Alpha Shape Approximation for Data Clusters
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Solution Overview
Problem
Conventional data analysis techniques fail to provide adequate tools for approximating data clusters effectively, especially in the presence of noise and outliers, which hampers accurate data visualization and decision-making processes.
Innovation Solution
The method involves calculating core data points and dilating them by a multiple of the epsilon distance, combining these dilations to form polygons that represent the data in a way that is not distorted by outliers or noise, using techniques like kernel density estimation and Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) to identify core points and k-nearest neighbors for epsilon distance calculation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional data analysis techniques are used to approximate data clusters, then the analysis process is simple, but the accuracy is poor due to distortion by outliers and noise
Solution Approach 1:
The patent segments the data analysis process into distinct stages: identifying core data points using density-based clustering, calculating epsilon distances for each core point, dilating core points by the epsilon distance to create protective zones, and finally generating polygon representations from the dilated regions. This segmentation allows the system to isolate and process different aspects of data clustering separately, improving accuracy while managing complexity through modular processing steps.
Solution Approach 2:
The patent performs preliminary actions by first identifying core data points before generating the final polygon representation. Core points are identified using density-based clustering algorithms, and epsilon distances are calculated in advance. These preliminary calculations create a foundation of reliable structural information that guides the subsequent polygon generation process, ensuring that the final representation is not distorted by outliers or noise.
2Reliability
If all data points including outliers are used to generate polygon representation, then the representation includes all data, but the underlying structure is distorted
Solution Approach 1:
The patent extracts and isolates core data points from the complete dataset using density-based clustering algorithms. By identifying regions of high data density and selecting only core points within these regions, the system separates meaningful structural information from outliers and noise. This extraction process removes harmful elements while preserving the essential cluster structure for reliable polygon representation.
Solution Approach 2:
The patent converts the presence of outliers and noise into a benefit by using density-based clustering to identify core points. The clustering algorithm's ability to distinguish dense regions from sparse regions allows the system to automatically filter outliers while capturing the true cluster structure. The epsilon distance calculation further leverages local density variations to create adaptive protective zones around core points, transforming potential harm into a robust representation method.
3Manufacturing precision
If core data points are dilated by multiple of epsilon distance, then the polygon representation is more robust, but the processing complexity increases
Solution Approach 1:
The patent changes the parameter of core point representation by dilating each core point by a multiple of its epsilon distance. This parameter transformation expands point representations into regions that capture local data density variations. The dilation factor can be adjusted to control the balance between robustness and precision, allowing flexible optimization of polygon boundary accuracy while managing computational complexity through parameter tuning.
Data Source
AI summary
Methods, systems, and storage media for generating a polygon representation of a plurality of data points are disclosed. Exemplary implementations can: receive a representation of data points from a data source, the representation comprising at least a two-dimensional (2D) data plot; calculate a core representation of the data points; dilate the core representation of the data points, comprising multiplying each data point by a multiple of an epsilon distance; generate dilated points based on the multiplying of each data point; generate a polygon representation of the data points based at least in part on intersections between the dilated points; and cause display of the polygon representation through a user interface.