Comprehending Knowledge-Space Diagrams: Experiments and a Model

Christof Körner University of Graz

ERASMUS Intensive Seminar

Graz 2005

Supported by

Other Hierarchical Graphs

Computer File System

More Hierachical Graphs

Organisation Chart

More Hierachical Graphs

Preference Graph

Visual Properties: Planarity

Non-crossedcrossed

Visual Properties: Slopes

uprightslanted

Visual Properties: Levels

horizontalnon-horizontal

Visual Properties and Graphs

Crossed, slanted, non-horizontalNon-crossed, upright, horizontal

Early Experiments: Paradigm

Early Experiments: Results

Different Prior Knowledge

PlanaritySlopesLevels

Early Experiments: Results

Number of Comparisons

PlanaritySlopesLevels

Early Experiments: Discussion

• Planarity is the most important visual property

• Slopes and Levels have only a minor effect

•Planarity is independent of the other properties

Question:

• Where (and when) does planarity exert its influence?

Recent Experiment: Sequential Processing

The 3-Stage Model (Körner, 2004)

Paradigm: Sequence of Events

Results

0

100

200

300

400

Planarity Slopes Levels

Lat

ency

Dif

fere

nce

(m

s)

0

0.5

1

1.5

2

Dif

fere

nce

of

Fix

atio

n N

um

ber

Data Analysis: Scanpath Decomposition

• When was the first object fixated? End of Stage 1

• When was the second object fixated? End of Stage 2

• What happens then? Start of Stage 3 ?

• When does the manual response occur?

Results

Results

Results

-0.5

0

0.5

1

1.5

2

Planarity Slopes Levels

Cu

mu

lati

ve D

iffe

ren

ce in

Fix

atio

n N

um

ber

Stage 1

Stages 1 + 2

Stages 1 + 2 + 3

Discussion

• Is graph processing in 3 stages a waste of time?

NO!

• Visual search for a target object amongst a set of distractor objects is highly efficient and effortless

• An additional search stage does not slow down graph processing much

• A pure reasoning stage can focus on the relation of the objects located earlier

• 3-stage model of sequential graph reasoning provides detailed account of the course of comprehension

• Model provides clear and testable predictions

• Empirical evidence supports the model

• Model needs to be tested more rigorously

• Model may be extended to other types of graphs

Summary & Conclusions

Current: Gaze Contingent Displays

Current: Gaze Contingent Displays

Thank you!

ResultsNumber of Fixations for Visual Properties and Different Stages of

the Postulated Comprehension Model

Stage 1 Stage 2 Stage 3

Source df

Planarity (P) 1

Slopes (S) 1

Levels (L) 1

P S 1

P L 1

S L 1

P S L 1

F

.327

6.50*

5.87*

0.033

4.00

2.87

8.60*

F

2.51

11.55**

0.13

1.75

9.33*

0.075

0.525

F

61.37**

2.69

0.76

3.57

0.39

7.17*

1.70

The Future: Where do we go next?

• Search stages are functionally equivalent

The Future - Results: Pilot Study

0

20

40

60

80

100

120

Planarity Slopes Levels

Tim

e t

o F

ixat

ion

Dif

fere

nce

(m

s)

0

0.1

0.2

0.3

0.4

0.5

0.6

Nu

mb

er

of

Fix

atio

ns

Dif

fere

nce

The Future: Graphs and Visual Search

The Future: Where do we go next?

• Search stages are functionally equivalent

• Reasoning stage is separated