# Slope-Dependent Rendering of Parallel Coordinates to Reduce Density Distortion and Ghost Clusters

## TL;DR

This paper addresses the slope-dependent distortion in parallel coordinates visualization by proposing a slope-based rendering technique that reduces density distortion and ghost clusters, improving pattern perception.

## Contribution

It formalizes the problem of slope-dependent distortion and introduces a novel, efficient rendering method that mitigates visual biases in parallel coordinates.

## Key findings

- Reduces density distortion and ghost clusters in parallel coordinates.
- Can be implemented with linear time complexity.
- Enhances pattern recognition in multi-dimensional data visualization.

## Abstract

Parallel coordinates are a popular technique to visualize multi-dimensional data. However, they face a significant problem influencing the perception and interpretation of patterns. The distance between two parallel lines differs based on their slope. Vertical lines are rendered longer and closer to each other than horizontal lines. This problem is inherent in the technique and has two main consequences: (1) clusters which have a steep slope between two axes are visually more prominent than horizontal clusters. (2) Noise and clutter can be perceived as clusters, as a few parallel vertical lines visually emerge as a ghost cluster. Our paper makes two contributions: First, we formalize the problem and show its impact. Second, we present a novel technique to reduce the effects by rendering the polylines of the parallel coordinates based on their slope: horizontal lines are rendered with the default width, lines with a steep slope with a thinner line. Our technique avoids density distortions of clusters, can be computed in linear time, and can be added on top of most parallel coordinate variations. To demonstrate the usefulness, we show examples and compare them to the classical rendering.