Enhancing Set-Analysis
through Scalable Visualizations
Presented by:
Hamid Haidarian Shahri
(hamid@cs.umd.edu)
Mudit Agrawal
(mudit@cs.umd.edu)
May 09, 2006
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Information Visualization Spring 2006
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Content
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Problem Definition
Motivation
Dataset
Architecture
Visualization Methods
Interaction Tools
Demo
Future Work
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Problem Definition
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Analysis of sets by
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representing the clusters graphically
depicting their internal and external links
Scaling visualization
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Motivation
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Sets are encountered in various domains
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websites
commodities
publications
anything that has attributes!!
Visualization of sets to aid human perception is still
an unsolved problem
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no direct relations between sets (or its elements) in spatial
domain
can be grouped based on various attributes
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Dataset
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2700 law cases
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Each case identified by a numerical id
ranging from 1000 to 3718
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Tuples in the dataset imply a referencing
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Relation is unidirectional and not symmetric
(the referencing also implies a temporal
constraint on the cases)
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Snapshot of the data
First 50 links (approximately 0.1 percent of whole dataset)
(1001,1105,'100 S.Ct. 318'),(1001,1612,'101
S.Ct. 2352'),(1001,1018,'107 S.Ct. 1232'),(1001,1016,'112
318')
S.Ct. 2886'),(1001,2923,'113 S.Ct. 2264'),(1001,1016,'120 L.Ed.2d 798'),(1001,2923,'124 L.Ed.2d
539'),(1001,2286,'138 F.3d 1036'),(1001,2396,'238 F.3d 382'),(1001,3410,'438 U.S.
104'),(1001,1105,'444 U.S. 51'),(1001,1612,'452 U.S. 264'),(1001,1018,'480 U.S. 470'),(1001,1016,'505
U.S. 1003'),(1001,2923,'508 U.S. 602'),(1001,3410,'57 L.Ed.2d 631'),(1001,1105,'62 L.Ed.2d
210'),(1001,1612,'69 L.Ed.2d 1'),(1001,1789,'926 F.2d 1169'),(1001,1018,'94 L.Ed.2d
472'),(1001,3410,'98 S.Ct. 2646'),(1002,1276,'100 S.Ct. 2138'),(1002,1101,'105 S.Ct.
3108'),(1002,1018,'107 S.Ct. 1232'),(1002,1098,'107 S.Ct. 2378'),(1002,1016,'112 S.Ct.
2886'),(1002,1015,'114 S.Ct. 2309'),(1002,1016,'120 L.Ed.2d 798'),(1002,1013,'121 S.Ct.
2448'),(1002,1012,'122 S.Ct. 1465'),(1002,1015,'129 L.Ed.2d 304'),(1002,2316,'142 F.3d
1319'),(1002,1013,'150 L.Ed.2d 592'),(1002,1012,'152 L.Ed.2d 517'),(1002,1121,'266 F.3d
487'),(1002,3028,'306 F.3d 113'),(1002,3410,'438 U.S. 104'),(1002,1276,'447 U.S. 255'),(1002,1101,'473
U.S. 172'),(1002,1018,'480 U.S. 470'),(1002,1098,'482 U.S. 304'),(1002,1016,'505 U.S.
1003'),(1002,1015,'512 U.S. 374'),(1002,1013,'533 U.S. 606'),(1002,1012,'535 U.S. 302'),(1002,3410,'57
L.Ed.2d 631'),(1002,2091,'59 F.3d 852'),(1002,1276,'65 L.Ed.2d 106'),(1002,1889,'746 F.2d
135'),(1002,1101,'87 L.Ed.2d 126'),(1002,1018,'94 L.Ed.2d 472'),(1002,2319,'953 F.2d
1299'),(1002,1098,'96 L.Ed.2d 250'),(1002,3410,'98 S.Ct. 2646'),(1002,1022,'980 F.2d
84'),(1002,2670,'989 F.2d 362'),(1003,1104,'100 S.Ct. 383'),(1003,1611,'104 S.Ct.
2862'),(1003,1100,'106 S.Ct. 1018'),(1003,1099,'107 S.Ct. 2076'),(1003,1016,'112 S.Ct.
2886'),(1003,3110,'116 S.Ct. 2432'),(1003,1016,'120 L.Ed.2d 798'),(1003,1012,'122 S.Ct.
1465'),(1003,1881,'13 F.3d 1192'),(1003,3054,'133 F.3d 893'),(1003,3110,'135 L.Ed.2d
964'),(1003,1012,'152 L.Ed.2d 517'),(1003,1047,'18 F.3d 1560'),(1003,1886,'265 F.3d
1237'),(1003,2689,'271 F.3d 1090'),(1003,1358,'271 F.3d 1327'),(1003,1149,'28 F.3d
1171'),(1003,1040,'331 F.3d 891')
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Architecture
Clustering
Data
Module
Clustered
Data
Visualization
Module
Similarity
Metric
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Routine K-Means Clustering
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Data points are in
vector space.
x and  are vectors.
j
This assumption does
not hold for cases
represented as sets.
Centroids are not
simple geometric
means.
In fact, mean does not
make any sense.
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k
V  
i 1 jS
i
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x 
j
2
j
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Routine Self Organizing Map
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Wv and D are assumed to be vectors.
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Wv(t + 1) = Wv(t) + Θ(t)α(t) [D(t) - Wv(t)]
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This assumption does not hold.
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Similarity Measures
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Jaccard similarity
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Reference-based
similarity
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Weighted referencebased similarity
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A B
J ( A, B ) 
A B
S ( A, B)  A  B
WS ( A, B) 
Information Visualization Spring 2006
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f ( x)
x A B
A B
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Contribution to clustering
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Applying K-means and SOM for producing better
visualizations
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Not apparent at first glance, but the above algorithms
are not applicable to set visualization directly
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They assume a 2D or nD (vector) representation for
each data point (i.e. law case). More specifically, the
attributes must form a vector space.
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This assumption does not hold
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no clear geometric attribute corresponding to the dataset
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Similarity Metrics  Geometric Metrics
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1-D Partitioning
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2-D Partitioning
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Sequential arrangement
Distance based arrangement
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K-Means
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K-Means
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SOM after K-Means
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Various Interactive Tools
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Referencing pattern (activating all
links)
Local referencing
Density map
Representative element
Tool tip
Link follow-up
Search
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Referencing Pattern
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Local Referencing
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Local Referencing
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Density Map
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Density Map
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Representative Element
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Link Follow-up
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Link Follow-up
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Link Follow-up
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Link Follow-up
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Link Follow-up
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Link Follow-up
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Link Follow-up
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Link Follow-up
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DEMO
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Future Work
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Other clustering algorithms can be explored:
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Spectral
Fuzzy C-means
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More similarity functions
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Better initial posting of data
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Zooming and Panning
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References
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Guimerà, R., Mossa, S., Turtschi, A., Amaral, L.A.N., The Worldwide Air Transportation Network:
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Jain, A.K., Murty, M.N., Flynn, P.J., Data Clustering: A Review. ACM Computing Surveys, 1999.
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Bioinformatics, Volume 35, No. 7, July 2002, pp. 80-86.
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Thanks!
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