Multidimensional (Multivariate)Data VisualizationData Visualization

—— IV Course Spring’14

Graduate Coursef UCASof UCAS

May 9th, 2014

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Data by Dimensionality• 1-D (Linear, Set and Sequences) SeeSoft, Info Mural

• 2-D (Map) GIS ArcView PageMaker2-D (Map) GIS, ArcView, PageMaker

• 3-D (Shape, the World) CAD, Medical, Architecture

• D (R l i l S i i l)• n-D (Relational, Statistical) Spotfire, Tableau

• Temporal LifeLines, Palantir

•• Tree (Hierarchy) Cone/Cam/Hyperbolic

• Network (Graph) Pajek, JUNG

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Relational Data Model• Represent data as a tableEach row (tuple) represents a single recordEach record is a fixed length tupleEach record is a fixed-length tupleEach column (attribute) represents a single variablerepresents a single variableEach attribute has a name and a data type

• A database is a collection of tables

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Statistical Data Model• Dimensions: Nominal/Ordinal variable describing data Dates, categories of values (independent variables)

• Measures: Interval/Ratio that can be aggregated Numbers to be analyzed (dependent variables) Aggregate as sum, count, average, std. deviation

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Data by Variable/Measurement Types• N - Nominal (labels) Fruits: Apples oranges Fruits: Apples, oranges, …

• O - Ordinal Sanitation of restaurants: A/B/C Sanitation of restaurants: A/B/C

• Q - Interval (No zero measure) D t J 19 2006 L ti (LAT 33 98 LONG 118 45) Date: Jan. 19, 2006; Location (LAT 33.98, LONG -118.45) Like a geometric point. Cannot compare directly Only differences (i e intervals) may be compared Only differences (i.e. intervals) may be compared

• Q - Ratio (zero fixed) Ph i l L h M T Physical measurement: Length, Mass, Temp, … Counts and amounts Lik t i t i i is i f l

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Like a geometric vector, origin is meaningful

Multivariate Data and Analysis• Definitions Multivariate analysis is based on the statistical principle of Multivariate analysis is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical outcome variable at a time. Multivariate statistics is a form of statistics encompassing the simultaneous observation and analysis of more than one outcome variable outcome variable.

• Multivariate Data: three main components Objects: Item of interests (students courses terms ) Objects: Item of interests (students, courses, terms, …) Attributes: Characteristics or properties of data (name, age, GPA, number, date, …)age, GPA, number, date, …) Relations: How two or more objects relate (student takes course, course during term, …)

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ExampleObObjects

(Entries/Cases) Metadata

LondonLondonOlympicGameGam

Performance

Attributes (Measures/Variables)

Relationshipamong

multiple objects &

tables

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tables

Example

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Multivariate Data Classification• Number of outcome/dependent variables per entry/caseentry/case　1 - Univariate data 2 - Bivariate data2 Bivariate data　3 - Trivariate data >3 - Hypervariate datayp

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Univariate Data Visualization

• Put independent variable/cases (Country) on x-axis• Put dependent variable/measures (#gold medal) on y-

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u p /m u ( g m ) yaxis

Bivariate Data Visualization

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Trivariate Data Visualization

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Trivariate Data Visualization

horsepower

mileage

price

cases

Represent each variable in separate charts

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Hypervariate Data Visualization• 4~20 variables/measures• nD > 2D projection (3D): in maths MDS/PCA/• nD -> 2D projection (3D): in maths, MDS/PCA/…

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Hypervariate Data Visualization• More visual channels: ~10 variables

A tensor fi ldfield

by tile visualizationvisualization

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x, y, color hue, saturation, value, size, shape, orientation, rotation, texture, etc.

Hypervariate Data Visualization• Separate charts, multiple views on different variablesvariables

casescases

variables variables

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cases

Hypervariate Data Visualization• TableLens Turn spreadsheet into statistical data graphics Turn spreadsheet into statistical data graphics　Leverage the basic bar and scatterplot design

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Change nominal values to scatterplots

Change quantitative values to bars

TableLens

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TableLens

19Focus + Context

Hypervariate Data Visualization

TableLens video (0:00~5:00)TableLens video (0:00~5:00)

I f Z idInfoZoom video

However, spreadsheet-like visualizations show no correlation among variablesshow no correlation among variables

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Scatterplot Matrix

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Scatterplot Matrix

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Pivot Table: Flexibly aggregating spreadsheets

Data Table

Pivot Tableot a

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OLAP Cubes: Multidimensional analytics in BI and Data Managementand Data Management

Slice

DiceDice

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OLAP Cubes

Drill-down

PiPivot

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OLAP Cubes

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Polaris: Multi-dimensional data visualization with extended Pivot Tables with extended Pivot Tables

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Tableau: Commercial version of Polaris:

Video demo: bl l f L P bTableau visualization of OLAP cube

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Still miss something on multidimensional data?g

No multidimensional relationships!No multidimensional relationships!

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Attribute Explorer

• Attribute histogram

• All objects on all attribute scalesattribute scales

• Interaction with attributes limits

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Attribute Explorer• Inter-relations between attributes – brushing

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Attribute Explorer• Color-encoded sensitivity

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Attribute Explorer

Old-fashioned Video Demo!

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Parallel Coordinate

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Parallel Coordinate• Sample multivariate data

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Parallel Coordinate• First data entry

V1 V2 V3 V4 V5V1 V2 V3 V4 V5

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Parallel Coordinate• Second data entry

V1 V2 V3 V4 V5V1 V2 V3 V4 V5

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Parallel Coordinate• Third data entry

V1 V2 V3 V4 V5V1 V2 V3 V4 V5

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Case Study: VLSI Chip Dataset• The Dataset: Production data for 473 batches of a VLSI chip Production data for 473 batches of a VLSI chip 16 process parameters:

X1: The yield: % of produced chips that are usefulX he y eld % of produced ch ps that are usefulX2: The quality of the produced chips (speed)X3 … X12: 10 types of defects (zero defects shown at top)X13 … X16: 4 physical parameters

Th Obj ti• The Objective: Raise the yield (X1) and maintain high quality (X2)

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A. Inselberg, Multidimensional Detective, Proceedings of IEEE Symposium on Information Visualization (InfoVis '97), 1997.

Case Study: VLSI Chip Dataset• Overview

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Case Study: VLSI Chip Dataset• Top Yield & Quality

D f tsDefects

S litSplits

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Case Study: VLSI Chip Dataset• Zero Defect: not the highest yield and quality

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Case Study: VLSI Chip Dataset• Best quality: some defects are necessary!

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Parallel Coordinate Demo

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Parallel Set• How about categorical data?

Live Demo

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Star Plot (Radar Map)• Rotate coordinate from Parallel Coordinate

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Star Plot (Radar Map)• Single-view v.s. Multiple-view

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Star Coordinate• Use data point instead of polyline in Star Plots Accumulate data value along a vector parallel to the axis Accumulate data value along a vector parallel to the axis

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SSummary

• Multivariate Data Model– Statistical and relational – Unvariate, Bivariate, Trivariate, Hypervariate

• Multivariate Data Visualization– Charts, scatterplot, spreadsheet and spreadsheet-like

visualization– Scatterplot matrix, pivot table, OLAP cube, Polaris and

Tableau– Parallel Coordinate and Parallel SetParallel Coordinate and Parallel Set– Star plot (Radar map) and star coordinate

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Questions?Questions?

What’s Next –Multivariate Data Visualization Fun Demos

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Final Project Checkpoint

Are you ready?y y

Team coordinators/Leaders Team coordinators/Leaders, please find Hanpengyu now

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Fun Visualizations and Demos

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FLINA: Flexible Linked Axes for Multivariate Data VisualizationMultivariate Data Visualization

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Chernoff Faces

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Mosaic Plot

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Dust & Magnetg

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Untangling Euler Diagramg g g

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