Representation. (R. Spence, 2007)

Transcription

1 Representation (R. Spence, 2007) InfoVis, Universidade de Aveiro Beatriz Sousa Santos

2 Data and gain insight We look at that picture Ah HA!! Information visualization The process of information visualization: graphically encoded data is viewed in order to form a mental model of that data (Spence, 2007)

3 DATA REPRESENTAT ION of data PRESENTATION of the represented data PERCEPTION INTERPRETATION HIGHER-ORDER COGNITIVE PROCESSES Problem (re)formulation Evaluation of options Strategy formulation Internal modelling etc. INTERACT ION to select the required view of data Decision making The scope of this book (Spence, 2007) Interaction with data governed by high-order cognitive processes: - Representation (how to code visually the data) - Presentation (what/when/where to show on the screen) - Interaction (how to let users explore the data) 3

4 The Human Visual system is the product of millions of years of evolution Although very flexible, it is tuned to data represented in specific ways If we understand how its mechanisms work we will be able to produce better results 4

5 Color may support users in many tasks: Example: Count the cherries (Ware, 2004) But, if not properly used, may make the task more difficult! It should be carefully selected

6 Representing quantitative data using color is particularly difficult Which map is easier to understand? 6 (Tufte, 1990)

7 Not everyone sees color: The most common form of color blindness is deuteranopia ( daltonism ) There are color blindness simulators / Normal vision Deuteranopia Tritanopia

8 Visual attributes as size, proximity, color are quickly processed by visual perception, before the cognitive processes come into play Example: mapping numerical values to the length of bars: Computers have been responsible for advances in InfoVis, due to: - Less expensive and more rapid memory - More processing power and faster - High resolution graphic displays (Mazza, 2009)

9 An example illustrating the potential benefit of rearranging the visual representation of the data: Results of an experiment: ten crops received seven different treatments. black square successful treatment white square not successful Rearranging rows and columns allows to better notice that groups of treatments seem effective for groups of crops Treatments Treatments A B C D E F G A D C E G B F Crops Rearrange Crops (Spence,2007)

10 But, after all, How to create a Visual representation?

11 Creating Visual Representations Good design is the key to success in producing a Visualization Visualization S/W can provide many visual templates In spite of variation, all S/W packages follow the same generation process reference model: (Mazza, 2009)

12 1. Preprocessing: Abstract data (which don t have a specific connection with physical space) are rarely in a suitable format for automatic treatment and visualization Raw data (data supplied by the world around us, a.k.a. datasets) have to be given an organized logical structure to be processed by the Visualization S/W

13 2. Visual mapping: It is necessary to decide: - which visual structures use to map the data Some types of abstract data can be easily mapped to a spatial location Examples:. data with a topological or geographical structure Many types of data don t have an easy correspondence with the dimensions of the physical space around us

14 Three structures must be defined in the visual mapping: - spatial substrate - graphical elements - graphical properties Graphical substrate - dimensions in physical space where the visual representation is created (can be defined in terms of axes and type of data) Graphical elements - anything visible appearing in the space points, lines, surfaces, volumes Graphical properties properties of the graphical elements to which the human retina is very sensitive - retinal variables: size, orientation, color, texture, and shape

15 - Spatial substrate axes (x, y, ) type of data (quantitative, ordinal, categorical) - Graphical elements points lines surfaces volumes - Graphical properties retinal variables: size, orientation color (depends on physiology and culture) texture shape

16 Association Selection Order Quantity The marks can be perceived as SIMILAR The marks are perceived as DIFFERENT, forming families The marks are perceived as ORDERED The marks are perceived as PROPORTIONAL to each other Size Value Texture Interpretation of Bertin s guidance regarding the suitability of various encoding methods to support common tasks (Spence, 2007) Colour Orientation Shape

17 Position Most accurate Length Angle Slope Area Volume Colour Density Least accurate The relative difficulty of assessing quantitative value as a function of encoding mechanism, as established by Cleveland and McGill (Spence, 2007)

18 Quantitative Ordinal Categorical Treble Position Length Angle Slope Area Volume Density Shape Position Density Colour saturation Colour hue Texture Connection Containment Length Angle Slope Area Volume Position Colour hue Texture Connection Containment Density Colour saturation Shape Length Angle Slope Area Volume Ba ss Mackinlay s guidance for the encoding of quantitative, ordinal and categorical data (Spence, 2007)

19 3. Creation of views : Views are the final result of the generation process Producing them corresponds to the computer graphics phase: Often the quantity of data to represent is too large for the available space (Spence, 2007) To overcome this problem there are presentation techniques as: Zooming Panning Scrolling Focus + context Magic lenses...

20 Designing a Visualization application The generation process must be preceded by good design The main problem in designing a visual representation is the choice of mapping, as to: - faithfully reproduce the information codified in the data - help the user to attain their goals The visual representation suitable depends on: - the nature of the data - the users profile - the type of information to represent - how it will be used,

21 Procedure to follow to create visual representations of abstract data 1. Define the problem 2. Examine the nature of the data to represent 3. Determine the number of attributes 4. Choose the data structures 5. Establish the type of interaction

22 Five reasons for Tukey s progress: Cleveland, B., The Collected Works of John W. Tukey: Graphics , Vol. 5, Chapman Hill, 1988 (p. xxxv) Tukey has defined the term Exploratory Data Analysis

23 nature of the problem communicate explore confirm nature of the data to represent quantitative ordinal categorical number of attributes univariate bivariate trivariate multivariate Next: representation methods organized according the n. of attributes data structures linear temporal spatial or geographical hierarchical network, static type of interaction transformable manipulable

24 Common Visualization Techniques for univariate, bivariate and trivariate data Univariate data dot plot box plot bar chart histogram pie chart Cherries Apples Kiwis Grapes Oranges Bivariate data scatter plot line plot time series y x Trivariate data surface plot contour plot 3D representation bubble plot x y 28 x z t

25 Representing univariate data A single number can be difficult to represent ensuring a user is made aware of it Example: the altimeter (Spence, 2007) stop 1200 The original aircraft altimeter, responsible for many accidents Two altimeter representations easily assumed to be the same due to change blindness The modern aircraft altimeter,

26 Example of change blindness (Spence, 2007)

27 Example of change blindness (Spence, 2007)

28 - Innattentional blindness - Change blindness

29 Representing univariate data (cont.) A more common situation consists in representing a set of values Well established techniques exist Dot plot Tukey boxplot 60 But new ones can be invented! Example: Price for a number of cars: - dots on a linear scale - box plot (that will answer many questions: median value, outliers,...) Price ( K) (Spence, 2007)

30 8 much of the data is aggregated precise detail is often not needed 6 4 We can represent derived values The histogram is a well known technique representing derived values Tipping over the bars of the histogram a bargram is obtained Price k Missing characteristic:empty bin Categorical or ordinal data can also be represented in bargrams Nissan Ford Ferrari MG Cadillac Price ( K) (Spence, 2007)

31 Simple (and common) representations of data Two common techniques not to be confused! Histogram Bar chart represents a distribution of numerical data represents the number of occurrences of a categorical/ordinal data Both represent data by rectangular bars(vertical or horizontal) with length proportional to the values they represent Tons Fruit production Cherries Apples Kiwis Grapes Oranges Marks of the Exam Bins (mark)

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33 Example: how to select simple charts? Temperatures along the month of February (in ºC): day Max T Min. T Q1- What were the maximum and minimum values of MaxT? Q2- What was the most frequent Max temperature? Q3- In how many days was that Max temperature attained? ºC n. of days day Max (ºC) Which chart would you use to answer Q1? Q2? And Q3? 11 ºC

34 Simple example Temperatures along the month of February (in ºC): day Max T Min. T ºC day Anything odd about this chart? Would you prefer this one? ºC day 40

35 Representing bivariate data The scatterplot is the conventional representation Example: A collection of houses characterized by: - Price - Number of bedrooms Each represented by a point on a two dimensional space N. of bedrooms Price (Spence, 2007) The axes are associated with these two attributes This representation affords awareness of: - general trends - local trade-offs - outliers

36 The time series is a special (and important) case of the scatterplot One of the axes represents time and the other some function of time Example Data set of 52 weekly stock prices for 1430 stocks The graph overview shows the entire data providing some idea of densities and distributions Timeboxes limit the display to items according to some time and price criteria (Spence, 2007)

37 Alternative representation of a time series More suited for gaining an initial impression of data Example: Level of ozone concentration over 10 years above Los Angeles - each square represents one day - and is colored to indicate the ozone level It is apparent that: - ozone levels are higher in Summer - the concentration has been decreasing (Spence, 2007)

38 If one attribute is more important than the other or must be examined first, it may be appropriate to employ logical or semantic zoom 60 Example: 50 Analyzing a list of cars: - price is the first attribute to examine Pri ce ( K) Ford Nissan VW M erc Jag Jag Ford SE AT - semantic zoom reveals data about a second attribute 10 (Spence, 2007) This technique is quite general: it can encompass many attributes and many levels of progressive zoom

39 Example: Zoom in Google Maps

40 Representing Trivariate data Since we live in a 3D world, representing trivariate data as points in a 3D space and displaying a 2D view is natural However, these representations can be ambiguous Price C D This can be solved by interaction, allowing the user to reorient the representation B Bedrooms A for 3D to be useful, you ve got to be able to move it (Spence, 2007) Time

41 Interaction (brushing) can help objects identified in one view are highlighted in the other two planes change blindness must be taken into account and ensure that the user notices the highlight in the other two planes (Spence, 2007) The highlighting of houses in one plane is brushed into the remaining planes.

42 Augmenting a scatterplot: representing 5 variables Hans Rosling's 200 Countries, 200 Years, 4 Minutes: values Income (x), Age expectancy (y), Time (t), Continent (colour), Population (size of circle)

43 Price An alternative representation for trivariate (and hypervariate) data is a structure formed from the three possible 2D views of the data Example: houses (price, number of bedrooms, time of journey to work ) Scatterplot matrix Price D C B Bedrooms A Time Bedrooms (Spence, 2007) A D B C

44 Simple representations of a function (field) of two variables Contour plots contour line (also isoline, isopleth, or equipotential curve) of a a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. Typical in meteorological charts (isobars and isothermal curves) and maps (to represent altitude or depth) 57

45 Surface plots May be combined with color 58

46 A special category of trivariate data: maps (latitute and longitude + a value) Population of major cities in England, Wales and Scotland. Circle area is proportional to population. (Spence, 2007) Things that pop-out

47 Pre-attentive processing: Things that pop out We can do certain things to symbols to make it much more likely that they will be visually identified even after a very brief exposure (Ware, 2004) Orientation Colour Where is the blue square? (Spence, 2007) Shape Enclosure

48 Representing Hypervariate (or multivariate) data Many real problems are of high dimensionality The challenge of representing hypervariate data is substantial and continues to stimulate invention Some of the mentioned representation techniques can be scaled to represent hypervariate data (to a limited extent)

49 Techniques for Hypervariate (or multivariate) data Visualization Coordinate plots parallel coordinate plots star plots Scatterplot Matrix Linked histograms Mosaic Plots Icons

50 Parallel coordinates plots are one of the most popular techniques for hypervariate data They have a very simple basis (Spence, 2007)

51 Consider a simple case of bivariate data: Nu mber of bedrooms A B 1- A scatterplot represents the price and number of bedrooms associated with two houses Price 2- the axes are detached and made parallel; each house is represented by a point on each axis Price Nu mber of bedrooms 3- To avoid ambiguity the pair of points representing a house are joined and labeled B A Price Nu mber of bedrooms

52 For objects characterized by many attributes the parallel coordinate plots offer many advantages A example for six objects, each characterized by seven attributes: trade-off between A and B objects correlation between B and C A B C D E F G attributes The trade-off between A and B, and the correlation between B and C, are immediately apparent. The trade-off between B and E, and the correlation between C and G, are not.

53 A parallel coordinate plot representation of a collection of cars, in which a range of the attribute Year has been selected to cause all those cars manufactured during that period to be highlighted.

54 Properties of parallel coordinate plots: Suitable to identify relations between attributes Objects are not easily discriminable; each object is represented by a polyline which intersects many others They offer attribute visibility (the characteristics of the separate attributes are particularly visible) The complexity of parallel coordinate plots (number of axes) is directly proportional to the number of attributes All attributes receive uniform treatment

55 Mathematics Star plots have many features in common with parallel coordinate plots Sport Physics Chemistry Literature An attribute value is represented by a point on a coordinate axis Attribute axes radiate from a common origin Art object Geography (Spence, 2007) History For a given object, points are joined by straight lines Other useful information such as average values or thresholds can be encoded

56 Mathematics Properties of star plots: Sport Chemistry Physics Literature Art Geography History Their shape can provide a reasonably rapid appreciation of the attributes of the objects They offer object visibility and are suitable to compare objects (by visibility it is meant the ability to gain insight pre-attentively; without a great cognitive effort) Bob s performance Tony s performance (Spence, 2007)

57 The scatterplot matrix is applicable to higher dimensions However, as the number of attributes increase, the number of different pairs of attributes increases rapidly: 2 attributes -> 1 scatterplot 3 attributes -> 3 scatterplots 4 attributes -> 6 scatterplots Scatterplot matrix for 6 attributes of a car dataset

58 A single scatterplot can be used together with other encoding techniques to represent data of higher dimension /product-demonstrationinteractive/expense-analytics bcentral/fileexchange/ bubbleplot-multidimensionalscatter-plots

59 Mosaic plots can be demonstrated by an example using data from the Titanic ( ( Survived Age Gender Class 1st 2nd 3rd Crew No Yes No Yes No Yes No Yes Adult Child Adult Child Male Female Details of the Titanic disaster involving 4 attributes: (Spence, 2007) Gender Survival Class Adult/child

60 (a) Total number of passengers + crew First Second Third Crew (b) Survived Female Female Died Survived Male Male Died Adult Ch ild First Second Third Crew First Second Third Crew (d) (c) Steps in the creation of a Mosaic Plot representing the Titanic disaster.

61 Icons represent a number of attributes qualitatively or quantitatively y A stranger (Tufte, 2001) x Chernoff Faces allow attribute values to be encoded in the features of cartoon faces They were originally used to study geological samples, each characterized by 18 attributes (

62 Multidimensional icons representing eight attributes of a dwelling house 400,000 garage central heating four bedrooms good repair large garde n Victoria 15 mins flat 300,000 no garage central heating two be drooms poor repair small garde n Victoria 20 mins house boat 200,000 no garage no central heating three bedrooms good repair no garden Victoria 15 mins Textual descriptions of the dwellings represented by the multidimensional icons (Spence, 2007)

63 Two examples of metaphorical icons: - with direct relation between icon and object (house icon) - no direct relation between facial features and attributes they represent (Chernoff faces) Data related glyphs (icons) seem more favored by users (Siirtola, 2005) Direct metaphorical icons find wide application (Miller and Stasko, 2001) (doi> /j.intcom ) The InfoCanvas

64 Example: Use visualization techniques to help answer the following questions: Is there a relation between wanted salary and experience? How many candidates ask for a salary in [30000, 50000] and in [55000, 75000]? How many candidates have an advanced level of English? Education Age Prof. Experience Gender English Wanted salary # (MSc/PhD) (years) (years) (F/M) (Bas/Adv) ($$/year) 1 MSc 22 0 M Advanced MSc 23 0 M Basic MSc 24 1 F Advanced PhD 30 7 F Advanced MSc 25 1 M Basic PhD 29 5 M Advanced MSc 31 7 M Advanced MSc 23 0 F Advanced MSc 26 2 F Intermediate PhD 32 9 M Intermediate BSc 30 7 M Intermediate PhD F Advanced MSc 28 4 M Advanced the complete table has many more candidates, but you may test with these

65 Bibliography Main Bibliography Spence, R., Information Visualization, Design for Interaction, 2nd ed., Prentice Hall, 2007 Munzner, T., Visualization Analysis and Design, A K Peters/CRC Press, 2014 Mazza, R., Introduction to Information Visualization, Springer, 2009 Ware, C., Information Visualization, Perception to Design, 2nd ed.,morgan Kaufmann,2004 Tufte, E., The Visual Display of Quantitative Information, 2 nd ed., Graphics Press, 2001 Acknowledgement The author of these slides is very grateful to Professor Robert Spence as he provided the electronic version of his book figures

66 Links Prize winning pie chart! Mandelblubs: 3D Fractals