Chapter 3 - Multidimensional Information Visualization II

Chapter 3 - Multidimensional

Information Visualization II

Concepts for visualizing univariate to

hypervariate data

Vorlesung „Informationsvisualisierung”

Prof. Dr. Florian Alt, WS 2013/14

Konzept und Folien (4th revised edition):

Outline

•

Reference model and data terminology

•

Visualizing data with < 4 variables

•

Visualizing multivariable data

– Geometric transformation

– Glyphs

– Pixel-based

– Downscaling of dimensions

•

Case studies: support for exploring multidimensional data

– Rank-by-feature

– Dust & magnet

Rank-By-Feature

•

Seo & Shneiderman 2004

•

Part of the Hierarchical Clustering Explorer (HCE)

(http://www.cs.umd.edu/hcil/multi-cluster/)

•

Tabs: histogram and scatterplot ordering

•

Implements systematic approach for data exploration

– (1) study 1D, study 2D, then find features

– (2) ranking guides insight, statistics confirm

•

T

ool provides low-dimensional projections as a histogram (1D) or

scatterplot (2D)

•

Users can select a feature detection criterion (e.g. test for normal

distribution (1D), correlation coe

ffi

cient (2D)) to rank projections

•

The ranking facility is particularly helpful when the number of

possible projections is too large to investigate: concentrate on

the interesting ones

Rank-By-Feature

•

Users start with 1D projections (histogram ordering)

•

Four coordinated views

– A: selection of ranking criterion

– B: overview of scores for all dimensions (color coding: the brighter the

color, the higher the score)

– C: numerical / statistical detail for each dimension (e.g. score, mean,

standard deviation)

– D: display of histogram + boxplot (minimum, first quartile, median,

third quartile, maximum)

Rank-By-Feature

•

Some basic statistical terms

– Mean: Sum of all values divided by the number of values

– Median: Middle value of a distribution of values when ranked in order of

magnitude

– Mode: Single most common value

– Variance: average squared deviation between the mean and the values

– Standard deviation: square root of the variance (translates the variance

into the original units of measurement)

•

Statistical tests supported by HCE for 1D ranking

– Normality of the distribution: distribution of items forms a symmetric,

bell-shaped curve

– Uniformity of the distribution: all of the values of a random variable occur

with equal probability (results in a flat histogram)

– Number of potential outliers

– Number of unique values

Mode

•

The most frequent score

•

Describes how most items behave

•

Pros:

– Easy to calculate and understand

– Can be used with nominal data

•

Cons:

– There can be more than one mode

– Mode can change dramatically by adding only one dataset

– Independent of all other data in the set

0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 Fr eq u en cy Score

Negatively Skewed Distribution

Median

•

Middle score of the distribution

Example data:

1 7 3 9 6 9 2

•

Sorted by magnitude:

9 9 7 6 3 2 1 median = 6

If #scores even average two middle scores

Example data:

1 7 3 9 4 6 9 2

•

Sorted by magnitude:

9 9 7 6 4 3 2 1 median = 5

•

Pros:

– Relatively una

ff

ected by outliers (very low or high scores) and

skewed distributions

– Can be used with ordinal, interval and ratio data

•

Cons:

– Does not consider all scores of the data set

– Not very stable

Mean

•

Sum of all scores divided by #scores:

•

Most often used if ‘average’ is mentioned

•

Pros:

– Considers every score

– most accurate summary of the data

– Resistant to sampling variation: removing one sample changes

the mean far less than mode or median

•

Cons:

– Heavily a

ff

ected by extreme scores and skewed distributions

– Can only be used with interval and ratio data

∑

=

X

n

m

1

Standard Deviation and Variance

•

How do you measure the accuracy of the mean?

•

Example data set 1:

5 5 5 5 5

mean = 5

•

Example data set 2:

6 8 4 1 6

mean = 5

•

Which of the data sets is better reflected by the mean?

•

If x

1

, x

2

, … x

n

are the data in a sample with mean m

– Deviation = di

ff

erence between mean and scores =

∑

(x

i

- m)

– Variance s

=

– Standard deviation (SD) s =

√

Var(X)

•

Both variance and standard deviations

measure the

– accuracy of the data set

– variability of the data

∑

(x

i

– m) )

n

2

2

Quantile, Quartile, and Percentile

•

Quantile

– ‘Cut points' that divide a sample of data into groups containing

(as far as possible) equal numbers of observations.

•

Quartile (Quantile of 4)

– Values that divide a sample of data into 4 groups containing

(as far as possible) equal numbers of observations

•

Percentile (Quantile of 100)

– Values that divide a sample of data into 100 groups containing

(as far as possible) equal numbers of observations

median

Rank-By-Feature

•

Move on to 2D projections (scatterplot ordering)

•

Identify pairwise relationships between dimensions

•

B: prism provides overview of scores for dimension pairs; score is color coded

•

D: scatterplot browser; multiple browsers are possible;

•

Ranking criteria

– Correlation coe

ffi

cient: direction and strength of linear relationship

– Least square error for simple linear / curvilinear regression: how well does the

regression model fit

Dust & Magnet

•

Yi et al. 2005

•

Data cases are represented as particles of iron

dust

•

Magnets represent the dimensions of the data set

•

Users manipulate the magnets to move the dust

•

Dust moves at different speed depending on its

Clutter Reduction Techniques

•

Clutter: crowded and disordered visual entities

that obscure the structure in visual displays

•

Avoiding clutter is one of the main challenges in

Information Visualization

•

Techniques to reduce clutter

– Dimension reordering

– Sampling

– Constant-density visualization

– Point displacement

– Aggregation / Clustering (one mark represents more than

one case, e.g. group day sales into months)

Dimension Reordering

•

Peng et al. 2004

•

Automatically identify the views with the least

amount of visual clutter

•

Clutter definition and algorithms for different

Sampling

•

Reduce the density of visual representation by

displaying a random subset of the data

•

Random sampling preserves the distribution of data

•

Overall trends (e.g. correlation) can still be detected at a

reduced density

•

Uniform sampling (Ellis & Dix 2004)

– Applying the same (manually or automatically defined)

sampling factor to the entire data space

– Problem: areas with low density may become empty

•

Non-uniform sampling (Bertini & Santucci 2004)

– Preserving relative density

– Model to compute where, how, and how much to sample to

preserve image characteristics

Sampling Lens

•

Ellis et al. 2005

•

Magic Lens approach to apply random sampling to

user-defined regions while maintaining the original data

density in the context

Constant Information Density

•

Woodru

ff

et al. 1998

•

Data objects in areas with high information density

are represented by small-sized low-detail glyphs

•

Objects in sparse-density areas are represented by

larger, more detailed glyphs

•

The number of information objects is kept constant

as the user scales and moves the view

Point Displacement

•

Items that would overlap other items are moved to adjacent

free positions

•

Position of the items and their distance should be preserved as

much as possible

•

Three algorithms for displacing pixels (e.g. adding abstract

data to geographical maps) (Keim & Hermann 1998)

– Nearest-Neighbor

– Curve-based

– Gridfit

•

Algorithms share the same

procedure

– All data points which have a unique

position are placed on the display

– New positions are determined for the

Point Displacement

•

Nearest-Neighbor algorithm

– For all points which have not been set in the first

step, place them on the nearest unoccupied

position

– Fast to compute, but limited effectiveness for very

dense displays (pixels may be placed very far from

their original positions)

•

Curve-based algorithm

– For all points which have not been set in the first

step

•

Compute the nearest unoccupied position on a given

screen-filling curve

•

Shift all points between the occupied pixel and the

unoccupied position along the screen-filling curve

Chapter 4 - Interaction with

Visualizations

Dynamic linking, brushing and filtering in

Information Visualization displays

Vorlesung „Informationsvisualisierung”

Prof. Dr. Florian Alt, WS 2013/14

Konzept und Folien (4th revised edition):

Outline

•

Definitions

•

Direct Manipulation (DM)

– Dynamic Queries

– Movable Filters

•

Common Interaction Techniques

– Select

– Explore

– Reconfigure

– Encode

– Abstract / Elaborate

– Filter

– Connect

InfoVis & Interaction

•

Information Visualization research originally: focus on finding

novel visual representations

•

Increasing interest in interaction design, HCI models and

evaluation as well as aesthetics in the InfoVis community

•

HCI Interaction models help us to better understand the

complex concepts of human-machine communication

•

Norman’s execution-evaluation cycle (Norman 1988)

– 1. Establishing the goal

– 2. Forming the intention

– 3. Specifying the action sequence

– 4. Executing the interaction

– 5. Perceiving the system state

– 6. Interpreting the system state

InfoVis & Interaction

•

InfoVis systems are composed of two major components:

– Representation

•

Roots lie in the field of Computer Graphics

•

Mapping from data to geometrical objects and

•

How these objects are rendered

– Interaction

•

Roots lie in the field of Human-Computer Interaction (HCI)

•

Dialog between user and the system

•

User explores the data from di

ff

erent perspectives to find

insights

Representation and Interaction

•

Although discussed as two separate components,

representation and interaction clearly are not

mutually exclusive.

For example: Interaction with a system may

activate a change in representation.

•

Representation component has received vast

majority of attention in InfoVis research.

•

Scan of recent conference proceedings and journal

issues in InfoVis uncovers many articles about new

representations of datasets but interaction is often

relegated to a secondary role.

Representation and Interaction

•

Interaction rarely is the main focus of research in InfoVis.

•

Making it the “little brother” of InfoVis

•

Interaction is overshadowed by the more noteworthy

representation aspects.

•

Interaction is an essential part of InfoVis

•

Without it, an InfoVis technique or system becomes a

static image or autonomously animated images.

•

Static images clearly have analytic and expressive value

•

But usefulness becomes more limited as the data set

they represent grows larger with more variables

Representation and Interaction

•

By the way: Also with a static image such as a poster, a user

(or reader) will often perform interactions

– Rotating the poster

– Looking closer/further

– Jotting down notes on the poster

•

Spence suggests the notion of “passive interaction” through

which the user’s mental model on the data set is changed

and enhanced.

•

Finally, through interaction, some limits of a representation

can be overcome, and the cognition of a user can be further

amplified.

•

Importance of interaction and the need for its further study

seem undisputed.

Definition

•

Interaction: Before discussing the term “interaction”, we will

find a solid definition for it.

•

But: Finding a solid definition for it is challenging!

•

In the broader context of Human-Computer Interaction (HCI)

it is simply described as

“…the communication between user and the system.”

[Dix et al., 2004]

•

Becker, Cleveland, and Wilks compactly define interaction

as…

“…direct manipulation and instantianeous change.”

Definition

•

“…asymmetry in data rates.”

[Ware, 2000]

•

The amount of data flowing from InfoVis systems to users is

far greater than from users to systems.

•

Thus, interaction techniques in InfoVis seem more designed

for changing and adjusting visual representation than for

entering data into systems, which clearly is an important

aspect of interaction in HCI.

Definition

•

We view interaction techniques in InfoVis as the

features that provide users with the ability to directly

or indirectly manipulate and interpret representation.

•

According to this view, a static image or an

autonomously animated representation does not have

associated interaction techniques.

•

However, a menu interface for changing from a scatter

plot to a parallel coordinates plot is an interaction

technique since it allows a user to manipulate a

representation even if it may be less interactive or

direct.

Direct Manipulation (DM)

•

Shneiderman 1982

•

DM features

– Visibility of all objects of interest

– Incremental actions with rapid feedback on all actions

– Reversibility of all actions, so that users are encouraged to explore

without penalties

– Syntactic correctness of all actions, so that every user action is a

legal operation

•

DM does not only make interaction easier for novice

Example: Brushing

•

Becker & Cleveland 1987

•

A collection of dynamic methods for viewing

multidimensional data

•

Brush is an interactive interface tool to select / mark

subsets of data in a single view, e.g. by sweeping a virtual

brush across items of interest

•

Given linked views (e.g. scatterplot matrix) the brushing can

support the identification of correlations across multiple

dimensions (brushing & linking)

•

Usually used to visually filter data (via highlighting)

•

Additional manipulation / operations may be performed on

the subsets (masking, magnification, labeling etc.)

•

Di

ff

erent types of brushes (Hauser et al. 2002)

– Simple brush via sweeping

– Composite brush: composed multiple single-axis brushes by the use of

logical operators

– Angular brush

Composite scatterplot

brushes - Hauser et

al. 2002

Example: Brushing

•

Brushing one dimension in parallel coordinates to

highlight car data objects with 4 cylinders

Angular Brush

•

Angular brush: brushing by

specifying a slope range –

highlight correlation and outliers

between two dimensions

Smooth Brush

•

Non-binary brushing

•

Degree-of-interest

defined by distance

to brushed range

•

Decreasing degree is

mapped to

decreasing drawing

intensity

Hauser et al.

Another Brushing Example

•

Example for composite (AND) brush in Parallel

Coordinate Plot – find the cities with high wages, small

prices and many paid holiday days

•

Demo InfoScope: http://www.macrofocus.com/public/

products/infoscope.html (free trial and applet)

Dynamic Queries

•

Shneiderman 1994

•

Explore and search databases

•

SQL example: SELECT customer_id, customer_name,

COUNT(order_id) as total FROM customers INNER JOIN

orders ON customers.customer_id = orders.customer_id

GROUP BY customer_id, customer_name HAVING

COUNT(order_id) > 5 ORDER BY COUNT(order_id) DESC

•

Problems

– Takes time to learn

– Takes time to formulate and reformulate

– User must know what she is looking for – only exact matches

– Lots of ways to fail

– SQL error messages helpful?

Dynamic Queries

•

Based on Direct Manipulation (DM)

•

DM principles with regard to Dynamic Queries

– Visual presentation of the query’s components

– Visual presentation of results

– Rapid, incremental, and reversible control of the query

– Selection by pointing, not typing

– Immediate, continuous feedback

•

Implementation approach

– Graphical query formulation: Users formulate queries by

adjusting sliders, pressing buttons, bounding box selection…

– Search results displayed are continuously updated (< 100 ms)

Examples

•

Visual representations of data to query?

•

Some examples: geographic data, starfields,

tables etc.

HomeFinder

•

One of the first DQ interfaces

FilmFinder

Dynamic Query Controls

•

Check boxes and buttons (Nominal with low cardinality)

•

Sliders and range slider (ordinal and quantitative data)

•

Alphaslider (ordinal data) (Ahlberg & Shneiderman 1994)

– Small-sized widget to search sorted lists

– Online-text output

– Two-tiled slider thumb for dragging operations with di

ff

erent

granularities

– Letter index visualizing the distribution of initial letters – jump to a

position in the slider

– Locating an item out of 10,000 items ~ 28s for novice users

– Pros and cons to text entry?

•

Extend data sliders with data visualization

(Eick 1994)

Dynamic Queries Online

•

Online examples:

– Apartment Search (http://immo.search.ch)

– Diamond search (http://www.bluenile.com)

DQ in current search interfaces

•

DQ have become widespread with fast search

algorithms and increased computing capacity

– search happens while typing in search terms in google search

– new routes are calculated while point is dragged in google

Making Money with Dynamic Queries

•

Starfield displays and

Dynamic Queries

provided the basis for

SpotFire

•

Christopher Ahlberg

– 1991: Visiting student from

Sweden at the HCIL

University of Maryland

– 1996: Founder of SpotFire

– 2007: SpotFire was sold

for 195 Mio. $

Summary Dynamic Queries

•

Users can rapidly, safely playfully explore a data space – no

false input possible

– Users can rapidly generate new queries based on incidental learning

– Visual representation of data supports data exploration

– Analysis by continuously developing and testing hypotheses (detect

clusters, outliers, trends in multivariate data)

– Provides straightforward undo and reversing of actions

•

Potential problems with DQ as implemented in the FilmFinder?

– Limit of query complexity – filters are always conjunctive

– Performance is limited for very large data sets and client / server

applications

– Controls require valuable display space

– Information is pruned