Dimensionality Reduction via Orthogonal Grid Mapping
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Solution Overview
Problem
Multidimensional databases with a large number of dimensions pose challenges in visualizing and understanding relationships or patterns within the data, especially when the data is sparse, making it difficult for users to analyze, particularly when variables of interest are non-numeric or unknown.
Innovation Solution
The apparent dimensionality of a data set is reduced by ranking combinations of dimensions and parts of dimensions in terms of their suitability for mapping to the axes of a grid display, allowing users to view dense lower-dimensional data that is easier to comprehend, using techniques such as assigning aggregate measures of orthogonality and identifying regions of orthogonality between combinations of locator-serving columns.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If the number of dimensions in a multidimensional database is increased to capture more data perspectives, then the comprehensiveness of data analysis is improved, but the difficulty of visualizing and understanding relationships in the data increases
Solution Approach 1:
The patent extracts and identifies orthogonal combinations of dimensions from the full multidimensional space. By taking out only the orthogonal dimension combinations that form a complete basis, the system reduces the visualized data to essential relationships while maintaining analytical completeness. This extraction transforms the problematic high-dimensional visualization into a manageable set of orthogonal relationships.
Solution Approach 2:
The patent changes the dimensional representation by transforming the original non-orthogonal dimensions into an orthogonal basis through linear combinations. This dimensionality transformation creates a new coordinate system where the data relationships are represented in terms of orthogonal axes, making visualization and understanding significantly easier while preserving the original data's analytical completeness.
2Adaptability or versatility
If the data is organized in a multidimensional cube with many dimensions, then the ability to analyze data from multiple perspectives is improved, but the sparsity of the data increases making most views empty
Solution Approach 1:
The patent extracts only the orthogonal dimension combinations that actually contain meaningful data relationships. By identifying and taking out only these orthogonal combinations rather than displaying all possible dimension combinations, the system eliminates empty cells while preserving all analytical perspectives. This extraction approach maintains multi-perspective analysis capability while dramatically improving data density.
Solution Approach 2:
The patent changes the parameter representation by transforming the data into an orthogonal basis where each dimension represents an independent relationship. This parameter transformation reorganizes the data structure so that only meaningful relationships are preserved, eliminating sparsity while maintaining the ability to analyze from multiple perspectives through the transformed orthogonal dimensions.
3Difficulty of detecting and measuring
If classic dimensionality reduction techniques are used, then the apparent dimensionality is reduced improving visualization, but the technique requires numeric variables which are not always available
Solution Approach 1:
The patent creates a universal dimensionality reduction approach that works with any data type by identifying orthogonal relationships in the data structure itself, rather than requiring numeric transformations. This universal method can handle categorical, ordinal, and numeric variables equally well by finding orthogonal combinations that work for the specific data type, making the technique broadly applicable across different data scenarios.
Solution Approach 2:
The patent introduces orthogonal combinations as an intermediary representation layer between the original dimensions and the visualization. This intermediary transforms the data into a form that is easily visualizable while preserving the relationships in the original non-numeric data. The orthogonal combinations serve as a mediator that bridges the gap between complex non-numeric data and simple visual representations.
Data Source
AI summary
A solution is provided wherein the apparent dimensionality of a data set is reduced by ranking combinations of dimensions and parts of dimensions in terms of their suitability for mapping to the axes of a grid display. A user may then be presented with dense lower dimensional views of the data that are much easier to understand than sparse high dimensional views. The user may then make further refinements, groupings, and analyses as needed.