Vector Space Newton Interpolation Cage for Measurement Vector Characterization
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Solution Overview
Problem
Existing machine learning algorithms for characterizing measurement vectors are often imprecise and not real-time capable, with methods like the k-nearest neighbors algorithm and artificial neural networks facing issues of inaccurate results and high computational complexity.
Innovation Solution
A computer-implemented method that determines an indication parameter of a measurement vector by selecting nearest neighbor database vectors and using a function to interpolate the indication parameter, allowing for precise characterization with reduced computational effort.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the k-nearest neighbors algorithm is used to characterize measurement vectors, then the computational effort is low and the method is easy to determine, but the accuracy of the determined nearest neighbor deviates significantly from the measurement vector
Solution Approach 1:
The algorithm segments the search process into multiple hierarchical levels. Instead of searching all database vectors at once, it divides the feature space into regions and performs coarse-to-fine searches, first identifying candidate regions with relaxed criteria, then progressively refining the search to find the true nearest neighbor with higher precision.
Solution Approach 2:
The algorithm introduces an additional dimensional aspect by considering multiple candidate neighbors simultaneously rather than just a single nearest neighbor. It evaluates k candidates and uses aggregation across these candidates to improve accuracy, effectively adding a dimension of candidate comparison to the traditional single-point nearest neighbor approach.
2Measurement precision
If artificial neural networks are used to improve accuracy, then the precision of characterization improves, but the algorithms are computationally and memory-intensive with long inference times
Solution Approach 1:
Instead of training complex neural networks, the algorithm creates simplified copies or approximations of the nearest neighbor search process. It uses multiple candidate neighbors as proxies for the true nearest neighbor and aggregates their information, providing accurate results without the computational burden of neural network training and inference.
Solution Approach 2:
The algorithm changes the parameters of the search process by adjusting the number of candidates k and the aggregation method. By optimizing these parameters, it achieves high accuracy comparable to neural networks while maintaining linear computational complexity and fast inference times suitable for real-time applications.
3Measurement precision
If large and deep artificial neural networks are used, then the accuracy improves, but the algorithms require large data storage capacities and are not real-time capable
Solution Approach 1:
The algorithm performs preliminary actions by pre-selecting k candidate neighbors and preparing their information before the final aggregation step. This preliminary organization of candidate data enables rapid real-time inference without requiring large memory capacities, as only k candidate vectors need to be stored and processed rather than entire neural network weights.
Solution Approach 2:
The algorithm introduces dynamics by allowing the number of candidates k to be adjusted based on computational resources and accuracy requirements. This dynamic parameter enables the system to adapt between real-time operation with smaller k and higher accuracy modes with larger k, providing flexibility that fixed-architecture neural networks lack.
Data Source
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AI summary
The present invention relates to a computer-implemented method for determining an indication parameter (y) of a measurement vector (x), comprising the steps: acquiring (S1) the measurement vector (x); selecting (S2) a first database vector (x1) and a second database vector (x2) from a plurality of database vectors stored in a database, wherein the selection of the first database vector (x1) from the database is such that the first database vector (x1) is a nearest neighbor of the measurement vector (x), and the selection of the second database vector (x2) from the database is dependent on the first database vector (x1) and the measurement vector (x), and a first known reference indication parameter (yi) is assigned to the first database vector (x1) and a second known reference indication parameter (y2) is assigned to the second database vector (x2);Determining (S3) a function, wherein the function is determined as a function of the first database vector (x1), the second database vector (x2), the first known reference indication parameter (yi), and the second known reference indication parameter (y2), such that evaluating the determined function on the first database vector (x1) yields the first known reference indication parameter (yi), and evaluating the function on the second database vector (x2) yields the second known reference indication parameter (y2); and determining (S4) the indication parameter (y) by evaluating the determined function on the measurement vector (x).