SVM Kernel Approximation via Single-Variable Lookup Tables
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Solution Overview
Problem
Existing support vector machine (SVM) classification methods require extensive computational resources and large memory for calculating kernel functions, especially when dealing with a large number of support vectors, due to the need for multiple lookup tables and complex operations.
Innovation Solution
The proposed solution involves approximating the multiple-variable kernel function as a product of single-variable functions using a lookup table, reducing the computational load and memory requirements by using a piecewise linear approximation of the single-variable function, allowing for efficient classification with reduced operation time and memory usage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional SVM classification methods are used to calculate kernel functions, then classification accuracy is maintained, but computational resources and memory requirements increase significantly
Solution Approach 1:
The patent segments the multi-variable kernel function into multiple single-variable functions, each operating independently on individual input features. This segmentation allows parallel computation and reduces the computational complexity from O(n²) to O(n), significantly lowering computational resource requirements while preserving classification accuracy through the additive kernel formulation.
Solution Approach 2:
The patent transforms the kernel function parameters by introducing a segmentation parameter that divides the multi-dimensional input space into independent single-dimensional projections. This parameter change enables the use of simpler single-variable functions instead of complex multi-variable kernel calculations, reducing computational burden while maintaining the essential classification capability.
2Measurement precision
If traditional SVM methods with multiple lookup tables are used, then classification precision is maintained, but memory requirements increase
Solution Approach 1:
The patent segments the large multi-dimensional lookup table into multiple small single-variable lookup tables, each storing information for only one input feature. This segmentation dramatically reduces memory requirements from storing a full D-dimensional table to storing D separate 1-dimensional tables, while the additive kernel formulation ensures classification precision is preserved through the sum of individual feature contributions.
3Measurement precision
If exact kernel function calculations are performed, then classification accuracy is maintained, but operation time increases
Solution Approach 1:
The patent segments the computation process into independent single-variable function evaluations that can be performed in parallel, eliminating the need for sequential multi-variable kernel calculations. This segmentation reduces operation time from O(n²) to O(n) by computing each feature's contribution independently and summing the results, while the additive kernel ensures classification accuracy is maintained.
Solution Approach 2:
The patent performs preliminary action by pre-computing and storing single-variable function values in lookup tables before the actual classification task. During classification, only simple table lookups and additions are needed instead of complex kernel function evaluations, significantly reducing operation time while maintaining accuracy through the pre-stored precise function values.
Data Source
AI summary
There is provided an information processing apparatus. A multidimensional input vector is input. For each dimension of the input vector, a function value of a single-variable function with an element of the dimension as a variable is derived, by referring to a lookup table indicating a correspondence between a variable and a function value of the single-variable function. A product of the single-variable functions approximates a function value of a multiple-variable function. For each dimension of the input vector, a product of the function value derived by the derivation unit and a predetermined coefficient corresponding to the dimension is calculated. A value calculated using the total of the products calculated by the product calculation unit for each dimension of the input vector is output as a classification index indicating a class of the input vector.