Location Relevance Scoring Using Taylor Series Approximation
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Solution Overview
Problem
Existing location-based services face inefficiencies in determining the relevance of categories to specific geographic locations, as they require computationally intensive calculations and resource-heavy storage for precise relevance scores, especially when dealing with numerous entities associated with categories.
Innovation Solution
A location relevance system pre-computes relevance scores for prominent locations and uses Taylor coefficients to approximate scores for other locations, reducing computational load and storage needs by evaluating a Taylor series based on physical distance between locations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If precise relevance scores are computed for all locations using traditional methods, then measurement precision is improved, but computational complexity and resource consumption increase significantly
Solution Approach 1:
The patent pre-computes and stores Taylor coefficients for relevance functions at prominent locations before runtime. These pre-computed coefficients are stored in a database, allowing the system to avoid performing complex relevance calculations from scratch for every location query. When a relevance score is needed for a non-prominent location, the system retrieves the pre-computed Taylor coefficients and performs a simple Taylor series approximation, dramatically reducing computational complexity while maintaining acceptable precision.
2Measurement precision
If traditional relevance computation methods are used for every location, then measurement precision is improved, but loss of time increases due to repeated calculations
Solution Approach 1:
The system performs preliminary computation of Taylor coefficients at prominent locations and stores them in advance. This pre-computation eliminates the need to recalculate complex relevance functions for every location query, reducing computation time significantly while maintaining accuracy through Taylor series approximation for non-prominent locations.
Solution Approach 2:
Instead of computing relevance scores from scratch for every location, the system creates approximations using Taylor series expansions based on pre-computed data from prominent locations. This copying approach uses the pre-computed Taylor coefficients to generate relevance scores for new locations through mathematical approximation, dramatically speeding up the process while maintaining acceptable accuracy.
3Quantity of substance
If relevance scores are computed for all possible locations, then completeness of information is improved, but storage requirements increase significantly
Solution Approach 1:
The patent segments the geographic space into prominent locations (where full relevance functions are pre-computed and stored) and non-prominent locations (where Taylor approximation is used). By storing Taylor coefficients only at prominent locations rather than pre-computing and storing all possible relevance scores, the system maintains information completeness for query purposes while dramatically reducing storage requirements. The segmentation allows the system to use different strategies for different location types.
Data Source
AI summary
Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for determining relevance scores for locations. In one aspect, a method includes storing a respective plurality of category-location relevance scores for each location of a plurality of geographic locations. A category-location relevance score is based on a plurality of category-entity-location relevance scores for a plurality of entities associated with the category at the location. A first category-location relevance score is determined for a first geographic location that is not one of the plurality of geographic locations. Determining the first category-location relevance score includes calculating the first category-location relevance score based on a second category-location relevance score for a second geographic location in the plurality of geographic locations and a physical distance between the first geographic location and the second geographic location.