Adaptive Kernel Function for Binary Vector Probability Calculation
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Solution Overview
Problem
Existing methods for calculating the occurrence probability of a vector in a binary space are not effective due to the non-uniform distribution of training vectors, leading to inaccurate calculations and a fixed degree of smoothing, which cannot be adaptively controlled.
Innovation Solution
A computing apparatus that generates a second kernel function based on the distribution of distances between a target vector and training vectors in a binary space, allowing for adaptive control of the degree of smoothing, thereby improving the accuracy of occurrence probability calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a fixed kernel function with constant degree of smoothing is used, then the calculation process is simple, but the accuracy of occurrence probability calculation deteriorates due to non-uniform distribution of training vectors
Solution Approach 1:
The patent applies dynamics by transforming the fixed kernel function into a dynamic one where the degree of smoothing is adaptively adjusted based on the distribution of training vectors. The kernel function dynamically selects different smoothing degrees for different regions of the feature space, allowing accurate occurrence probability calculation while maintaining manageable complexity through automated adaptation.
Solution Approach 2:
The patent changes the parameter of smoothing degree from a fixed constant to a variable that adapts to the local density of training vectors. By modifying this critical parameter based on the distribution characteristics of training data, the system achieves higher measurement precision without requiring a completely complex redesign of the calculation framework.
2Measurement precision
If adaptive control of smoothing degree is implemented, then the accuracy of occurrence probability calculation improves, but the computational complexity increases
Solution Approach 1:
The system performs self-service by automatically analyzing the distribution of training vectors and independently determining the appropriate smoothing degree without external intervention. This self-adaptive mechanism improves accuracy while minimizing the need for manual tuning or complex computational overhead, as the system serves its own optimization needs.
Solution Approach 2:
The patent implements feedback by using the distribution characteristics of training vectors to adjust the smoothing degree of the kernel function. This feedback loop allows the system to continuously optimize its performance based on the actual data distribution, achieving higher accuracy while maintaining computational efficiency through data-driven adaptation.
3Measurement precision
If Euclidean space methods are applied to binary space, then the calculation approach remains simple, but the measurement precision deteriorates due to fundamental differences in space structure
Solution Approach 1:
The patent applies local quality by recognizing that different regions of the binary space have different density characteristics and applying appropriate smoothing degrees to each region. This localized adaptation allows the system to handle the unique properties of binary space effectively, improving measurement precision while maintaining the simplicity of the overall approach through region-specific optimization.
Data Source
AI summary
According to an embodiment, a computing apparatus includes a memory, and a processor. The memory stores N first vectors in a d-dimensional binary vector space consisting of binary values. The processor acquires a second vector in the d-dimensional binary vector space. The processor extracts M first vectors having a distance from the second vector satisfying a first condition out of the N first vectors, and calculate a distribution of distances of the M first vectors from the second vector. The processor acquires a first kernel function per a first distance between the M first vectors and the second vector in a first range. The processor generates a second kernel function based on the distribution and the first kernel functions. The processor calculates an occurrence probability of the second vector in the N first vectors based on the second kernel function.