Enhancing Set-Analysis through Scalable Visualizations

1
Enhancing Set-Analysis through Scalable
Visualizations
Presented by Hamid Haidarian Shahri
(hamid_at_cs.umd.edu) Mudit Agrawal (mudit_at_cs.umd.e
du)
2
Content

• Problem Definition
• Motivation
• Dataset
• Architecture
• Visualization Methods
• Interaction Tools
• Demo
• Future Work

3
Problem Definition

• Analysis of sets by
• representing the clusters graphically
• depicting their internal and external links
• Scaling visualization

4
Motivation

• Sets are encountered in various domains
• websites
• commodities
• publications
• anything that has attributes!!
• Visualization of sets to aid human perception is
  still an unsolved problem
• no direct relations between sets (or its
  elements) in spatial domain
• can be grouped based on various attributes

5
Dataset

• 2700 law cases
• Each case identified by a numerical id ranging
  from 1000 to 3718
• Tuples in the dataset imply a referencing
• 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 S.Ct. 2886'),(1001,2923,'11
  3 S.Ct. 2264'),(1001,1016,'120 L.Ed.2d
  798'),(1001,2923,'124 L.Ed.2d 539'),(1001,2286,'13
  8 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,'4
  80 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,'10
  7 S.Ct. 2378'),(1002,1016,'112 S.Ct.
  2886'),(1002,1015,'114 S.Ct. 2309'),(1002,1016,'12
  0 L.Ed.2d 798'),(1002,1013,'121 S.Ct.
  2448'),(1002,1012,'122 S.Ct. 1465'),(1002,1015,'12
  9 L.Ed.2d 304'),(1002,2316,'142 F.3d
  1319'),(1002,1013,'150 L.Ed.2d 592'),(1002,1012,'1
  52 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,'1
  00 S.Ct. 383'),(1003,1611,'104 S.Ct.
  2862'),(1003,1100,'106 S.Ct. 1018'),(1003,1099,'10
  7 S.Ct. 2076'),(1003,1016,'112 S.Ct.
  2886'),(1003,3110,'116 S.Ct. 2432'),(1003,1016,'12
  0 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')

(1001,1105,'100 S.Ct. 318')
7
Architecture
Visualization Module
Clustering Module
Clustered Data
Data
Similarity Metric
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Routine K-Means Clustering

• Data points are in vector space.
• x and are vectors.
• 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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Routine Self Organizing Map

• Wv and D are assumed to be vectors.
• Wv(t 1) Wv(t) T(t)a(t) D(t) - Wv(t)
• This assumption does not hold.

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Similarity Measures

• Jaccard similarity
• Reference-based similarity
• Weighted reference-based similarity

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Contribution to clustering

• Applying K-means and SOM for producing better
  visualizations
• Not apparent at first glance, but the above
  algorithms are not applicable to set
  visualization directly
• 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.
• This assumption does not hold
• no clear geometric attribute corresponding to the
  dataset

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Similarity Metrics ? Geometric Metrics

• 1-D Partitioning
• 2-D Partitioning
• Sequential arrangement
• Distance based arrangement

1 2 5 9
3 4 7 12
6 8 11 14
10 13 15 16
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K-Means
14
K-Means
15
SOM after K-Means
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Various Interactive Tools

• 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
22
Representative Element
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Link Follow-up
24
Link Follow-up
25
Link Follow-up
26
Link Follow-up
27
Link Follow-up
28
Link Follow-up
29
Link Follow-up
30
Link Follow-up
31
DEMO
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Future Work

• Other clustering algorithms can be explored
• Spectral
• Fuzzy C-means
• More similarity functions
• Better initial posting of data
• Zooming and Panning

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Thanks!