Range Search Mapping With Space-Filling Curves for High-Dimensional k-NN
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Solution Overview
Problem
The increasing dimensions of training data lead to a significant increase in calculation time and complexity in k-nearest neighbor algorithms, particularly when using primitive implementations without range search techniques.
Innovation Solution
A range determination device and method that utilizes multiple space-filling curves to convert multi-dimensional data into one-dimensional data, determines neighbor ranges on these curves, and sets candidate areas, ultimately selecting the area with the smallest data count as the search area.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the number of training data is increased to improve classification accuracy, then the accuracy is improved, but the calculation time increases
Solution Approach 1:
The patent divides the vector space into multiple regions using space-filling curves, segmenting the search space into manageable parts. This allows the system to process large datasets by working with smaller regional subsets rather than the entire dataset, thereby maintaining accuracy while reducing calculation time.
Solution Approach 2:
The patent introduces a new dimensional approach by mapping multi-dimensional data onto one-dimensional space-filling curves. This dimensionality transformation enables efficient range searches by converting complex multi-dimensional proximity queries into simpler one-dimensional interval queries, significantly reducing computational overhead.
2Adaptability or versatility
If the dimension of training data is increased to improve model capability, then the model capability is improved, but the amount of calculation increases
Solution Approach 1:
The patent handles high-dimensional data by transforming it into one-dimensional space using space-filling curves. This approach maintains the adaptability needed for high-dimensional data while reducing the computational complexity of range searches, as the curved mapping preserves spatial relationships in a lower-dimensional representation.
Solution Approach 2:
The space-filling curve acts as an intermediary that bridges high-dimensional data and efficient one-dimensional search structures. By introducing this intermediate representation, the system can work with complex high-dimensional data without directly承受 the full computational burden of high-dimensional space searches.
Data Source
AI summary
The range determination device 100 includes one-dimensionalization means 101 for generating multiple types of one-dimensional data from multiple multi-dimensional data using each of multiple space-filling curves, query data placement means 102 for placing query data on each of the multiple space-filling curves on which the one-dimensional data is placed, candidate area determination means 103 for determining a neighbor range of the query data on each of the multiple space-filling curves, and setting an area on each of multiple multi-dimensional planes corresponding to the neighbor range as a candidate area, and search range determination means 104 for determining an area with the smallest number of included data among multiple candidate areas as a search area.