1. Visualizing the Relationship of Multi-dimensional Data in 2D Relationship Space
Strength of relation
High
Low
Number of data
Relationship
Data
Mapping Between 2D Data Space and 2D Relationship Space
The intensity shows the number of data under each relation strength.
The spatial relationship of the grids encodes the relationship of data points
The properties of the relationship space depend on the different relations.
Lei Wang and Arie Kaufman
Computer Science Department, Stony Brook University
Possible Applications:
Data Analysis: Visualize the relationship between data and features.
Data Classification: Classify the data according to the relationship.
Data Feature Detection: Extract features with special relation properties.
Data Visualization: Visualize the data based on the relationship.
Data Registration: Register the data with similar relationship in two data sets.
Volume Data Analysis
Noise
Bias
Distortion
The relationship space is calculated from the features of the 3D volume data, using feature distance as a relation.
The relationship space is invariant under noise, bias, and distortion. It shows the relationship of the data.
Volume Data Visualization
The relationship of the space is used for transfer function designation.
Bonsai
Lobster
Volume Data Classification
Volume
Feature
Relationship
The classification is obtained by classifying the grids in the relationship space.
We use 2D data for the convenience of display. The algorithm and properties are same in high-dimensional data space.