Multivariate visualization: A Taxonomy and novel visualization methods

While intuitive visualizations for bivariate analyses are numerous and able to be constructed with relative ease, the same is not true for multivariate analyses. Commonly utilized multivariate visualization strategies are often cognitively taxing for readers and there is little guidance for researchers seeking to decide upon the proper visualization for their analysis. In this paper we seek to rectify these limitations by developing a data analysis taxonomy that allows one to easily identify appropriate visualizations. This taxonomy aims to provide guidance to researchers in their decision-making regarding which multivariate visualization strategy best fits their research question. Our taxonomy classifies research questions into five different categories (zero-order effects, conditioning, moderation, mediation, and clustering), providing example research questions and analyses for each. Throughout, we identify tools appropriate for multivariate visualizations, including ghost lines, added variable plots, and paneling. All these tools are freely available in R through the Flexplot package, as well as in the Visual Modeling module in JASP.

Multivariate visualization of the global COVID-19 pandemic: A comparison of 161 countries

Background The aim of the study was to visualize the global spread of the COVID-19 pandemic over the first 90 days, through the principal component analysis approach of dimensionality reduction. Methods This study used data from the Global COVID-19 Index provided by PEMANDU Associates. The sample, representing 161 countries, comprised the number of confirmed cases, deaths, stringency indices, population density and GNI per capita (USD). Correlation matrices were computed to reveal the association between the variables at three time points: day-30, day-60 and day-90. Three separate principal component analyses were computed for similar time points, and several standardized plots were produced. Results Confirmed cases and deaths due to COVID-19 showed positive but weak correlation with stringency and GNI per capita. Through principal component analysis, the first two principal components captured close to 70% of the variance of the data. The first component can be viewed as the severity of the COVID-19 surge in countries, whereas the second component largely corresponded to population density, followed by GNI per capita of countries. Multivariate visualization of the two dominating principal components provided a standardized comparison of the situation in the161 countries, performed on day-30, day-60 and day-90 since the first confirmed cases in countries worldwide. Conclusion Visualization of the global spread of COVID-19 showed the unequal severity of the pandemic across continents and over time. Distinct patterns in clusters of countries, which separated many European countries from those in Africa, suggested a contrast in terms of stringency measures and wealth of a country. The African continent appeared to fare better in terms of the COVID-19 pandemic and the burden of mortality in the first 90 days. A noticeable worsening trend was observed in several countries in the same relative time frame of the disease’s first 90 days, especially in the United States of America.

Visualization of Multivariate Data on Surfaces

This research builds upon ideas introduced and discussed many years ago that focus on the problem of visualizing multiple attributes on surfaces in a single view. Here we present a new perspective to this problem as well as a solution that allows us to design, visualize and interact with multivariate data on surfaces. Building upon multidisciplinary aspects, we present a new way to visualize multivariate data on surfaces by exploiting the concept of layering. First, we introduce a new real-time rendering technique and the concept of Decal-Maps, which fills a gap in the literature and allow us to create 2D visual representations such as glyphs that follow the surface geometry. Building on this technique, we propose the layering framework to facilitate the multivariate visualization design on surfaces. The use of this concept and framework allows us to connect and generalize concepts established in flat space, such as 2D maps, to arbitrary surfaces. Decal-maps opens up other new possibilities such as the use of interaction techniques. Here we demonstrate this potential by introducing a new interaction technique that allows us to explore multivariate data and to create customized focus+context visualizations on surfaces. This is achieved by introducing a new category of lenses, Decal-Lenses, which extends the concept of magic-lenses from flat space to general surfaces. Finally, this thesis showcases the process of multivariate visual design and data exploration through a series of examples from several domains such as Medicine and Geology.