History and Principles of Data Visualization

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1 History and Principles of Data Visualization (CMSC Topics in Scientific Computing; Autumn 2014) Sept 30, 2014 Gordon Kindlmann

2 How to learn about a set of numbers? Summary statistics Sets I, II, III, IV of (xi,yi) have identical: mean, variance {xi} mean, variance {yi} line of best fit (least-squares sense)

3 Anscombe s quartet

4 Anscombe s message A computer should make both calculations and [Anscombe-GraphsInStatAn-1973] graphs. Both sorts of output should be studied; each will contribute to understanding Thought and ingenuity devoted to devising good graphs are likely to pay off In practice,we do not know that the theoretical description is correct, we should generally suspect that it is not, and we cannot therefore heave a sigh of relief when the regression calculation has been made, knowing that statistical justice has been done. (i.e. If you re doing computations on data, you need to see what you re doing!)

5 2012 Presidential Election REPUBLICAN DEMOCRAT

6 2012 Presidential Election

7 2012 Presidential Election

8 2012 Presidential Election

9 2012 Presidential Election

10 Clarifying distortions Tube map from

11 Clarifying distortions Harry Beck

12 Clarifying distortions

13 Clarifying distortions Joachim Böttger, Ulrik Brandes, Oliver Deussen, Hendrik Ziezold, Map Warping for the Annotation of Metro Maps IEEE Computer Graphics and Applications, 28(5):56-65, 2008

14 Maps reflect conventions, choices, and priorities A single map is but one of an indefinitely large number of maps that might be produced for the same situation or from the same data. Mark Monmonier How to Lie with Maps, 1991

15 Showing population flux moving in moving out Note use of (roughly) opponent hues in colormap, centered around gray (neutral) to indicate zero

16 Different tasks for colormaps

17 Value of showing isocontours Quality/Utility of colormap hinges on perceptual psychology

18 Affordances uncomfortable object design by Katarina Kamprani Our experiences of the affordances in design is also part of psychology

19 Three main bodies of knowledge Cartography / Geography Statistics Psychology

20 Fields of Visualization Statistics, Machine Learning Computer Science Computer Graphics Human-computer interaction Perceptual Psychology Information Visualization Calculus, Numerical Methods Scientific Visualization Data Visualization Infographics Scientific Illustration

21 This class: Goal: understand the underlying principles at play in data visualization (practice & research), and their history How: 1) Read, present, discuss the commonly cited literature and its context 2) Do a project implementing a vis method Why this class?

22 What is being visualized? Data = set of values (or datum) X Spreadsheet: {Xi}i=1..N; Xi=(ai,bi,ci,...) coordinates may be spatial or geographical Function of time: X = F(t) Function over 2D X = F(u,v) i.e. an image, or volume F(u,v,w), or 3D surface F(s,t) Graph: X = (Vert,Edge) or (Vert,Arrow) Each X is a label or number (or vector of them) Each different type (or flavor) of number has its own mathematical structure: scales of measurement

23 Scales of measurement

24 Later Some Stevens 4 scales of measurements Nominal Categorical Qualitative Ordinal Interval Ratio scales specialize earlier scales examples of these...

25 Ratio The structure of data values discrete qualitative Categorical Ordinal Understanding the nature of the data helps choose sensible ways to show it continuous quantitative Interval 0 Scalars Vectors Tensors

26 Value of showing isocontours

27 Fields of Visualization related to data {Xi}i=1..N; Xi=(ai,bi,ci,...) Information Visualization X = F(t) X = (Vert,Edge) X = F(u,v) Scientific Visualization X = F(u,v,w) X = F(s,t) (3D surface) X : vectors, tensors

of seeing data: survey of fields of visualization

Ways A Gordon of seeing data: survey of fields of visualization Kindlmann glk@uchicago.edu Nov 19, 2012 Part of the talk series Show and Tell: Visualizing the Life of the Mind http://rcc.uchicago.edu/news/show_and_tell_abstracts.html