  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.
