Hyperbolic Smoothing Clustering for Multidimensional Data
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Solution Overview
Problem
Existing clustering algorithms face challenges in efficiently solving the global optimization problem of unsupervised clustering in multidimensional space, particularly in reducing computational effort and achieving robust results, especially when dealing with large datasets and varying distance metrics.
Innovation Solution
The proposed methodologies, including Hyperbolic Smoothing Clustering and Boundary and Gravitational Regions Partition, transform the nondifferentiable clustering problem into a differentiable one by using smoothing functions and partitioning techniques, allowing for the calculation of minimum distances in a Euclidean multidimensional space, thereby reducing computational complexity and improving response times.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional clustering algorithms are used to solve the global optimization problem of unsupervised clustering in multidimensional space, then clustering solutions can be obtained, but computational effort is excessive and response times are slow
Solution Approach 1:
The patent segments the set of observations into two distinct groups: data in the frontier and data in gravitational regions. This segmentation allows the algorithm to apply different computational strategies to different subsets of data, reducing the overall computational effort required for clustering while maintaining solution quality
Solution Approach 2:
The patent performs preliminary classification of data points into frontier and gravitational regions before executing the full clustering computation. This preliminary action enables the algorithm to focus computational resources on the most critical data points (frontier), thereby reducing total computation time and improving response times
2Measurement precision
If traditional minimum distance calculation methods are used in clustering, then distance measurements can be obtained, but the calculations are computationally intensive and time-consuming
Solution Approach 1:
The patent applies segmentation to the distance calculation process by separately handling frontier data and gravitational region data. This allows for optimized computation where only frontier points require intensive minimum distance calculations, while gravitational region points can be processed more efficiently, thereby improving computational speed without sacrificing measurement precision
Solution Approach 2:
The patent applies different computational approaches to different local regions of the data space. Frontier data points receive more computationally intensive treatment to ensure accurate distance measurements, while gravitational region points use simplified methods. This local differentiation optimizes the balance between measurement precision and computational speed
Data Source
AI summary
The invention concerns four methodologies regarding the unsupervised clustering of a set of observations in multidimensional space, considering a defined number of clusters. The invention comprises a special procedure for calculating the minimum distance of a given point to a set of points in a multidimensional space, the main component of the first methodology.