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

Abstract

a) Regular rendering (b) Slope-dependent rendering (c) Regular rendering (d) Slope-dependent rendering Figure 1: Comparison of regular parallel coordinates with our slope-dependent polyline rendering. Parallel coordinates face two problems, which are inherent in the technique: (a) depicts three clusters of the same diameter and size across all dimensions. Diagonal changes of the clusters are visually more prominent, as diagonal lines are rendered more closely. (c) shows 200 data points of uniform random clutter/noise in all dimensions. Zig-zag clusters are visible as diagonal lines and are perceived as clusters, although there are no such clusters in the data (ghost clusters). We propose to render each line segment based on its slope between two axes. As a result, clusters are not distorted by their shape (b), and the ghost clusters effect is reduced (d). ABSTRACTParallel coordinates are a popular technique to visualize multidimensional 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.

PC-Expo: A Metrics-Based Interactive Axes Reordering Method for Parallel Coordinate Displays

“…They propose that data scaling using root and log transforms can reveal patterns in PCP lines. Pomerenke et al [38] describe the existence of ghost clusters in PCPs because of line patterns, which can be prevented by adjusting line widths in PCPs at specific positions based on projection angles. Peng et al [36] show how to properly cluster the PCP lines with a strategy that assigns each point to a PCP cluster.…”

Active Pattern Classification for Automatic Visual Exploration of Multi-Dimensional Data

“…The Scagnostics approach for detecting anomalies in SPLOM (scatterplot ma-trix) [34,35] and subsequent improvements [36][37][38][39][40][41] are representative. Following the idea of Scagnostics, researchers have proposed many other indicators for a variety of visualization techniques, such as time series [42,43], treemap [44,45], parallel coordinates [46][47][48][49][50], parallel sets [51], star glyphs [52], and pixel-oriented displays [53]. Seo and Shneiderman [54] used ordinary statistics to select the most suitable views for showing filtered data.…”