Topological Data Analysis for Multidimensional Dataset Clustering

The patent applies segmentation by dividing the data analysis process into distinct topological operations (filtering, covering, clustering) that preserve local relationships. Instead of treating the entire dataset as a single unit for clustering, the method segments the reference space into covered regions that maintain the connectivity and relationships among data points, thereby preventing the loss of important relationships while still enabling computational processing.

The patent introduces an intermediary reference space and covering mechanism between the original high-dimensional data and the final clustering result. This intermediary structure (the covered reference space with overlapping regions) acts as a mediator that preserves relationships during the transformation process, allowing data points to maintain their contextual connections while being processed computationally.

The patent transforms the data analysis from direct high-dimensional space processing to a reference space with a covering structure. This dimensional transformation allows the method to handle large-scale distances in the reference space while preserving fine-grained details through the overlapping cover regions, effectively decoupling the sensitivity to scale from the detail retention capability.

The patent applies local quality by using overlapping cover regions in the reference space where different regions can have different resolution properties. This allows the method to maintain high measurement precision in local regions while handling global large-scale distances, as each covered region can be analyzed with appropriate detail without being affected by the overall scale of the entire dataset.

The patent introduces dynamics by making the data analysis system interactive and adaptable. The method allows users to modify analysis parameters, explore different coverings, and interactively adjust the reference space transformation, enabling rapid exploration of relationships without requiring time-consuming expert interpretation of static graphs. The system responds dynamically to user inputs and allows exploratory analysis.

The patent enables self-service by allowing users to directly interact with and modify the analysis parameters and explore the data relationships themselves, rather than requiring sophisticated experts to interpret complex static graphs. The interactive nature of the method empowers users to perform their own exploratory data analysis by adjusting parameters and observing results in real-time.