Geometric Data Analysis for Nonlinear Interactive Systems
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Solution Overview
Problem
Conventional data analysis methods are ineffective for datasets representing interactive systems that evolve nonlinearly, necessitating improved representation and control techniques.
Innovation Solution
A computer-implemented method involving geometric data analysis, where a dataset is prepared for analysis based on problem type, generating results from geometric nodes and configuration nodes, and iteratively using geometric controls to manage the state of the configuration node, with specified conditions determining further actions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional data analysis methods are used, then the analysis process is simple, but the methods are ineffective for datasets representing interactive systems that evolve nonlinearly
Solution Approach 1:
The patent transforms data analysis from conventional linear methods to geometric analysis by changing the fundamental parameters of representation. Data points are mapped to geometric coordinates, and analysis operations are performed using geometric transformations (rotations, reflections, projections) rather than traditional statistical methods. This parameter change enables effective analysis of nonlinearly evolving interactive systems while maintaining computational tractability.
Solution Approach 2:
The patent replaces conventional data analysis mechanisms with geometric mechanisms. Instead of using traditional algorithms for pattern recognition and system modeling, the system uses geometric constructions (triangulations, convex hulls, Voronoi diagrams) and geometric computations to analyze data. This substitution provides a more appropriate framework for capturing the nonlinear dynamics of interactive systems.
2Ease of operation
If geometric analysis operations are performed interactively, then user control and feedback are improved, but the system complexity increases
Solution Approach 1:
The patent segments the geometric analysis system into distinct operational nodes (geometric node, configuration node, control node) that can be independently manipulated and controlled. Each node performs a specific geometric operation, and users can interact with individual nodes to control the analysis process. This segmentation provides fine-grained interactive control while organizing system complexity into manageable, modular components.
Solution Approach 2:
The patent implements a dynamic geometric analysis system where the geometric configuration can be continuously adjusted and transformed based on user input and data changes. The system allows real-time modifications to geometric parameters, iterative refinements of the analysis, and adaptive reconfiguration of the data representation. This dynamic capability enhances interactive control while the underlying geometric framework provides structural organization.
Data Source
AI summary
In one exemplary embodiment, a computer-implemented method includes obtaining a data set from a data source. The data set is prepared for an analysis operation according to a problem type. A result is generated from an interactive geometric node based a geometric property of the data set. A specified condition is determined with the result from the interactive geometric node based on a query to the interactive geometric node. A system's geometric configuration is determined. A geometric control criterion is determined.