovation Solution
The Stable Approximate Vanishing Ideal (SAVI) technique, which includes an initialization engine, projection engine, subtraction engine, singular value decomposition (SVD) engine, and partitioning engine, processes data points to generate stable approximately-zero polynomials for each class, effectively handling noise and distortion by iteratively refining candidate polynomials and computing singular value decomposition of subtraction matrices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If Approximate Vanishing Ideal (AVI) technique is used for data classification, then classification speed is improved, but classification accuracy deteriorates in the presence of noise
Solution Approach 1:
The SAVI technique performs preliminary actions by iteratively refining candidate polynomials before final classification. The algorithm pre-processes the polynomial candidates through multiple iterations, adjusting coefficients and eliminating poor candidates before the actual classification occurs, thereby preparing more robust classifiers that can handle noisy data
Solution Approach 2:
The SAVI technique implements feedback mechanisms by evaluating polynomial candidates against training data and using the results to refine subsequent candidates. The algorithm computes classification errors and uses this feedback to adjust polynomial coefficients and select better candidates in the next iteration, continuously improving accuracy while maintaining reasonable speed
2Manufacturing precision
If polynomial degree is increased to improve classification accuracy, then manufacturing precision of classification boundary is improved, but device complexity increases
Solution Approach 1:
The SAVI technique applies partial action by using polynomial degrees that are sufficient but not excessive for the given problem. The algorithm dynamically selects the appropriate polynomial degree based on the complexity of the classification task and the quality of candidate polynomials found during iteration, avoiding unnecessary complexity while achieving adequate precision
Solution Approach 2:
The SAVI technique changes parameters by adjusting polynomial coefficients, degrees, and selection criteria during iteration. The algorithm modifies these parameters based on feedback from classification performance, finding an optimal balance between boundary precision and polynomial complexity for each specific classification problem
Data Source
AI summary
A method includes obtaining, by executing a module stored on a non-transitory computer-readable storage device, approximately-zero polynomials for each of multiple classes. The method further includes evaluating the approximately-zero polynomials for each class on a plurality of points to compute distances from each point to each of the classes. The method also includes scaling the approximately-zero polynomials based on the distances and classifying the points based on the scaled approximately-zero polynomials.