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Lost in Magnitudes: Exploring Visualization Designs for Large Value Ranges

Katerina Batziakoudi, Florent Cabric, Stéphanie Rey, Jean-Daniel Fekete

TL;DR

The paper presents a design-space approach for visualizing order-of-magnitude values by separating mantissa and exponent, guided by perception research and GoG principles. It introduces the EplusM scale and the Facet encoding, and systematically generates and qualitatively evaluates a wide set of designs, deriving four core guidelines (AcM, DeM, CoM, PaC). Through a crowdsourced experiment comparing EplusM and Facet against linear, logarithmic, and the Scale-Stacked Bar Chart, the authors demonstrate that mantissa–exponent visualizations can achieve comparable or superior accuracy, speed, and confidence for quantitative OMV tasks, particularly when comparing values within similar magnitudes. The work advances OMV visualization practice, provides an open-source tool (OMVis) and data, and outlines future directions for expanding the design space, incorporating interactivity, and broadening audiences. Overall, the study argues that preserving the two-component structure of OMVs while employing collinear positional encodings can enhance precision and user understanding in large value-range visualizations.

Abstract

We explore the design of visualizations for values spanning multiple orders of magnitude; we call them Orders of Magnitude Values (OMVs). Visualization researchers have shown that separating OMVs into two components, the mantissa and the exponent, and encoding them separately overcomes limitations of linear and logarithmic scales. However, only a small number of such visualizations have been tested, and the design guidelines for visualizing the mantissa and exponent separately remain under-explored. To initiate this exploration, better understand the factors influencing the effectiveness of these visualizations, and create guidelines, we adopt a multi-stage workflow. We introduce a design space for visualizing mantissa and exponent, systematically generating and qualitatively evaluating all possible visualizations within it. From this evaluation, we derive guidelines. We select two visualizations that align with our guidelines and test them using a crowdsourcing experiment, showing they facilitate quantitative comparisons and increase confidence in interpretation compared to the state-of-the-art.

Lost in Magnitudes: Exploring Visualization Designs for Large Value Ranges

TL;DR

The paper presents a design-space approach for visualizing order-of-magnitude values by separating mantissa and exponent, guided by perception research and GoG principles. It introduces the EplusM scale and the Facet encoding, and systematically generates and qualitatively evaluates a wide set of designs, deriving four core guidelines (AcM, DeM, CoM, PaC). Through a crowdsourced experiment comparing EplusM and Facet against linear, logarithmic, and the Scale-Stacked Bar Chart, the authors demonstrate that mantissa–exponent visualizations can achieve comparable or superior accuracy, speed, and confidence for quantitative OMV tasks, particularly when comparing values within similar magnitudes. The work advances OMV visualization practice, provides an open-source tool (OMVis) and data, and outlines future directions for expanding the design space, incorporating interactivity, and broadening audiences. Overall, the study argues that preserving the two-component structure of OMVs while employing collinear positional encodings can enhance precision and user understanding in large value-range visualizations.

Abstract

We explore the design of visualizations for values spanning multiple orders of magnitude; we call them Orders of Magnitude Values (OMVs). Visualization researchers have shown that separating OMVs into two components, the mantissa and the exponent, and encoding them separately overcomes limitations of linear and logarithmic scales. However, only a small number of such visualizations have been tested, and the design guidelines for visualizing the mantissa and exponent separately remain under-explored. To initiate this exploration, better understand the factors influencing the effectiveness of these visualizations, and create guidelines, we adopt a multi-stage workflow. We introduce a design space for visualizing mantissa and exponent, systematically generating and qualitatively evaluating all possible visualizations within it. From this evaluation, we derive guidelines. We select two visualizations that align with our guidelines and test them using a crowdsourcing experiment, showing they facilitate quantitative comparisons and increase confidence in interpretation compared to the state-of-the-art.
Paper Structure (56 sections, 2 equations, 11 figures, 2 tables)

This paper contains 56 sections, 2 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Definition and Terminology
  4. Visualization and Perception of Large Value Ranges
  5. Graphical Perception and Visualization Effectiveness
  6. Design space
  7. Boundaries
  8. Dimensions
  9. Data
  10. Marks
  11. Visual channels
  12. Description of Visualizations
  13. Scales
  14. EplusM Scale
  15. Constraints
  16. ...and 41 more sections

Figures (11)

  • Figure 1: Linear bar chart (left) and logarithmic bar chart (right) illustrating a sample of the French government's budget allocations, showcasing order-of-magnitude differences.
  • Figure 2: Mantissa-exponent visualizations: \ref{['fig:SSB']} Scale-Stacked Bar Charts (\ref{['SSB']}) hlawatsch_scale-stack_2013, \ref{['fig:WSB']} Width-Scale Bar Charts (\ref{['WSB']}) hohn_width-scale_2020, \ref{['fig:OMM']} Order of Magnitude Markers (\ref{['OMM']}) borgo_order_2014, \ref{['fig:OML']} Order of Magnitude Color and Line Chart (\ref{['OML']}) braun_reclaiming_2023, \ref{['fig:OMH']} Order of Magnitude Horizon Graph (\ref{['OMH']}) braun_reclaiming_2023.
  • Figure 3: Point, Exp. $\mapsto \textsf{Row}\xspace$ and Intensity, Mant. $\mapsto \textsf{PosY}\xspace$, Nominal $\mapsto \textsf{PosX}\xspace$
  • Figure 4: Two examples of visualizations per dataset: \ref{['fig:vNominal']} Nominal, \ref{['fig:vQuantitative']} Quantitative, \ref{['fig:vTemporal']} Temporal, and \ref{['fig:vOrdinal']} Ordinal. All the visualizations were generated using our OMVis Tool. At the top, visualizations are described according to the design space dimensions (see \ref{['fig:description-of-visualization']}).
  • Figure 5: Sample of "Effective assignments" combinations (3/25) . At the top, visualizations are described according to the design space (see \ref{['fig:description-of-visualization']}), while at the bottom are abbreviations for the guidelines (see \ref{['sec:guidelines']}) each visualization follows (✓). This sample of visualizations use positional channels for both the mantissa and exponent: the first two demonstrate the EplusM scale on the y-axis, and the third provides an example of Facet (the exponent is encoded with Row, and the mantissa with PosY).
  • ...and 6 more figures