Abstract The application of parallel axes for the interactive visual analysis of multidimensional data is a widely used concept. While multidimensional data sets are commonly heterogeneous in nature, i.e. data items contain both numerical and categorical (including ordinal) attribute values, the use of parallel axes often assumes either numerical or categorical attributes. While Parallel Coordinates and their large variety of extensions focus on numerical data, Parallel Sets and related methods focus on categorical attributes. While both concepts allow for displaying heterogeneous data, no clear strategies have been defined for representing categories in Parallel Coordinates or discretization of continuous ranges in Parallel Sets. In practice, type conversion as a pre‐processing step can be used as well as coordinated views of numerical and categorical data visualizations. We evaluate traditional and state‐of‐the‐art approaches with respect to the interplay of categorical and numerical dimensions for querying probability‐based events. We also compare against a heterogeneous Parallel Coordinates/Parallel Set approach with a novel interface between categorical and numerical axes . We show that approaches for mapping categorical data to numerical axis representations can lead to lower accuracy in answering probability‐based questions and higher response times than hybrid approaches in multiple‐event scenarios.

Abstract Mixed data sets containing numerical and categorical attributes are nowadays ubiquitous. Converting them to one attribute type may lead to a loss of information. We present an approach for handling numerical and categorical attributes in a holistic view. For data sets with many attributes, dimensionality reduction (DR) methods can help to generate visual representations involving all attributes. While automatic DR for mixed data sets is possible using weighted combinations, the impact of each attribute on the resulting projection is difficult to measure. Interactive support allows the user to understand the impact of data dimensions in the formation of patterns. Star Coordinates is a well‐known interactive linear DR technique for multi‐dimensional numerical data sets. We propose to extend Star Coordinates and its initial configuration schemes to mixed data sets. In conjunction with analysing numerical attributes, our extension allows for exploring the impact of categorical dimensions and individual categories on the structure of the entire data set. The main challenge when interacting with Star Coordinates is typically to find a good configuration of the attribute axes. We propose a guided mixed data analysis based on maximizing projection quality measures by the use of recommended transformations, named hints, in order to find a proper configuration of the attribute axes.

Principal curves are a long-standing and well-known method for summarizing large scatterplots. They are defined as self-consistent curves (or curve sets in the more general case) that locally pass through the middle of the scatterplot data. However, computing principal curves that capture well complex scatterplot topologies and are robust to noise is hard and/or slow for large scatterplots. We present a fast and robust approach for computing principal graphs (a generalization of principal curves for more complex topologies) inspired by the similarity to medial descriptors (curves locally centered in a shape). Compared to state-of-the-art methods for computing principal graphs, we outperform these in terms of computational scalability and robustness to noise and resolution. We also demonstrate the advantages of our method over other scatterplot summarization approaches.

Scatterplot matrices (SPLOMs) are widely used for exploring multidimensional data. Scatterplot diagnostics (scagnostics) approaches measure characteristics of scatterplots to automatically find potentially interesting plots, thereby making SPLOMs more scalable with the dimension count. While statistical measures such as regression lines can capture orientation, and graph-theoretic scagnostics measures can capture shape, there is no scatterplot characterization measure that uses both descriptors. Based on well-known results in shape analysis, we propose a scagnostics approach that captures both scatterplot shape and orientation using skeletons (or medial axes). Our representation can handle complex spatial distributions, helps discovery of principal trends in a multiscale way, scales visually well with the number of samples, is robust to noise, and is automatic and fast to compute. We define skeleton-based similarity metrics for the visual exploration and analysis of SPLOMs. We perform a user study to measure the human perception of scatterplot similarity and compare the outcome to our results as well as to graph-based scagnostics and other visual quality metrics. Our skeleton-based metrics outperform previously defined measures both in terms of closeness to perceptually-based similarity and computation time efficiency.