Universal Information Graphs via Hierarchical Graph Maps and Graph Fusion

1
Universal Information Graphs
via Hierarchical Graph Maps
and Graph Fusion

• James Abello, DyDAn Rutgers University
• Portions of this work have been done jointly
  with
• J. Crobak (Rutgers) , R. Dementiev(U.
  Karslhube) , I. Khan(Rutgers), H. Schulz (U.
  Rostock)
• Partially supported by LLNL (in
  consultation with Scott Kohn )

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Universal Information Graphs Encode
multiple relations among a set of entities.
Usually, each entity has associated with it a set
of possibly labeled attributes. Entities
people, organizations, places, events,
documents, telecommunication activities,
computer addresses, web page descriptors,
images, videos, parts of speech, etc.
Entities are associated when they co-occur in
a logical unit of interest. Associated entity
pairs get tagged by a vector of labels and by a
weight vector that measures the strength of the
associations. Patterns correspond to special
subsets of entities and their inter
relations.
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• Overall Goal
• To efficiently uncover and classify patterns
  that can be used as triggers to take preventive
  actions against potential society threats
• How ?
• 1. Design similarity measures among data
  entities via a semantic dot product. This
  amounts to quantification via some weighting
  mechanism of the set of attributes shared by a
  set of entities.
• The main question is how to learn these
  weights and how to determine levels of
  agreement that correspond to cluster pattern
  formation in the data.
• Instead of some form of relational data base
• Use vertex and edge weighted labeled
  multi-graphs.
• 2. Since scale and interactivity are essential
  we opt for
• Hierarchical Graph Map methods that are
• a. I/O efficient and
• b. parameterized by the amount of RAM and
  real state screen available to an analyst
  posing queries (semi-external algorithms).

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What have we done? A Client- Server
SystemThe server uses our C library hgv. It
creates hierarchical maps of semi-external graphs
(up to billion edges on an 8Gb RAM commodity
machine). It provides parameterized abstractions
of the data.The client is used to interactively
navigate server graph answers. It builds up on
our previous work on graph visualization systems
( GraphView ).
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Major Computations Structural Groupings

• Connected components
• Peripheral Trees
• Biconnected components
• Clusters based on topology and labeling
  information
• Graph Abstractions ( via Sparse Cuts )

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Server Side Hierarchy Creation

• INPUT Weighted simple undirected input graph G
  (V,E)
• E possibly larger than will fit in RAM.
• Apply external memory weighted contraction
  algorithm (MST or Matching)1.
• Find antichain/slice/cut in the hierarchy that
  just fits in RAM by iteratively contracting edges.

Binary hierarchy on semi-external graph
Binary hierarchy on internal graph
1 J. Abello, Hierarchical Graph Maps, Computer
Graphics, 2004
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Visualization Client Interactivity

• Process each chunk of IH edges using the
  hierarchical map obtained via our topological
  grouping/clustering algorithms.
• Starting from the higher level groups/clusters,
  layout each subgraph on demand.
• If we hit the leaf nodes of the current chunk,
  load the next chunk into memory, process it in
  the same way and hook it to the hierarchy.

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Visualization Samples Wordnet, Sample of General
Queries, Terrorist Incidents, From an SQL query
to its graph (via PubMed Descriptors).
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Global Terrorist Data Base Picks

• Terrorist Incidents in Country_Name
• perpetrated by Group_Name
• Sample 1 Terrorist Incidents in Cyprus
  perpetrated by Lebanese.
• Comment The answer set is very focused
• Terrorist Incidents in ltCountrygt
• Sample 2 Terrorist Incidents in Bolivia.
  Comment The answer set is split into several
  connected pieces each with a distinctive
  characteristic

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Global Terrorist Data Base Picks (cont)

• Sample 2
• Terrorist Incidents in Bolivia (continued)
• Comment Notice the connection with the
  pro-palestinian group.

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Global Terrorist Data Base Picks (cont)

• Terrorist Incidents with ltAttack_Typegt and
  ltFatalitiesgt
• Terrorist Incidents with Kidnapping
• and Fatalities.
• Comment A more varied answer set.
• Notice the several connected pieces with
  distinctive characteristics.

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Global Terrorist Data Base Picks (cont)

• Terrorist
• Incidents with
• Kidnapping
• and Fatalities.
• Comment A more varied answer set.
• Notice the several
• connected pieces
• with distinctive
• characteristics.

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Global Terrorist Data Base Picks (cont)

• Terrorist
• Incidents with
• Kidnapping
• and Fatalities.
• Comment A more varied answer set.
• Notice the several
• connected pieces
• with distinctive
• characteristics.

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Global Terrorist Data Base Picks (cont)

• Terrorist
• Incidents with
• Kidnapping
• and Fatalities.
• Comment A more varied answer set.
• Notice the several
• connected pieces
• with distinctive
• characteristics.

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Kidnappings with fatalities (cont)
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Graph Fusion (supported by LLNL)

• Problem Statement Given a collection of entities
  each with an associated set of attributes the
  corresponding Universal Graph pre-supposes that
  we have the ability to efficiently compute a
  notion of semantic similarity between every pair
  of entities (a quadratic computation). Graph
  Fusion is the reverse process, i.e. how much of
  the Universal Graph can we efficiently recover
  from its collection of projections into selected
  subsets of attributes?
• Typical scenario an entity may have identities
  in email, call detail, web pages, blogs, instant
  messaging, chat rooms, etc. As such it has its
  own graph neigborhoods on each of these networks.
  The question is how to approximate from these
  local neighborhoods the neighborhood of this
  persona in the Universal Graph.
• Our current approach deals with the restricted
  case in which there is a known Taxonomy for the
  set of entity attributes of the Universal graph.
• We have developed some graph fusion mechanisms
  for this case and have applied them to the PubMed
  data base (Research supported by LLNL). These
  methods are based on Spanning Trees and
  Matchings.

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PubMed Data Base SamplesKeyPhrases eyes OR
vitamin
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PubMed Data Base SamplesKeyPhrases eyes OR
vitamin
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Graph Fusion via a DAG Taxonomy.

• Fuse Multirelational Data Stats on the vertexes
  and edges of a DAG Taxonomy
• For a vertex v in the DAG and an entity type
  EType in the Collection
• Let EType(v, Collection) entities of Etype
  with label(v)
• Example In PubMed, Number of papers with a
  given Mesh
• Similarly Number of Authors with a given
  Mesh, etc
• For an edge (u,v) in the DAG and an entity
  type EType in the Collection
• Let Etype((u,v), Collection) SimilarityOf(
  Etype entities with labels label(u) and label(v)
  )
• Example In PubMed DAG,
• Paperweight(u,v) JaccardCoefficient(Papers
  with label(u) or label(v))
• Authorweight(u,v) JaccardCoefficient(Authors
  with label(u) or label(v))
• Example The DAG Taxonomy on Meshes from PubMed
  (Demo samples).

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How good is a partition(i.e. a MAC)? Use
Information Loss

• General View Each point has certain probability
  of being a member of one of the sets in the
  partition. If a random variable X takes values on
  Range(X) is natural then to partition Range(X) in
  such a manner that a random variable P over the
  partition representatives becomes a reasonable
  quantization of X.
• The quality of P can be measured as I(X) I(P)
  /Information Loss /
• The expectation of X is the unique optimal vector
  s that achieves the minimal expected distortion
  Evdivergence(X,s). This suggests to define a
  divergence based measure of information I(X) as
  Evdivergence(X, EvX)
• Recent advances characterize the class of
  functions that admits kmeans iterative relocation
  schemes where a corresponding distortion based
  global objective function is progressively
  decreased. These include Square Loss, KL
  Divergence, Logistic Loss, Mahalanobis Distance
  and the Itakura-Saito distances used in signal
  processing.

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What About Multiple Hierarchies(Taxonomies) ?

• For two hierarchies the approach can be
  generalized via restrictewd cross products.
• As an example video demo of Matrix Zoom. One
  hierarchy is the geography and the other is
  application dependent.
• Go to Video of Matrix Zoom.

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Some interactivity Tricks

• Since views get cluttered some efforts have been
  made to alleviate this.
• Video demo of Fish EyeViews and Edge Lenses.

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Conclusions

• Advantages
• With parameter tuning and adequate Ram
  resources these type of systems remain
  interactive even when dealing with very large
  graphs via graph maps derived from hierarchy
  trees. Currently, extending it to graph maps
  derived from hierarchy DAGs.
• The approach is applicable to almost any type of
  graph, regardless of density. It turns out that
  large degree which is usually considered just a
  nuisance now becomes a delicate issue.
• Parameterized interactivity allows it to run on
  less powerful systems
• Structural grouping/clustering algorithms
  performs well (removal of subtrees helps a lot)
• Needed Improvements/Extensions
• Extend the system to directed multi-graphs
  (currently it handles undirected graphs).
• Add Data Streaming Capabilities

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Conclusions (cont)

• Needed Improvements/Extensions
• Extend the system to directed multi-graphs
  (currently it handles undirected graphs).
• Add Data Streaming Capabilities
• Improved ways to effectively summarize contents
  of a group/cluster. Currently, we use a
  hierarchical frequency based group labeling
  algorithm.
• Need ways to better guide users to potentially
  interesting
• pieces of the data.

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Questions?

• Contact Info
• James Abello abello_at_dimacs.rutgers.edu
• Related Publications
• Semi-External Induced Subgraphs, J. Abello and
  R. Dementiev, in preparation.
• HGV A C Library to compute Hierarchical Graph
  Views, J. Abello and J. Crobak, in preparation.
• Name That Cluster, J. Abello, H. Schulz,, B.
  Gaudin, C. Tominski, in Infovis 2006, IEEE,
  Sacramento, CA.
• CVG Coordinate Graph Visualizations, J.
  Abello, C. Tominski, H. Schumann, in Infovis
  2006, IEEE, Sacramento, CA.

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• attackid attacklabel shortlabel
• 3 Assassination ass
• 4 Bombing bom
• 5 Facility Attack fac
• 6 Hijacking hij
• 7 Kidnapping kid
• 8 Maiming mai
• 9 Assault alt
• 10 Mass Disruption md
• 11 Arson ars
•  
•  

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TargetType Table

•  targetid targetlabel shortlabel
• 0 - -
• 1 US Diplomat udi
• 2 US Police/Military upm
• 3 US Other uot
• 4 US Unknown uun
• 5 US Government ugo
• 6 US Political Parties upp
• 7 US Media ume
• 8 US Business ubu
• 9 US Transportation utr
• 10 US Utilities uut
• 11 Foreign Business fbu
• 12 Domestic Business dbu
• 13 Transportation tra
• 14 Utilities uti
• 15 Media med
• 16 Diplomat dip
• 17 Government gov