Editor: Visualization Viewpoints Theresa-Marie Rhyne Pathways for Theoretical Advances in Visualization Min Chen Jessie Kennedy University of Oxford Edinburgh Napier University Georges Grinstein Melanie Tory University of Massachusetts Tableau Software Chris R. Johnson University of Utah ore than a decade ago, Chris Johnson Visualization theory is commonly viewed as a re- proposed the “Theory of Visualization” search focus for only a few individual researchers. as one of the top research problems in Its outcomes, perhaps in the form of theorems or Mvisualization.1 Since then, there have been several laws, are perceived as too distant from practice to be theory-focused events, including three workshops useful. Perhaps inspired by well-known theoretical and three panels at IEEE Visualization (VIS) Con- breakthroughs in the history of science, visualiza- ferences. Together, these events have produced a tion researchers may unconsciously have high ex- set of convincing arguments: pectations for the originality, rigor, and significance of the theoretical advancements to be made in a ■ As in all scientific and scholarly subjects, theo- research project or presented in a research paper. retical development in visualization is a neces- On the contrary, although textbooks tend to sary and integral part of the progression of the attribute major breakthroughs to single pioneers subject itself. at specific times and places, in most cases, such ■ Theoretical developments in visualization can breakthroughs generally take years or even decades draw on theoretical advances in many disci- and are usually the product of numerous incremen- plines, including, for example, mathematics, tal developments, including a substantial number computer science, engineering science, psychol- of erroneous solutions suggested by the pioneers ogy, neuroscience, and the social sciences. themselves as well as many lesser-known individu- ■ Visualization holds a distinctive position, con- als. Many complex discoveries did not initially ap- necting human-centric processes (such as hu- pear to have elegant proofs, and it has taken some man perception, cognition, interaction, and challenging and often questionable steps to obtain communication) with machine-centric pro- the well-formulated solutions we find in modern cesses (such as statistics, algorithms, and ma- textbooks. For example, most readers associate the chine learning). It therefore provides a unique theory of general relativity with Albert Einstein’s platform to conduct theoretical studies that may November 1915 discovery in Berlin. According impact on other disciplines. to Petro Ferreira,2 Einstein first speculated about ■ Compared with many mature disciplines (such the generalization in 1907. He then published two as mathematics, physics, biology, psychology, and papers with Marcel Grossmann (Zurich) in 1913 philosophy), theoretical research activities in vi- that sketched out the theory and worked with sualization are sparse. The subject can therefore David Hilbert (Göttingen) on the problem in benefit from a significantly increased effort to June 1915. Some of the most important discover- make new theoretical advances. ies related to the theory of general relativity are Published by the IEEE Computer Society 0272-1716/16/$33.00 © 2016 IEEE IEEE Computer Graphics and Applications 103 Visualization Viewpoints Providing mathematical validation and numerical prediction Enabling measurement, abstraction, and deduction of laws Suggesting Providing context casual relations and structure Quantitative Taxonomies Principles Conceptual Theoretic laws and and ontologies and guidelines models frameworks theoretic systems Subset becoming a model Model becoming a system Transforming to axioms, theorems, and conjectures Providing denitions, categorization, and suggested relations Figure 1. A theoretical foundation typically evolves through iterative developments. The development of each aspect both influences and benefits from that of others. A successful transformation between different aspects indicates a theoretical enhancement of understanding. Note that the third aspect, “Conceptual Models and Theoretic Frameworks,” is represented by two boxes in the figure. Mercury’s perihelion shift (Le Verrier, 1859), the In this article, we first review four major aspects 1919 eclipse expedition (Edington, Cottingham, of a theoretical foundation and then discuss the Crommelin, and Davidson), the evolving universe interactions and transformations between them. (Fredmann, 1922; Lemaître, 1927), the expanding Figure 1 provides an overview of the discourse in universe (Slipper, 1915; Lundmark, 1924; Hubble this article. and Humason, 1929), the big bang (Lemaître, 1931), and the black hole (Schwarzschild 1916, Taxonomies and Ontologies Chandrasekhar, 1935; Landau, 1938; Oppenheimer For millennia, humans have been classifying and his students, 1939). Some ill-fated solutions things in the world around them by describing also followed Einstein’s 1915 discovery, the most and naming concepts to facilitate communication notable of which were perhaps the static universe (see the “History of Taxonomy and Ontology” (Einstein and de Sitter) and the suspended uni- sidebar). The most significant and enduring effort verse (Eddington). is the classification of life on Earth, which com- During an Alan Turing Institute event in Lon- menced in Aristotle’s time, became mainstream don in April 2016 on the theoretical foundation of through the work of Linnaeus, and continues to visual analytics, discussions on the need to build this day with new species being identified and al- such a theoretical foundation varied greatly, with ternative classifications of existing species being opinions ranging from “Visualization should not proposed.3 Alternative classifications taxonomies( ) be physics-envy” to “It is irresponsible for academ- arise over time as a result of differing opinions ics not to try.” After two days of presentations, about the importance of differentiating character- discussions, and debates, the attendees gradually istics used in creating the concepts (taxa). These converged on a common understanding that a differing opinions are usually the result of new theoretical foundation consists of several aspects information becoming available, often through (see the “Major Aspects of a Theoretical Founda- technological advances, which can result in the tion” sidebar for more details) and that every visu- same organism being classified according to dif- alization researcher should be able to make direct ferent taxonomic opinions and subsequently hav- contributions to some aspect of the theoretical ing several alternative names, which may in turn foundation of visualization. lead to miscommunication. Newer classifications During the IEEE VIS Conference in Baltimore, are usually improvements on previous ones, but Maryland, in October 2016, a discussion panel took sometimes the existence of alternative classifica- this viewpoint further by outlining avenues for pur- tions reflects a disagreement as to how to interpret suing theoretical research in each aspect. This ar- the data on which the classification is based. ticle is a structured reflection by the panelists about Ontologies are representations of different rela- the discussions during that IEEE VIS 2016 panel. tionships among various concepts. Naturally, they 104 July/August 2017 Major Aspects of a Theoretical Foundation are built on the taxonomic classification of the concepts of both entities and relationships. Tax- ttendees at an Alan Turing Institute event in London in April 2016 onomies and ontologies are means of conceptu- Aon the theoretical foundation of visual analytics reached a con- alizing, understanding, organizing, and reasoning sensus that a theoretical foundation consists of the following aspects. about these entities and relationships. They are central to communicating about the world around Taxonomies and Ontologies us. They play an increasing role in understanding In scientific and scholarly disciplines, a collection of concepts are in the visualization field, allowing us to organize commonly organized into a taxonomy or ontology. In the former, and formalize our knowledge. concepts are known as taxa and are typically arranged hierarchically A brief review of the literature over the past three using a tree structure. In the latter, concepts, often in conjunction decades reveals at least 70 publications containing with their instances, attributes, and other entities, are organized some form of visualization taxonomy.3 Three ques- into a schematic network, where edges represent various relations tions are relevant when considering visualization and rules. taxonomies: What is being classified (domain)? Why is the taxonomy being developed (purpose)? Principles and Guidelines How is the taxonomy constructed (process)? Tax- A principle is a law or rule that must be followed and is usually ex- onomies have been proposed to classify many as- pressed in a qualitative description. A guideline describes a process pects of visualization, including systems, tools, or a set of actions that may lead to a desired outcome or, alterna- techniques, interaction approaches, data types, tively, actions to be avoided to prevent an undesired outcome. The user tasks, visual encodings, input methods, and former usually implies a confidence in the high degree of generali- evaluation strategies. These aspects can be classi- ty and certainty of the causality concerned, whereas the latter sug-