Choropleth Map Design Using Row Minima Clustering
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Solution Overview
Problem
Existing methods for designing choropleth maps are limited as they either do not produce optimal K-means clustering or are too slow, particularly when dealing with large datasets.
Innovation Solution
A computer-implemented method that uses a linear-time Row Minima Searching algorithm to compute the optimal K-means clustering of numerical values, allowing for efficient assignment of colorations to clusters and resulting in a high-quality choropleth map.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing clustering algorithms (Jenks natural breaks, Head-tail breaks) are used for choropleth map design, then the clustering can be computed, but the clustering is not optimal and the computation is too slow for large datasets
Solution Approach 1:
The patent segments the computational problem into dynamic programming subproblems, where the clustering computation is divided into smaller stages based on the number of clusters formed. This allows the algorithm to build optimal solutions incrementally, achieving both optimal clustering quality and improved computation efficiency for large datasets.
Solution Approach 2:
The patent employs a dynamic programming approach where the algorithm adapts its computation based on the data characteristics and cluster requirements. The computational complexity is optimized dynamically by using memoization and by adjusting the search space based on previously computed results, enabling optimal clustering without excessive computation time.
2Measurement precision
If optimal K-means clustering is computed using traditional algorithms, then the clustering quality is improved, but the algorithmic complexity increases making it unsuitable for large datasets
Solution Approach 1:
The patent performs preliminary actions by pre-sorting the data and pre-computing distance metrics before the main clustering computation. This preliminary processing organizes the data in a way that reduces the complexity of the subsequent optimal clustering computation, making it feasible for large datasets while maintaining clustering optimality.
Solution Approach 2:
The patent replaces the traditional iterative mechanical K-means algorithm with a dynamic programming approach that uses mathematical optimization. This substitution eliminates the need for repeated iterative computations and random initialization, providing guaranteed optimal clustering with reduced algorithmic complexity suitable for large-scale data processing.
Data Source
AI summary
The invention notably relates to a computer-implemented method of designing a choropleth map, wherein the method comprises providing a map, and a number (n) of numerical values (x1, . . . , xn) that represent a statistical variable at respective areas of the map; computing the optimal K-means clustering of the numerical values for a predetermined number of clusters, wherein the computing includes iterating, a number of times corresponding to the predetermined number of clusters, a linear-time Row Minima Searching algorithm applied to a square matrix of order equal to the number of numerical values; assigning a respective coloration to each cluster of the computed clustering; and at all areas of the map at which a respective numerical value is provided, applying the coloration assigned to the cluster to which the respective numerical value belongs.Such a method improves the design of a choropleth map.