marti hearst sims 247 sims 247 lecture 4 graphing multivariate information january 29, 1998

Marti HearstSIMS 247

SIMS 247 Lecture 4SIMS 247 Lecture 4Graphing Multivariate InformationGraphing Multivariate Information

January 29, 1998January 29, 1998


Follow-up previous lectureFollow-up previous lecture

• Docuverse: Docuverse: – length of arc is proportional to number of subdirectories– radius for a given arc is long enough to

contain marks for all the files in the directory

• Nightingale’s “coxcomb”Nightingale’s “coxcomb”– keep arc length constant– vary radius length (proportional to sqrt(freq))


Today: Multivariate InformationToday: Multivariate Information

• We see a 3D worldWe see a 3D world• How do we handle more than 3 How do we handle more than 3

variables?variables?– multi-functioning elements

• Tufte examples• cinematography example

– multiple views


Example Data SetsExample Data SetsHow do we handle 9 variables?How do we handle 9 variables?– Our web access dataset– Factors involved in alcoholism

• ALCOHOL – USE– AVAILABILITY– CONCERN ABOUT USE– COPING MECHANISMS

• PERSONALITY MEASURES– EXTROVERSION– DISINHIBITION

• OTHER– GENDER– GPA


Graphing Multivariate InformationGraphing Multivariate Information

How do we handle cases with more How do we handle cases with more than three variables?than three variables?– Scatterplot matrices– Parallel coordinates– Multiple views– Overlay space and time– Interaction/animation across time


Multiple Variables: Scatterplot MatricesMultiple Variables: Scatterplot Matrices(from Wegman et al.)(from Wegman et al.)


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Multiple Views: Star PlotMultiple Views: Star Plot(Discussed in Feinberg 79. Works better with animation. Example (Discussed in Feinberg 79. Works better with animation. Example

taken from Behrans & Yu 95.)taken from Behrans & Yu 95.)


Multiple Dimensions: Parallel CoordinatesMultiple Dimensions: Parallel Coordinates(earthquake data, color indicates longitude, y axis severity (earthquake data, color indicates longitude, y axis severity

of earthquake, from Schall 95)of earthquake, from Schall 95)


Multiple Dimensions: Multivariate Star PlotMultiple Dimensions: Multivariate Star Plot(from Behran & Yu 95)(from Behran & Yu 95)


Chernoff FacesChernoff Faces• Assumption: people have built-in face Assumption: people have built-in face

recognizersrecognizers• Map variables to features of a cartoon faceMap variables to features of a cartoon face

– Example: eyes• location, separation, angle, shape, width

– Example: entire face• area, shape, nose length, mouth location, smile

curve

• Originally tongue-in-cheek, but taken seriouslyOriginally tongue-in-cheek, but taken seriously• Sometimes seems to work for small numbers Sometimes seems to work for small numbers

of pointsof points


Chernoff Example Chernoff Example (Marchette)(Marchette)

• Three groups of pointsThree groups of points– each drawn from a different distribution with

5 variables

• First show scatter-plot matrixFirst show scatter-plot matrix• Then graph with Chernoff facesThen graph with Chernoff faces

– vary faces overall– vary eyes– vary mouth and eyebrows

• Which seems to be most effective?Which seems to be most effective?


Chernoff Experiment Chernoff Experiment (Marchette)(Marchette)


Overlaying Space and TimeOverlaying Space and Time(Minard’s graph of Napolean’s march through Russia)(Minard’s graph of Napolean’s march through Russia)


A Detective StoryA Detective Story(Inselberg 97)(Inselberg 97)

• Domain: Manufacture of computer chipsDomain: Manufacture of computer chips• Objectives: create batches with Objectives: create batches with

– high yield (X1)– high quality (X2)

• Hypothesized cause of problem:Hypothesized cause of problem:– 9 types of defects (X3-X12)

• Some physical properties (X13-X16)Some physical properties (X13-X16)

• Approach:Approach:– examine data for 473 batches– use interactive parallel coordinates


Multidimensional DetectiveMultidimensional Detective

• Long term objectives: Long term objectives: – high quality, high yield

• Logical approach given the Logical approach given the hypothesis:hypothesis:– try to eliminate defects

• First clue: First clue: – what patterns can be found among

batches with high yield and quality?


Detectives aren’t intimidated!Detectives aren’t intimidated!

X1 seems to be normally distributed; X2 bipolar


High quality yields obtained despite defectsHigh quality yields obtained despite defects

goodbatches

some low X3defect batchesdon’t appear here

X15breaksinto twoclusters(importantphysicalproperty)

at least onegood batch withdefects


Low-defect batches are not highest quality!Low-defect batches are not highest quality!few defects

lowyield,low quality


Original plot shows defect X6 behaves Original plot shows defect X6 behaves differently; exclude it from the 9-out-of-10 differently; exclude it from the 9-out-of-10 defects constraint; the best batches returndefects constraint; the best batches return


Isolate the best batches.Isolate the best batches.Conclusion: defects are necessary!Conclusion: defects are necessary!

The very best batchhas X3 and X6 defects

Ensure this is not anoutlier -- look attop few batches.The same result is found.


How to graph web page traversals? How to graph web page traversals?


References for this LectureReferences for this Lecture

• Visualization Techniques of Different Dimensions, John Behrens and Chong Ho Visualization Techniques of Different Dimensions, John Behrens and Chong Ho Yu, 1995 Yu, 1995 http://seamonkey.ed.asu.edu/~behrens/asu/reports/compre/comp1.htmlhttp://seamonkey.ed.asu.edu/~behrens/asu/reports/compre/comp1.html

• Feinberg, S. E. Graphical methods in statistics. Feinberg, S. E. Graphical methods in statistics. American Statisticians, 33, American Statisticians, 33, 165-165-178, 1979178, 1979

• Friendly, Michael, Gallery of Data Visualization. Friendly, Michael, Gallery of Data Visualization. http://www.math.yorku.ca/SCS/Galleryhttp://www.math.yorku.ca/SCS/Gallery– scan of Minard’s graph from Tufte 1983– multivariate means comparison

• Wegman, Edward J. and Luo, Qiang. High Dimensional Clustering Using Parallel Wegman, Edward J. and Luo, Qiang. High Dimensional Clustering Using Parallel Coordinates and the Grand Tour., Conference of the German Classification Coordinates and the Grand Tour., Conference of the German Classification Society, Freiberg, Germany, 1996. http://galaxy.gmu.edu/papers/inter96.htmlSociety, Freiberg, Germany, 1996. http://galaxy.gmu.edu/papers/inter96.html

• Cook, Dennis R and Weisberg, Sanford. An Introduction to Regression Graphics, Cook, Dennis R and Weisberg, Sanford. An Introduction to Regression Graphics, 1995. http://stat.umn.edu/~rcode/node3.html1995. http://stat.umn.edu/~rcode/node3.html

• Schall, Matthew. SPSS DIAMOND: a visual exploratory data analysis tool. Schall, Matthew. SPSS DIAMOND: a visual exploratory data analysis tool. Perspective, 18 (2), Perspective, 18 (2), 1995. http://www.spss.com/cool/papers/diamondw.html1995. http://www.spss.com/cool/papers/diamondw.html

• Marchette, David. An Investigation of Chernoff Faces for High Dimensional Marchette, David. An Investigation of Chernoff Faces for High Dimensional Data Exploration. http://farside.nswc.navy.mil/CSI803/Dave/chern.htmlData Exploration. http://farside.nswc.navy.mil/CSI803/Dave/chern.html

• Chernoff, H. The use of Faces to Represent Points in k-Dimensional Space Chernoff, H. The use of Faces to Represent Points in k-Dimensional Space Graphically. Graphically. Journal of the American Statistical Association, 68,Journal of the American Statistical Association, 68, 361-368, 1973. 361-368, 1973.


Next Time: Brushing and LinkingNext Time: Brushing and Linking

• An interactive techniqueAn interactive technique• Brushing:Brushing:

– pick out some points from one viewpoint

– see how this effects other viewpoints– (Cleveland scatterplot matrix

example)

• Graphs must be linked togetherGraphs must be linked together


Brushing and Linking SystemsBrushing and Linking Systems

• VISAGE: Roth et. alVISAGE: Roth et. al• Attribute Explorer: Tweedie et. alAttribute Explorer: Tweedie et. al• SpotFire (IVEE): Ahlberg et. alSpotFire (IVEE): Ahlberg et. al

marti hearst sims 247 sims 247 lecture 4 graphing multivariate information january 29, 1998

Documents

length of arc

timemultiple variables

best batches returnisolate

multiple dimensions

highest quality

nose length

multivariate informationwe

multivariate informationhow