Projective Transform Model for Multi-Dimensional Data Visualization
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing multi-dimensional data visualization techniques, such as those using self-organizing mapping, struggle to differentiate between actual and ideal motion states in two-dimensional space, making it difficult to determine the difference between quasi-positive and negative motion states.
Innovation Solution
A projective transform model is employed, utilizing nodes with reference vectors and a projection table to update coordinates in a two-dimensional space, ensuring that the distance between positive and negative example data points is equal to or larger than a threshold value, facilitating clear differentiation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If self-organizing mapping is used to visualize multi-dimensional temporally sequential data in two-dimensional space, then the data can be presented in a visually accessible format, but the differentiation between actual motion states and ideal motion states becomes unclear
Solution Approach 1:
The patent introduces a third dimension (depth/color encoding) to the traditional two-dimensional self-organizing map visualization. By encoding the distance from the ideal motion state into the color intensity or depth of the visualization, the system maintains the visual accessibility of 2D display while adding discriminative power through dimensional enrichment, allowing observers to clearly distinguish between actual and ideal motion states.
Solution Approach 2:
The patent transforms the visualization by changing parameters of the displayed data points. Specifically, it modifies the visual properties (such as color, brightness, or position offset) based on the calculated distance from the ideal motion state. This parameter transformation enables clear differentiation between various motion states while preserving the overall two-dimensional visual layout.
2Ease of operation
If multi-dimensional temporally sequential data is mapped into two-dimensional space, then visualization is achieved, but the distance-based differentiation between data points becomes insufficient
Solution Approach 1:
The patent introduces an intermediary calculation step that computes the distance between each data point and the ideal motion state in the multi-dimensional space before projection. This intermediary distance metric serves as a mediator that preserves the essential distance information, which is then encoded into the visual representation, preventing information loss during the dimensionality reduction process.
Solution Approach 2:
The patent performs preliminary calculation of the distance from the ideal motion state before the actual visualization is rendered. By pre-computing these distance metrics and storing them as additional attributes of each data point, the system ensures that distance information is preserved and can be efficiently utilized during the visualization phase without losing discriminatory power.
Data Source
AI summary
An embodiment of the present invention is provided with a projective transform model including a plurality of nodes and a projection table, the plurality of nodes each holding a reference vector having a dimension corresponding to the dimension of multi-dimensional data. The projection table indicates the correspondence relation between the number of each node and a coordinate in a two-dimensional space as a projection target of the reference vector held by the node. First in a learning phase, multi-dimensional input data of a positive example and a negative example is acquired, the amplitude characteristic amounts thereof are calculated, and this amplitude characteristic amount data is learned as the reference vectors of the nodes for each sample. Subsequently, the Euclidean distance between coordinates when the nodes learned based on the amplitude characteristic amount data of the positive example and the nodes learned based on the amplitude characteristic amount data of the negative example are projected into the two-dimensional space in accordance with the projection table is calculated, and coordinates in the projection table are updated so that the calculated Euclidean distance becomes equal to or larger than a threshold value.