Small World Networks: Applications in Document Clustering and Healthcare

1
Small World Networks Applications in Document
Clustering and Healthcare

• Brant Chee
• Bruce Schatz
• University of Illinois
• http//www.beespace.uiuc.edu

2
Small World Graph
Clauset et al., 2004
3
Small World Graph

• Characteristic Path Length
• The typical separation of nodes in a graph.
• lrand ln(N)/ln(z)
• Clustering Coefficient C
• Average fraction of pairs of neighbors of a node
  which are also neighbors of each other.
• Average number of nodes that are cliques!
• Crand z/N
• Small World Graph
• C gtgt Crand
• L Lrand
• Ngtgt z gtgt ln(N)

Newman, 2000
4
SW MI Graph
Sole et al., 2003
5
PurposeSo What?

• Facilitate Exploratory Process
• Search result clustering
• Information discovery
• Develop Middle Ground Algorithms
• Interactive responses AND
• Useful clusters
• Language as a Small World Network
• Make use of underlying structure of language

6
System Overview
7
Graph Construction

• A node is a term in the index
• Terms bounded by frequency cutoff.
• Terms occurring lt 5 documents gt 25 documents are
  removed.
• Edges between nodes are determined by Mutual
  Information
• P(x,y) is calculated in a window of the size of
  the abstract

log2
Church and Hanks, 1989
8
What threshold?
Threshold N z l lrand ?l C Crand
0.001 6612 9.85 4.31 3.85 .46 0.57 0.002
0.002 4087 5.09 4.84 5.11 .27 0.68 0.001
0.005 1342 2.66 5.51 7.36 1.85 0.75 0.002
0.01 517 1.69 1.21 11.91 10.7 0.81 0.003
0.02 161 1.22 0.34 25.55 25.2 0.91 0.008
0.05 25 1.12 0.06 28.40 28.3 1.0 0.045
9
Where to cut?
10
Clustering Algorithm

• Clauset, Newman and Moore, 2004
• Generalization for nodes based upon Newmans
  algorithm.
• Based upon modularity The fraction of edges
  within communities versus the fraction falling at
  random in the same network. 0 if little
  community structure, between .3 if there is
  significant structure.
• If just looking at the fraction of nodes within
  communities, then max modularity will always be
  when all nodes are in one cluster.

?(ci,cj) 1 if ci and cj are in the same
community
2m of edges in graph
11
Experiments

• 3 clustering algorithms
• Complete Link (Cluto)
• K means (Cluto)
• Small World

12
Test Collections
Collection Search Terms Number of Abstracts Number of Terms
C1 General plasticity OR acetylcholine 81,746 267,981
C2 Specific microarray OR muscarinic OR plasticity OR ((cholinergic OR noradrenergic) AND receptor) 74,533 285,623
13
Experimental Setup

• Parameters left at package defaults
• Clustered with n 50,100,150 and 200.
• Clusters with less than 4 elements or more than
  50 elements were eliminated and the clustering
  which resulted in less than 40 clusters was
  chosen to be evaluated.

14
Quantitative Results
15
(No Transcript)
16
Conclusions

• Developed Balanced Clustering System
• Fast running time
• Good clustering results
• Modified Small World Algorithm
• Clustered text based on language model
• Produced many similar sized clusters

17
Social Networks as Small World Networks

• Social Network
• Network demonstrating who interacts with whom
• Threaded messages in a Newsgroup
• Create a network based on various characteristics
• Homophily
• Similar people tend to interact more than those
  who are dissimilar
• Race, Age, Gender, Social Class

18
Social Networks Inform Healthcare

• You do what your peers do
• Framingham Study
• 20 years of data
• Manually constructed networks
• Smoking Cessation
• Obesity
• Happiness
• Can we construct Social Networks automatically?

19
Social Network Construction and Evaluation

• We have lots of text available
• 30K message groups from Yahoo! Health
• Utilize threaded messaging to establish network
• Our cognitive model is evident in what we write
• Differentiate Schizophrenic from
  non-Schizophrenic
• LIWC
• Poets who commit suicide vs those that do not
• Differentiate depressed vs non depressed college
  students
• Sentiment positive or negative polarity
• Score evaluation metric

20
Example Message

• Hi All, I need your input. I'm havingabout
  27,000 extra pre-ventricular beats in a24 hour
  period, per a Holter monitor test.
  Myelectrophysiologist and cardiologist agree
  thatI should go on ltLinkgtsotalollt/Linkgt/Betapace
  . They are putting me in the hospitalon February
  26 to titrate me up on it. I'verefused the drug
  in the past because it is sucha dangerous
  drug. Is there anyone out there who couldgive
  me an idea of how you've done on thisdrug? I'd
  sure appreciate hearing about yourexperiences.
  Thanks so much.

21
Sentiment
22
Results

• Sentiment over all messages
• Proxy for mental model how happy they are
• Difference in average sentiment between two
  people
• Higher between random people in a network
• Lower for pairs that are closely connected
• Test methodology
• Compare means of differences between highly
  connected nodes vs random pairs of nodes
• T-Test for statistical significance
• P-value lt .0001 for 10 randomly selected groups

23
Acknowledgements

• Nyla Ismail for evaluating results
• Todd Littell for the MI code

24
Questions?

• Live demonstration available at
• http//www.beespace.uiuc.edu

25
References

• Church, K. W. and Hanks, P., (1989). Word
  association norms, mutual information, and
  lexicography. in Proc. of the 27th Annual
  Conference of the Association of Computational
  Linguistics, (Vancouver, B.C.), ACM Press, 76-83.
  
• Clauset, A., Newman, M. E. J., and Moore, C.,
  (2004). Finding community structure in very
  large networks. Phys. Rev. E, 70 (6), 066111.
• Kuhlthau, C. C., (1989). Information search
  process A Summary of research and implications
  for school library media programs. SLMQ, 18(1).
• Newman, M. E. J., (2000). Models of the small
  world. J. Stat. Phys., 101, 819-841.
• Solé, R., Ferrer-Cancho, R., Montoya, J. M., and
  Valverde, S., (2003). Selection, tinkering, and
  emergence in complex networks. Complexity, 8 (1),
  20-33.