Multidimensional Data Analysis

Multidimensional Data Analysis

IS 247 Information Visualization and Presentation

22 February 2002

James ReffellMoryma Aydelott

Jean-Anne Fitzpatrick

Problem Statement

• How to effectively present more than 3 dimensions of information in a visual display with 2 (to 3) dimensions?

• How to effectively visualize “inherently abstract” data?

• How to effectively visualize very large, often complex data sets?

• How to effectively display results – when you don’t know what those results will be?

Key Goals

• More than 3 dimensions of data simultaneously

• Support “fuzzyness” (similarity queries, vector space, tolerance ranges)

• Support exploratory, opportunistic, “what-if” queries

• Allow identification of “interesting data properties” through pattern recognition

• Explore various dimensions without losing overview

Another Statement of Goals

Visualization of multidimensional data• Without loss of information• With:

– Minimal complexity– Any number of dimensions– Variables treated uniformly– Objects remain recognizable across

transformations– Easy / intuitive conveyance of information– Mathematically / algorithmically rigorous

(Adapted from Inselberg)

Purposes / Uses

• Find clusters of similar data• Find “hot spots” (exceptional items in

otherwise homogeneous regions)• Show relationships between multiple

variables• Similarity retrieval rather than boolean

matching, show near misses

“Searching for patterns in the big picture and fluidly investigating interesting details without losing framing context” (Rao & Card)

Characteristics• “Data-dense displays” (large number of

dimensions and/or values)– Often combine color with position / proximity

representing relevance “distance” – Often provide multiple views

• Build on concepts from previous weeks:– Retinal properties of marks– Gestalt concepts, e.g., grouping– Direct manipulation / interactive queries– Incremental construction of queries– Dynamic feedback

• Some require specialized input devices or unique gesture vocabulary

ExamplesWarning: These visualizations

are not easy to grasp at “first

glance”!

DON’T PANIC

Influence Explorer / Prosection Matrix

(Tweedie et. al.)

• We saw the video• Abstract one-way mathematical

models: multiple parameters, multiple variables

• Data through sampling• Colour coding, esp. near misses• Task: Make the red bit as big as

possible!

Influence Explorer / Prosection Matrix

(Tweedie et. al.)

• Selecting performance limits

Influence Explorer / Prosection Matrix

(Tweedie et. al.)

• The colours go in two directions!

Influence Explorer / Prosection Matrix

(Tweedie et. al.)

• Fitting tolerance region (yellow box) to acceptability (red region) gives high yield for minimum cost

The Table Lens (Rao and Card)

• - Tools: zoom, adjust, slide

• - Cell contents coded by color (nominal) or bar length (interval)

• - Special mouse gesture vocabulary

• Search / browse (spotlighting)

The Table Lens (Rao and Card)

The Table Lens (Rao and Card)

http://www.tablelens.com

Parallel Coordinates(Inselberg)

• Transformation of multiple graphs by using parallel axes in a 2D representation.

• Users attempt to recognize patterns between the axes - adding or removing parts of the data to see general patterns or more closely examine particular interactions.

• Article offers suggestions on how to most effectively use this system.

Parallel Coordinates(Inselberg)

Dataset in a Cartesian graph

Same dataset in parallel coordinates

Parallel Coordinates applet - http://csgrad.cs.vt.edu/~agoel/parallel_coordinates/

Parallel Coordinates(Inselberg)

Strengths – • Works for any N• Clearly displays data characteristics of the data (without

needing beaucoup explanations)• Easy to adjust or focus displays/ queries • Testing showed that it showed problems missed using other

forms of process control• Can be used in decision support when used as a visual

modeling tool (to see how adjusting one parameter effects others).

Weaknesses – • Formation of complex queries can be tricky (if you want to

get results that are useful and easy to interpret).

Polaris(Stolte and Hanharan)

• Extends pivot tables to generate graphic displays

• Multiple graphs on one screen• Designed to “combine

statistical analysis and visualization”

(a pivot table)

(polaris)

Polaris(Stolte and Hanharan)

• Table algebra automatically generated via drag and drop.

• Suitable graphic types are system selected based on query/result criteria. Include tables, bar charts, dot plot, gantt charts, matrices of scatterplots, maps.

• Users can select marks (marks differ by shape, size, orientation and color).

Polaris(Stolte and Hanharan)

Strengths – • Can be used with existing DB systems• Direct manipulation - drag and drop • Users can play with appearance of

display• Linking and Brushing supported

Weaknesses – • User only sees aggregated (not original)

data

• System performs a number of functions automatically (conversion of variables, aggregation) - user may not know or not be able to control how their data is changed.

Worlds Within Worlds(Fiener and Beshers)

• Basic approach: graph 3 dimensions, while holding “extra” dimensions constant

• Visually represent “extra” dimensions as space within which graph(s) are placed– Position of “inner world” graph axis zero point

equals set of constant values in “outer world”

• Tools:– Dipstick– Waterline– Magnifying box

The following images from: http://www-courses.cs.uiuc.edu/~cs419/multidim.ppt

Worlds Within Worlds

• Constraints:– Uses special input device (“Data Glove”)

and output device (liquid crystal stereo glasses); use without these special devices less than optimal

• Technical details:– Suspend calculation of “child” details during

movement– Algorithm for prioritizing overlapping objects– Need to “turn off” gesture recognition to

allow normal use of hand

Worlds Within Worlds I/O Devices

Techniques for plotting multivariate functions

(Mihalisin et al)

• Multiples showing component dimensions, color codes for dimensions applied across multiples

• Or, for categorical data, select mth category from nth dimension

• Or, plot nested boxes, step values of independent variables and color-coding dependent variable

Techniques for plotting multivariate functions

(Mihalisin et al)

• Tools:– General zoom: look at smaller range

of data in same amount of space– Subspace zoom: select view of

particular dimension’s input to function

– Decimate tool: sample fewer values within range

from http://www.cs.umd.edu/class/spring2001/cmsc838b/presentations/Zhijian_Pan/mdmv.ppt

from http://www.cs.umd.edu/class/spring2001/cmsc838b/presentations/Zhijian_Pan/mdmv.ppt

VisDB(Keim & Kriegel)

• Mapping entries from relational database to pixels on the screen

• Include “approximate” answers, with placement and color-coding based on relevance

• Data points laid out in:– Rectangular spiral– Or, with axes representing positive/negative

values for two selected dimensions– Or, group dimensions together (easier to

interpret than very large number of dimensions)

from http://infovis.cs.vt.edu/cs5984/students/VisDB.ppt

VisDB - Relevance

• Relevance calculation based on “distance” of each variable from query specification

• Distance calculation depends on data type– Numeric: mathematical – String: character/substring matching, lexical,

phonetic?, syntactic?– Nominal: predefined distance matrix– Possibly other “domain-specific” distance

metrics

VisDB – Screen Resolution

• Stated screen resolution seems reasonable by today’s standards:19 inch display, 1024x1280 pixels= 1.3 million data points

• However, controls take up a lot of space!

from http://www1.ics.uci.edu/~kobsa/courses/ICS280/notes/presentations/Keim-VisDB.ppt

VisDB – Implementation

• Requires features not available in commercial databases:– Partial query results– Incremental changes to queries– Speed? (1994 vs today)

Limitations and Issues

• (intro to following slides and/or Tweedie’s words of wisdom?)

Complexity

• Simplest approach to representing N dimensions is N controls, N one-dimensional outputs – but this fails to represent complex relationships

• Middle ground achieved by some?

Abstract data

• These visualizations are oriented toward abstract data

• For “naturally” two or three-dimensional data (things that vary over time or space, e.g., geographic data) visualizations which exploit those properties may exist and be more effective

User Testing?

• Many of these systems seem only appropriate for expert use

Future Work

• Save query parameters for reference / sharing results

• Automated query generation or filtering – Intelligent agents?

Words of wisdomfrom Tweedie et al

• Trade-off between amount of information, simplicity, and accuracy

• “It is often hard to judge what users will find intuitive and how [a visualization] will support a particular task”