Principle:DistrictDataLabs Yellowbrick RadViz Visualization

Knowledge Sources	Yellowbrick Docs Yellowbrick Hoffman et al., 1997
Domains	Machine_Learning, Feature_Analysis, Visualization
Last Updated	2026-02-08 00:00 GMT

Overview

RadViz (Radial Visualization) is a multivariate visualization technique that maps high-dimensional data points onto a two-dimensional circle by treating each feature as a spring attached to a point on the circumference.

Description

In a RadViz plot, $m$ feature axes are distributed uniformly around the circumference of a unit circle. Each data point is positioned inside the circle at the location where the spring forces from all feature axes reach equilibrium. The "force" exerted by each feature axis is proportional to the normalized value of that feature for the given instance. The result is a scatter plot inside the circle where the spatial position of each point encodes its full multivariate profile.

Points that are pulled strongly toward a particular feature axis have a high value for that feature relative to others. Points near the center have roughly equal values across all features. When colored by class, clusters of same-colored points reveal features that jointly discriminate between classes, while overlapping colors indicate regions of the feature space where classes are difficult to separate.

RadViz is most effective for datasets with a moderate number of features (typically 3 to 12) because the circumference becomes crowded with too many axes. The technique requires that all features be min-max normalized to the $[0,1]$ interval so that the spring analogy is meaningful.

Usage

RadViz visualization is used to:

• Explore class separability in a compact two-dimensional view that encodes all features.
• Identify dominant features by observing which axes attract certain classes.
• Detect data uniformity when points cluster near the center, indicating features with similar magnitudes.
• Compare feature importance by examining the angular distribution of class clusters.

Theoretical Basis

Spring Analogy

Given $m$ features, anchor points ${\mathbf{𝐬}}_j$ are placed on the unit circle at angles:

${\theta }_j=\frac{2\pi j}{m},j=0,1,\dots ,m-1$

so that ${\mathbf{𝐬}}_j=(\cos {\theta }_j,\sin {\theta }_j)$.

Point Projection

Each instance ${\mathbf{𝐱}}_i=(x_{i1},\dots ,x_{im})$ is first min-max normalized to $\mathbf{𝐱}{\text{'}}_i$ in $[0,1{]}^m$. The projected position ${\mathbf{𝐩}}_i$ in the plane is then:

${\mathbf{𝐩}}_i=\frac{\sum _{j=1}^{m}x{\text{'}}_{ij}\cdot {\mathbf{𝐬}}_j}{\sum _{j=1}^{m}x{\text{'}}_{ij}}$

This is the weighted average of the anchor positions, where the weights are the normalized feature values. Points with a single dominant feature are pulled close to that feature's anchor; points with balanced features sit near the origin.

Properties

• All projected points lie within the unit circle.
• The visualization is sensitive to feature ordering around the circumference (adjacent features interact visually).
• Features with zero or near-zero variance contribute negligible spring force.

Related Pages

Implemented By

• Implementation:DistrictDataLabs_Yellowbrick_RadViz_Visualizer