The ability to perceive patterns in parallel coordinates plots (PCPs) is heavily influenced by the ordering of the dimensions. While the community has proposed over 30 automatic ordering strategies, we still lack empirical guidance for choosing an appropriate strategy for a given task. In this paper, we first propose a classification of tasks and patterns and analyze which PCP reordering strategies help in detecting them. Based on our classification, we then conduct an empirical user study with 31 participants to evaluate reordering strategies for cluster identification tasks. We particularly measure time, identification quality, and the users’ confidence for two different strategies using both synthetic and real‐world datasets. Our results show that, somewhat unexpectedly, participants tend to focus on dissimilar rather than similar dimension pairs when detecting clusters, and are more confident in their answers. This is especially true when increasing the amount of clutter in the data. As a result of these findings, we propose a new reordering strategy based on the dissimilarity of neighboring dimension pairs.
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.
Learning arguments is highly relevant to the field of explainable artificial intelligence. It is a family of symbolic machine learning techniques that is particularly human-interpretable. These techniques learn a set of arguments as an intermediate representation. Arguments are small rules with exceptions that can be chained to larger arguments for making predictions or decisions. We investigate the learning of arguments, specifically the learning of arguments from a 'case model' proposed by Verheij [32]. The case model in Verheij's approach are cases or scenarios in a legal setting. The number of cases in a case model are relatively low. Here, we investigate whether Verheij's approach can be used for learning arguments from other types of data sets with a much larger number of instances. We compare the learning of arguments from a case model with the HeRO algorithm [15] and learning a decision tree.
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