Data Visualization A talk for Computer Graphics Seminar Lauri - - PowerPoint PPT Presentation

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Data Visualization

A talk for Computer Graphics Seminar Lauri Listak lauri@listak.net

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Table of Contents

Data visualization: what for? The human perception Information visualization To see and to listen References Thank you!

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Data visualization: what for?

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Problem statement

We want to represent information in a graphical way to gain a better understanding of it. Technology gives us ways to enhance the representation. Do you think nothing happened before computers?

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Data visualization, formally

Mapping from data domain to graphics domain It is OK and even needed to lose some information

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Information visualization

Abstract data is to be represented in a visual form That kind of data is mostly represented "in a weird way", so have to think of a way to represent it in a sensible way Use cases: statistics and it's relatives

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Information visualization: Newcomb fraternity

Actually a visualization of a friendship graph 17 men, 15 weekly ratings Evolution of rank is shown by length, balance is shown by angle Diagonal shows the average deviation of nominations from expected value

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Scientific visualization

We know the representation of the data, let's draw it! Use cases: anything to do with STEM, mostly 3D representations

Scientific visualization: human skull

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Scientific visualization: a 3D contour plot with heatmaps

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Technical visualization

One of the areas of domain-specific visualization 2D for technical drawings 3D for design, modeling, simulation Use cases: Computer Aided Design, Computer Aided Manufacturing

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Technical visualization: a simulation of turning

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The human perception

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Color

RGB is for computers and CMYK for printers Human beings have eyes: different color schemes have been thought about that, such as HSL, HSV and HSI

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From RGB to HSV

V = max(R,G,B) D = V – min(R,G,B) S = D/V if V == R: H = (G-B)/D elif V == G: H = (B-R)/D else: H = (R-G)/D H = (60*H) mod 360

Value - distance from black Saturation - distance from gray Hue - angle around the color wheel

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Hue circle

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Choosing a color scheme: colorbrewer

http://colorbrewer2.org/

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Size and scale

Use the context to help deliver perception about size and scale

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Comparison of other methods

From most accurate to least accurate:

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The mapping of methods, Tableau/Polaris system

Four visual channels with regards to data type:

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Perspective

Using anything 3D must be really thought about Our perception of distance influences our perception of size of the object

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Memory

Avoid animation: it is hard to remember things Just draw multiple plots

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Seeing change

To see an object change, it is necessary to attend to it. (Rensink)

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Seeing change: flicker

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Seeing change: frame A

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Seeing change: frame B

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Tufte's principles

Redacted and simplified: tell the truth data is the most important use minimal ink graphical effects are not required use sparklines

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Shneiderman's Visual Information Seeking Mantra

Overview first, zoom and filter, then details-on-demand

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Information visualization

Isarithmic map

Very easy to misuse Think about your data: continuous values vs discrete points Interpolation for continuous values, kernel density for discrete points

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Heat map

Interpolate colors according to matrix values Perform clustering Perform seriation

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Contour plot

Can be both in 2D and 3D Also known as isolines, isopleths, isochrones, isarithms, isodistances, etc - depending on the domain and type of the map Usually known from geography and meteorology, but useful everywhere in the natural sciences

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The CONREC algorithm

Input: contouring levels, samples of the surface, horizontal and vertical coordinates of each sample point Output: horizontal and vertical coordinates of line segments with contour level

• 1. Consider a rectangle
• 2. Assign a value to the center of the rectangle
• 3. Cut along the diagonals to get 4 triangles
• 4. Bisect the triangles with the contour plane
• 5. Consider the possible cases

d(i, j), d(i + 1, j), d(i, j + 1), d(i + 1, j + 1)

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CONREC: possible cases

a) All the vertices lie below the contour level. b) Two vertices lie below and one on the contour level. c) Two vertices lie below and one above the contour level. d) One vertex lies below and two on the contour level. e) One vertex lies below, one on and one above the contour level. f) One vertex lies below and two above the contour level. g) Three vertices lie on the contour level. h) Two vertices lie on and one above the contour level. i) One vertex lies on and two above the contour level. j) All the vertices lie above the contour level.

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CONREC: cases visually

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CONREC: in progress

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CONREC: landscape example

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Stacked graphs

Used for visualizing time series

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Usual stacked graph

The general formula for a layer is

= + gi g0 Σi

j=1fj

Baseline is set at 0:

= 0 g0

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ThemeRiver optimization

Try to use a layout symmetric around the -axis

x + = 0 g0 gn 2 + = 0 g0 Σn

i=1fi

= − g0

1 2 Σn i=1fi

Minimizes sum of squares of top and bottom silhouette, sum of squares of slopes of and at each point

g0 gn

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Streamgraph ordering

• 1. total weight
• f each series
• 2. in case of

, add to bottom, else add next series to top

wi i ( +. . . + ) > ( +. . . + ) wi wn/2 wn/2+1 wn

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Graph embedding

Wagner's theorem: a graph is planar iff it's minors do not include

• r

G G K5 K3,3

A graph minor is obtained when deleting edges, vertices or by edge contraction: remove an edge and merge the two vertices

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Tutte embedding

Input: graph G

• 1. find the boundary nodes and assign them 2D positions
• 2. create the Laplacian matrix

, where for edge between node and node

• 3. zero out rows for already used nodes

4.

• 5. Solve for coordinates:
• 6. Solve for coordinates:

L = Lij

1 deg(i)

i j A = I − L x Ax = bx y Ax = by

Actually can be solved other way also: do step 1 and iteratively average positions for the rest of the nodes

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When Tutte fails

Tutte embedding does not work for nodes

> 100

Tutte embedding can sometimes look not nice enough:

Alternative: force-directed graph drawing

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Alternative: force-directed graph drawing

Then force-directed graph drawing is used, where center of the graph has a gravitational pull and nodes exert force on each

• ther: they have "springs" or energy between them

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Multidimensional scaling

A set of input points and a distance matrix with

n , . . . , x1 xn M n × n = dist( , ), i, j = 1, . . . , n Mi,j xi xj

Claimed: distance is not actually required to be a metric After that, use your favorite optimization method to minimize for:

(||( , ) − ( , )|| − Σj=1..n−1Σi=i+1..j xi yi xj yj dij)2

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Multidimensional scaling: flattening meshes

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Parallel coordinates

For plotting multivariate data Basically, parallel axes are placed on the Cartesian coordinate system

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Parallel coordinates: example

Discrete parallel coordinates for hurricane Isabel at 50x50x10 spatial resolution

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Scattering points in parallel coordinates

Can be integrated with scatter plots

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Line integral convolution

Used for modeling a vector field or for motion blur Input: an image, a vector field Output: convolution of the intensity values over the integral curves of the vector field Vector field - each point is assigned a vector Integral curve - how much does the vector field affect the particle? Convolution - pick a suitable kernel

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To see and to listen

• B. Shneiderman. The Eyes Have It: A Task by Data Type Taxonomy for Information Visualizations

Edward Tufte, The Visual Display of Quantitative Information Tamara Munzner: Keynote on Visualization Principles (available at Vimeo) Raymond C. H. Lo, William C. Y. Lo. OpenGL Data Visualization Cookbook

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References

John C. Hart. Data Visualization. Coursera. Christopher G. Healey. Perception in Visualization. Ricardo David Castaneda Marin. Using Line Integral Convolution to Render Effects on Images Roberto Tamassia. Handbook of Graph Drawing and Visualization Lee Byron & Martin Wattenberg. Stacked Graphs – Geometry & Aesthetics

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Thank you!