Data Clustering Using Eigenvector Curvature for Topological Distinction
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Solution Overview
Problem
Existing data clustering methods face challenges in accurately distinguishing between point group data sets with similar topological shapes due to the generation of similar feature values, leading to degraded training precision and incorrect polygon selection, especially when the overall shape of the data is unknown.
Innovation Solution
The proposed solution involves calculating eigenvectors for each point in the point group data using principal component analysis and determining the curvature of a multidimensional function at extreme points, which allows for the generation of accurate feature values that differentiate between data sets based on curvature-wise local differences, enabling precise clustering and polygon fitting.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional feature extraction methods are used for point group data, then the processing is simpler, but the training precision degrades when data sets have similar topological shapes
Solution Approach 1:
The patent segments the point group data by calculating eigenvectors for each individual point through principal component analysis. This divides the overall feature extraction into point-level operations, where each point's local curvature characteristics are computed independently. The segmentation enables differentiation of local geometric features even when global topological shapes are similar, thereby improving training precision without overwhelming system complexity through modular point-by-point processing.
Solution Approach 2:
The patent transforms the feature extraction from traditional topological shape analysis into a new dimensional space by computing curvature values along eigenvector directions. This dimensionality change introduces curvature-wise local differences as a new feature dimension, allowing the system to distinguish between data sets with similar topological shapes by analyzing their local curvature characteristics in the eigenvector-defined coordinate system.
2Reliability
If curvature calculation is performed for each point using principal component analysis, then the distinction between data sets improves, but the computational complexity increases
Solution Approach 1:
The computational process is segmented into independent point-level operations where each point undergoes principal component analysis and curvature calculation separately. This segmentation allows parallel processing of individual points, improving clustering accuracy through comprehensive local feature analysis while managing computational complexity by breaking down the overall computation into manageable point-by-point steps that can be efficiently processed.
Solution Approach 2:
Each point in the point group data performs self-service by autonomously computing its own eigenvectors and curvature characteristics through principal component analysis. This self-service approach at the point level enables the system to gather comprehensive local geometric information across all points, improving clustering reliability while distributing the computational workload in a systematic manner that manages overall complexity.
3Measurement precision
If local curvature features are extracted for each point, then the feature values become more accurate, but the processing time increases
Solution Approach 1:
The feature extraction process is segmented into point-level operations where each point's local curvature is computed independently using principal component analysis. This segmentation enables efficient parallel processing of individual points, achieving high feature value accuracy through detailed local analysis while managing processing time by dividing the computation into manageable units that can be processed concurrently or in optimized sequences.
Solution Approach 2:
The patent performs preliminary principal component analysis to establish eigenvector directions for each point before computing the final curvature values. This preliminary action of determining the coordinate system and eigenvector orientations beforehand allows for more efficient subsequent curvature calculations, improving feature value accuracy while reducing overall processing time by preparing the computational framework in advance.
Data Source
AI summary
A non-transitory computer-readable recording medium stores therein a data clustering program that causes a computer to execute a process. The process includes calculating, for each of plural points included in a set of point group data, an eigenvector by using principal component analysis for a set of point group data that is present within a predetermined distance from a point; calculating a curvature of a multidimensional function having an extreme point that is a point positioned nearest to the eigenvector calculated; executing, on the basis of the curvature for each of the plural points of the set of point group data, clustering of the plural points; and outputting a result of execution of the clustering.