High-Dimensional Data Visualization via Minimum Spanning Tree Indexing
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Solution Overview
Problem
The challenge lies in efficiently visualizing and retrieving information from large databases with high-dimensional data, which is computationally intensive and resource-demanding, especially when dealing with datasets containing millions of objects, requiring significant memory and processing power, and existing methods struggle to preserve locality and interpretability.
Innovation Solution
A computer-implemented method that establishes an index structure using locality sensitive hashing, searches for nearest neighbors, generates a minimum spanning tree, and employs a probabilistic layout algorithm to generate visualization data, allowing for efficient visualization of high-dimensional data in a low-dimensional space.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional dimensionality reduction methods (e.g., t-SNE, UMAP) are used to visualize high-dimensional data, then visualization quality and locality preservation are improved, but computational complexity and memory requirements increase significantly
Solution Approach 1:
The patent segments the high-dimensional data visualization task into multiple stages: (1) dimensionality reduction to intermediate dimensions using randomized projections, (2) further reduction to final 2D/3D visualization dimensions, and (3) progressive refinement of the visualization. This segmentation allows each stage to operate on smaller data subsets, reducing memory requirements while maintaining visualization quality.
Solution Approach 2:
The patent introduces intermediate dimensional stages between the original high-dimensional space and the final 2D/3D visualization. Data points are first projected to an intermediate dimension (e.g., 10-100 dimensions) using randomized projections, then further reduced to the final visualization dimensions. This dimensional transition strategy reduces computational complexity at each step while preserving locality.
2Quantity of substance
If large databases with millions of objects are processed to maintain comprehensive data coverage, then data completeness is improved, but memory bandwidth requirements and processing time increase significantly
Solution Approach 1:
The patent performs preliminary dimensionality reduction and clustering on the entire large database to identify representative subsets and cluster structures before generating the final visualization. This preliminary action allows the system to work with compressed representations of the data, reducing memory bandwidth requirements during the actual visualization generation while maintaining data completeness.
Solution Approach 2:
The patent creates compressed representations and proxies of the original high-dimensional data through randomized projections and clustering. These copies retain the essential structural information and locality relationships of the original data but occupy significantly less memory, enabling efficient processing of large databases with millions of objects.
3Measurement precision
If exhaustive nearest neighbor searches are performed to ensure accurate similarity identification, then search accuracy is improved, but processing time increases significantly
Solution Approach 1:
The patent segments the nearest neighbor search process by performing searches in the reduced intermediate dimensional space rather than the original high-dimensional space. The segmented approach first identifies candidate neighbors in the compressed representation, then verifies their similarity in the original space if needed, significantly reducing processing time while maintaining search accuracy.
Solution Approach 2:
The patent changes the dimensional parameters of the search space by performing nearest neighbor searches in the reduced intermediate dimensional representation rather than the original high-dimensional space. This parameter change exploits the fact that locality relationships are preserved in the reduced space, enabling fast approximate searches that can be refined selectively for the most important results.
Data Source
AI summary
A computer-implemented information retrieval method for generating visualization data from a database of objects, the method comprising the steps of establishing an index structure for a plurality of database objects, searching the index structure for nearest neighbors of database objects, generating a minimum spanning tree from nearest neighbors found, and generating visualization data from the minimum spanning tree. Further provided is a method of visualization of data objects in a database, the method comprising establishing an index structure for a plurality of database objects, searching the index structure for nearest neighbors of database objects, generating a minimum spanning tree from nearest neighbors found, generating visualization data from the minimum spanning tree and generating a display based on the visualization data.