Topic Notes Multivariate Data Tables and Graphs CS 7450 Information Visualization Sep 4 2013 John Stasko Agenda Data and its characteristics Tables and graphs Design principles Fall 2013 CS 7450 2 1 Data Data is taken from and or representing some phenomena from the world Data models something of interest to us Fall 2013 CS 7450 3 Data Sets Data comes in many different forms Typically not in the way you want them What is available to me in the raw Fall 2013 CS 7450 4 2 Example Cars make model year miles per gallon cost number of cylinders weights Fall 2013 CS 7450 5 CS 7450 6 Example Web pages Fall 2013 3 Data Models Often characterize data through three components Objects Items of interest students courses terms Attributes Characteristics or properties of data name age GPA number date Relations How two or more objects relate student takes course course during term Fall 2013 CS 7450 7 Data 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 Fall 2013 CS 7450 8 4 Data Table Format Case1 Case2 Case3 Variable1 Value11 Value21 Value31 Variable2 Value12 Value22 Value32 Variable3 Value13 Value23 Value33 Think of as a function f case1 Val11 Val12 Fall 2013 CS 7450 9 Example Mary Jim Sally Mitch SSN 145 294 563 823 Age 23 17 47 29 Hair brown black GPA 2 9 3 7 blonde red 3 4 2 1 People in class Fall 2013 CS 7450 10 5 Or P1 P2 P3 P4 Name Mary Jim Sally Mitch SSN 145 294 563 823 Age 23 17 47 29 Hair brown black GPA 2 9 3 7 blonde red 3 4 2 1 People in class Fall 2013 CS 7450 11 CS 7450 12 Example Baseball statistics Fall 2013 6 Variable 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 age Fall 2013 CS 7450 13 Alternate Characterization Two types of data Quantitative Relationships between values Ranking Ratio Correlation Categorical How attributes relate to each other Nominal Ordinal Interval Hierarchical From S Few Fall 2013 CS 7450 14 7 Metadata 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 16 Fall 2013 CS 7450 15 Data Cleaning Data may be missing corrupted Remove Modify You may want to adjust values Use inverse Map nominal to ordinal quantitative Normalize values Scale between 0 and 1 Fall 2013 CS 7450 16 8 How Many Variables Data sets of dimensions 1 2 3 are common Number of variables per class 1 Univariate data 2 Bivariate data 3 Trivariate data 3 Hypervariate data Fall 2013 CS 7450 17 Representation What are two main ways of presenting multivariate data sets Directly textually Tables Symbolically pictures Graphs When use which Fall 2013 CS 7450 18 9 S Few Strengths Show Me the Numbers Use tables when Use graphs 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 Fall 2013 The message is contained in the shape of the values The document will be used to reveal relationships among values CS 7450 19 Effective 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 Fall 2013 CS 7450 20 10 Example Fall 2013 CS 7450 21 CS 7450 22 Example Fall 2013 11 Basic Symbolic Displays Graphs Charts Maps Diagrams From S Kosslyn Understanding charts and graphs Applied Cognitive Psychology 1989 Fall 2013 CS 7450 23 1 Graph Showing the relationships between variables values in a data table 100 80 60 East 40 West North 20 0 Fall 2013 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr CS 7450 24 12 Properties 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 comprehended Fall 2013 CS 7450 25 Issues 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 money Fall 2013 CS 7450 time 26 13 Graph Components Framework Measurement types scale Content Marks lines points Labels Title axes ticks Fall 2013 CS 7450 27 Many Examples www nationmaster com Fall 2013 CS 7450 28 14 Quick Aside Other symbolic displays Chart Map Diagram Fall 2013 CS 7450 29 2 Chart Structure is important relates entities to each other Primarily uses lines enclosure position to link entities Examples flowchart family tree org chart Fall 2013 CS 7450 30 15 3 Map Representation of spatial relations Locations identified by labels Fall 2013 CS 7450 31 4 Diagram Schematic picture of object or entity Parts are symbolic Examples figures steps in a manual illustrations Fall 2013 CS 7450 32 16 Some History Which is older map or graph Maps from about 2300 BC Graphs from 1600 s Rene Descartes William Playfair late 1700 s Fall 2013 CS 7450 33 Details What are the constituent pieces of these four symbolic displays What are the building blocks Fall 2013 CS 7450 34 17 Visual Structures Composed of Spatial substrate Marks Graphical properties of marks Fall 2013 CS 7450 35 Space Visually dominant Often put axes on space to assist Use techniques of composition alignment folding recursion overloading to 1 increase use of space 2 do data encodings Fall 2013 CS 7450 36 18 Marks Things that occur in space Points Lines Areas Volumes Fall 2013 CS 7450 37 Graphical Properties Size shape color orientation Spatial properties Object properties Expressing extent Position Size Grayscale Differentiating marks Orientation Fall 2013 Color Shape Texture CS 7450 38 19 Back to Data What were the different types of data sets Number of variables per class 1 Univariate data 2 Bivariate data 3 Trivariate data 3 Hypervariate data Fall 2013 CS 7450 39 Univariate Data Representations 7 Bill Tukey box plot 5 low 3 1 high Mean 0 Fall 2013 Middle 50 CS 7450 20 40 20 What Goes Where In univariate representations we often think of the data case as being shown along one dimension and the value in another Line graph Fall 2013 Bar graph Y axis is quantitative variable Y axis is quantitative variable See changes over consecutive values Compare relative point values CS