Varied-Scale Topological Construct for Multidimensional Data
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Solution Overview
Problem
Conventional data-visualization systems face challenges in efficiently generating and modifying topological visualizations of multidimensional data, particularly with the Mapper algorithm, which requires cumbersome client-device interactions and fixed scales that obscure connections and patterns, and the Multiscale-Mapper algorithm necessitates multiple visualizations for varying scales.
Innovation Solution
The system generates and renders a varied-scale-topological construct by combining an initial topological construct with a local topological construct for a subset of the data at a different scale, allowing for varying scales within a single visualization, and selects regions for magnification based on relative densities and contractibility principles.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If the Mapper algorithm is executed at a fixed scale for the entire dataset, then the algorithm can be executed with a single topological visualization, but the fixed scale may visually obscure or misrepresent various connections or patterns in the multidimensional dataset
Solution Approach 1:
The patent applies local quality by allowing different regions of the topological visualization to have different scales. Specifically, the system identifies regions of interest within the initial topological construct and generates local topological constructs at alternative scales for those specific regions, while maintaining the original scale for other regions. This enables accurate representation of connections and patterns at appropriate scales for each region without requiring multiple complete visualizations.
2Measurement precision
If the Multiscale-Mapper algorithm is executed to generate multiple simplicial complexes at different scales, then varying scales can be achieved, but additional computing resources and time are required to render and compare multiple topological visualizations
Solution Approach 1:
The patent applies segmentation by dividing the dataset and visualization into regions of interest and non-regions of interest. The system executes the Mapper algorithm on the entire dataset to generate an initial topological construct, then identifies specific regions that require alternative scales, and finally executes the Mapper algorithm only on those identified regions to generate local topological constructs. This segmented approach reduces computing resources and rendering time compared to generating multiple complete visualizations.
Solution Approach 2:
The patent merges the initial topological construct with local topological constructs to form a varied-scale topological construct. The system combines the globally-scaled initial visualization with locally-scaled constructs for regions of interest, creating a single unified visualization that incorporates multiple scales. This merging eliminates the need to separately render and compare multiple complete visualizations, reducing computing resources and analyst time.
3Measurement precision
If the Mapper algorithm requires trial and error to fine tune parameter combinations, then a Mapper graph of acceptable scale can be generated, but the process becomes cumbersome for client devices and users
Solution Approach 1:
The patent applies preliminary action by first executing the Mapper algorithm on the entire dataset to generate an initial topological construct at a default or preliminary scale. This initial visualization provides a overview that guides the subsequent identification of regions of interest. By performing this preliminary global analysis first, the system reduces the need for extensive trial and error in parameter tuning, as the initial construct informs subsequent local refinements.
Solution Approach 2:
The patent applies self-service by enabling the system to automatically identify regions of interest within the initial topological construct and automatically generate local topological constructs for those regions. The system uses automated criteria (such as data density thresholds or user-specified region selections) to determine which regions require alternative scales, eliminating the need for users to manually adjust parameters through trial and error. The varied-scale topological construct is generated automatically, simplifying client-device interactions.
Data Source
AI summary
This disclosure relates to methods, non-transitory computer readable media, and systems that generate and render a varied-scale-topological construct for a multidimensional dataset to visually represent portions of the multidimensional dataset at different topological scales. In certain implementations, for example, the disclosed systems generate and combine (i) an initial topological construct for a multidimensional dataset at one scale and (ii) a local topological construct for a subset of the multidimensional dataset at another scale to form a varied-scale-topological construct. To identify a region from an initial topological construct to vary in scale, the disclosed systems can determine the relative densities of subsets of multidimensional data corresponding to regions of the initial topological construct and select one or more such regions to change in scale.