Visualizing the Relationship of Multi-dimensional Data in 2D Relationship Space

Lei Wang and Arie KaufmanComputer Science Department, Stony Brook University

We use 2D data for the convenience of display. The algorithm and properties are same in high-dimensional data space.

Relationship Space

Strength of relation High Low

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RelationshipData

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. 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 VisualizationThe 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.