Modularity-Based Manifold Tearing for High-Dimensional Data Visualization
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Solution Overview
Problem
Conventional visualization generation systems are inaccurate, inefficient, and inflexible when processing large-scale and high-dimensional digital data volumes, often resulting in inaccurate visual representations due to projection losses, high computational demands, and limitations in adapting to large datasets and high-dimensional data.
Innovation Solution
The system utilizes landmark data points and modularity-based manifold tearing to generate interactive visual shape representations by constructing an augmented nearest neighbor network graph, selecting landmarks, and compressing the network graph using community detection algorithms, allowing for efficient and flexible exploration of large data volumes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Volume of moving object
If dimensionality reduction models (UMAP, t-SNE) are used to transform high-dimensional data into low-dimensional representation, then the data can be visualized in lower dimensions, but projection losses occur causing points separated in high-dimensional space to appear in the same neighborhood in the lower-dimensional projection
Solution Approach 1:
The patent divides the high-dimensional data manifold into multiple lower-dimensional patches or charts, each representing a local region. Instead of applying a single global dimensionality reduction, the system segments the data space and creates separate low-dimensional representations for each segment, then stitches them together to form a complete visualization. This segmentation approach preserves local structures while avoiding the projection losses inherent in global dimensionality reduction.
2Ease of manufacture
If dimensionality reduction models are employed to generate visual representations, then the visualization can be created, but significant computational resources (memory, processing time, power) are required
Solution Approach 1:
The patent segments the large dataset into smaller manageable patches, allowing dimensionality reduction to be applied locally to each patch rather than to the entire dataset at once. This segmentation reduces the computational burden on each processing unit, enabling parallel processing and reducing overall memory requirements and energy consumption while still achieving comprehensive visualization coverage.
Solution Approach 2:
The system applies dimensionality reduction partially to only the necessary portions of the data (selected patches) rather than processing the entire high-dimensional dataset. This partial action approach reduces computational resource consumption by focusing processing efforts only on regions that need to be visualized, rather than performing exhaustive processing on all data points.
3Adaptability or versatility
If conventional dimensionality reduction models are used, then visualization can be achieved, but the systems are incapable of flexibly adapting to large datasets with millions or billions of data points
Solution Approach 1:
The patent implements a segmented approach where the large dataset is divided into multiple patches that can be processed independently and in parallel. This segmentation enables the system to scale to large datasets by distributing processing across multiple computational units, maintaining processing efficiency while increasing adaptability to dataset size. The modular patch-based structure allows the system to handle datasets of varying sizes flexibly.
Solution Approach 2:
The patent introduces a new dimensional organization for the data by creating a tiled manifold structure where patches are arranged in a systematic grid or hierarchy. This dimensional reorganization allows efficient navigation and processing of large datasets by providing structured access patterns, enabling the system to scale to billions of data points while maintaining productivity through organized parallel processing.
4Reliability
If the mapper algorithm is used to alleviate dimensionality reduction problems, then some improvements are achieved, but the algorithm still requires a filter function (often a dimensionality reduction model) and suffers from significant computational demands and parameter-tuning requirements
Solution Approach 1:
The patent extracts and removes the dependency on complex filter functions by directly working with the manifold structure of the data. Instead of requiring an external dimensionality reduction model as a filter, the system extracts the essential geometric and topological properties directly from the data patches, eliminating the need for parameter-intensive filtering steps while maintaining visualization reliability.
Solution Approach 2:
The patent simplifies the algorithm by reducing the number of parameters that need to be tuned. The patch-based manifold tearing approach uses intrinsic geometric parameters derived from the data itself rather than requiring extensive external parameter configuration. This parameter change strategy reduces algorithm complexity while preserving the ability to generate reliable visualizations.
Data Source
AI summary
The present disclosure relates to systems, methods, and non-transitory computer-readable media that generate interactive visual shape representation of digital datasets. For example, the disclosed systems can generate an augmented nearest neighbor network graph from a sampled subset of digital data points using a nearest neighbor model and witness complex model. The disclosed system can further generate a landmark network graph based on the augmented nearest neighbor network graph utilizing a plurality of random walks. The disclosed systems can also generate a loop-augmented spanning network graph based on a partition of the landmark network graph by adding community edges between communities of landmark groups based on modularity and to complete community loops. Based on the loop-augmented spanning network graph, the disclosed systems can generate an interactive visual shape representation for display on a client device.