Multivariate Data &Tables and GraphsCS 4460/7450 - Information VisualizationJan. 13, 2009John StaskoSpring 2009 CS 4460/7450 2Agenda• Data and its characteristics• Tables and graphs• Design principlesData• Data is taken from and/or representing some phenomena from the world• Data models something of interest to usSpring 2009 CS 4460/7450 3Spring 2009 CS 4460/7450 4Data Sets• Data comes in many different forms• Typically, not in the way you want them• What is available to me (in the raw)?Spring 2009 CS 4460/7450 5Example• Cars− make− model− year− miles per gallon− cost− number of cylinders− weights− ...Spring 2009 CS 4460/7450 6Example• Web pagesData Models• Often characterize data through three components− ObjectsItems of interest(students, courses, terms, …)− AttributesCharacteristics or properties of data(name, age, GPA, number, date, …)− RelationsHow two or more objects relate(student takes course, course during term, …)Spring 2009 CS 4460/7450 7Spring 2009 CS 4460/7450 8Data Tables• We take raw data and transform it into a model/form that is more workable• Main idea:− Individual items are called cases− Cases have variables(attributes)− Relational: Relations between cases (not our main focus today)Spring 2009 CS 4460/7450 9Data Table FormatCase1Case2Case3...Variable1Variable2Variable3...Value11 Value21 Value31Value12 Value22 Value32Value13 Value23 Value33Think of as a functionf(case1) = <Val11, Val12,…>Spring 2009 CS 4460/7450 10ExamplePeople in classMary Jim Sally Mitch ...SSNAgeHairGPA...145 294 563 82323 17 47 29brown black blonde red2.9 3.7 3.4 2.1Spring 2009 CS 4460/7450 11OrPeople in classP1 P2 P3 P4 ...NameSSNAgeHairGPA...145 294 563 82323 17 47 29brown black blonde red2.9 3.7 3.4 2.1Mary Jim Sally MitchSpring 2009 CS 4460/7450 12ExampleBaseballstatisticsSpring 2009 CS 4460/7450 13Variable Types• Three main types of variables− N-Nominal (equal or not equal to other values)Example: gender− O-Ordinal (obeys < relation, ordered set)Example: fr,so,jr,sr− Q-Quantitative (can do math on them)Example: ageAlternate Characterization• Two types of data− QuantitativeRelationships between values:RankingRatioCorrelation− CategoricalHow attributes relate to each other:NominalOrdinalIntervalHierarchicalSpring 2009 CS 4460/7450 14From S. FewSpring 2009 CS 4460/7450 15Metadata• Descriptive information about the data− Might be something as simple as the type of a variable, or could be more complex− For times when the table itself just isn’t enough− Example: if variable1 is “l”, then variable3 can only be 3, 7 or 16Spring 2009 CS 4460/7450 16How Many Variables?• Data sets of dimensions 1, 2, 3 are common• Number of variables per class− 1 -Univariatedata− 2 - Bivariate data− 3 - Trivariate data− >3 - Hypervariate dataSpring 2009 CS 4460/7450 17Representation• What are two main ways of presenting multivariate data sets?− Directly (textually) → Tables− Symbolically (pictures) → Graphs• When use which?Strengths?• Use tables when− The document will be used to look up individual values− The document will be used to compare individual values− Precise values are required− The quantitative info to be communicated involves more than one unit of measure• Use graphs when− The message is contained in the shape of the values− The document will be used to reveal relationships among valuesSpring 2009 CS 4460/7450 18S. FewShow Me the NumbersEffective Table Design• See Show Me the Numbers• Proper and effective use of layout, typography, shading, etc. can go a long way• (Tables may be underused)Spring 2009 CS 4460/7450 19ExampleSpring 2009 CS 4460/7450 20ExampleSpring 2009 CS 4460/7450 21Spring 2009 CS 4460/7450 22Basic Symbolic Displays• Graphs Å• Charts• Maps• DiagramsFrom:S. Kosslyn, “Understanding chartsand graphs”, Applied CognitivePsychology, 1989.Spring 2009 CS 4460/7450 231. GraphShowing the relationships between variables’values in a data table0204060801001stQtr2ndQtr3rdQtr4thQtrEastWestNorthSpring 2009 CS 4460/7450 24Properties• Graph− Visual display that illustrates one or more relationships among entities− Shorthand way to present information− Allows a trend, pattern or comparison to be easily comprehendedSpring 2009 CS 4460/7450 25Issues• Critical to remain task-centric− Why do you need a graph?− What questions are being answered?− What data is needed to answer those questions?− Who is the audience?timemoneySpring 2009 CS 4460/7450 26Graph Components• Framework− Measurement types, scale• Content− Marks, lines, points• Labels− Title, axes, ticksSpring 2009 CS 4460/7450 27Many Exampleswww.nationmaster.comSpring 2009 CS 4460/7450 28Quick Aside• Other symbolic displays− Chart− Map− DiagramSpring 2009 CS 4460/7450 292. Chart• Structure is important, relates entities to each other• Primarily uses lines, enclosure, position to link entitiesExamples: flowchart, family tree, org chart, ...Spring 2009 CS 4460/7450 303. MapRepresentation ofspatial relationsLocations identifiedby labelsSpring 2009 CS 4460/7450 314. Diagram• Schematic picture of object or entity• Parts are symbolicExamples: figures, steps in a manual, illustrations,...Some History• Which is older, map or graph?• Maps from about 2300 BC• Graphs from 1600’s− Rene Descartes− William Playfair, late 1700’sSpring 2009 CS 4460/7450 32Spring 2009 CS 4460/7450 33Details• What are the constituent pieces of these four symbolic displays?• What are the building blocks?Spring 2009 CS 4460/7450 34Visual Structures• Composed of− Spatial substrate− Marks− Graphical properties of marksSpring 2009 CS 4460/7450 35Space• Visually dominant• Often put axes on space to assist• Use techniques ofcomposition, alignment, folding,recursion, overloading to 1) increase use of space2) do data encodingsSpring 2009 CS 4460/7450 36Marks• Things that occur in space− Points− Lines− Areas− VolumesSpring 2009 CS 4460/7450 37Graphical Properties• Size, shape, color, orientation...Spatial