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Visual Analysis Algebra


Visual Analysis Algebra Anna Shaverdian, Hao Zhou H. V. Jagadish, George Michailidis University of Michigan – PowerPoint PPT presentation

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Title: Visual Analysis Algebra

Visual Analysis Algebra
  • Anna Shaverdian, Hao Zhou
  • H. V. Jagadish, George Michailidis
  • University of Michigan

Find a criminal network within a network? 50
different solutions, 5 minute videos to explain
process, pages of text
Desired Features in Visual Analysis
  • Mix and match ideas from multiple projects
  • Compare/Validate tools and techniques
  • Document and reproduce results from anothers
    visual analysis
  • Not ambiguous
  • Not wordy
  • Optimize techniques

Visual Analysis Algebra
  • Graph Model
  • Predicate/ Witness
  • Graph Matching Function
  • Operators
  • Selection
  • Labeling
  • Aggregation
  • Helper Functions
  • Visual Operators

Graph Model
  • Attributed Graph D G,X
  • Graph G (V,E)
  • Each node assigned unique id through ?(vertex)
  • Allows directed, multi-edge graphs
  • (Direction captured as an edge attribute)
  • Attributes X (XV, XE, XG)
  • Each attribute has a name, type, and value
  • Attributes can be intrinsic or computed
  • Intrinsic independent features which stay
    constant if graph topology changes
  • Computed Created through composition functions
  • Examples degree, betweeness, centrality

Example Graph Model
  • Cell Phone Network node represents a phone and
    an edge represents a call between two phones
  • D G (V,E), X (Xv XphoneID, XE
    Xdate, Xduration, Xtower, XcallerID, XG )
  • Initial data set with intrinsic attributes
  • Perform operations on sets of attributed graphs
    (closed algebra)
  • Dday1, Dday2, , Dday10

Predicate Definition
  • p (V, E, XV, XE, XG, !E)
  • V,E describe the graph structure
  • XV, XE, XG describe the conditions on the
    attributes in V, E
  • Example Xv.weight.node12 lt Xv.weight.node10 in
  • !E describe the excluded edges
  • An edge e1 in !E doesnt exist in the graph G and
    given a closed universe U, for all S where G is a
    subgraph of S, then e1 doesnt exist in S either

  • An attributed graph where there exists
  • Bijection mapping between nodes
  • The predicates conditions all hold on its node,
    edge, and graph attributes

Example Excluded Edges Witness
  • Predicate Attributed Graph

Graph Matching Function (? ) Subroutine used by
  • Inputs an attributed graph D and predicate p
  • Outputs
  • A list of witnesses W
  • Attributes of the nodes, edges, and graph of
    witness include all attributes of those
    respective elements in D
  • If one or more witnesses share ids attributes
    (ex. same but different rotation) combine to
    arbitrary one
  • A model witness X
  • Set of mapping lists of the witnesses in W to X

Graph Matching Function (?) Example
Attributed Graph
Age 12
Age 22
Age 16
Age 12
Witness found
Model witness
ID Model ID
1 6
2 7
3 8
4 9
Age 16
Selection Operator s
  • There are two types of selection operators
  • Work at the attributed graph level
  • Work at the element (nodes edges level)
  • Both operate on a set of attributed graphs and
    output a set of graphs

Set Selection sset
  • Given a set of attributed graphs D and a
    predicate p
  • Set Selection outputs the set of graphs where
    there exists a witness for the predicate
  • Example
  • The graphs with an average degree greater than 42
  • p (V , E , XV , XE ,
    XG Xg.averageDegree
    gt 42,!E )
  • sset, p(D1, D2, , D10) D
  • where D subset of D, for any Di in D,
    Xg.averageDegree gt 42

Element Selection selement
  • Given a set of attributed graphs and a predicate
  • s element,p (D1, D2, , Dn) Ui Di
  • where each Di Wi.p.1, , Wi.p.k the k
    witnesses of predicate p found in Di
  • An attributed graph for each witness found in the
    set of graphs

Example Element Selection selement
  • Select a subgraph from a set of graphs
  • p (V 1, 2, 3, E e12, e23, XV , XE
    , XG ,!E )
  • D1 (V(1,2,3,4), E e12, e14 , e23 , e34,
    X (,,)

s element,p (D1)
Labeling Operator
  • During graph analysis, need a way to select
    nodes of interest, mark them somehow, and
    continue analysis, sometimes referring to the
    marked nodes
  • We do this by labeling
  • Given a set of graphs and a predicate
  • We modify each graph to remember its match to the

Labeling Operator
  • For each attributed graph Di where there exists a
    witness for the predicate (using ? function)
  • Create the model witness structure x within Di
  • Label it with a unique group id
  • For each witness wj found in Di
  • Use the mapping lists to create directed edges
    between the wj and x

Labeling Example
Each edge has a group id to say its an edge to a
model witness and a structure id, to say its one
witness found
Attributed Graph
Example Labeling Visual Analysis
  • Given a Social Network
  • We have a suspected terrorist subnetwork and some
    features of interest
  • Analyze the subgraphs that match the suspected
  • Predicate structure isnt the final structure
    were looking for, its an intermediate step
  • VAST 2009 challenge

Example Labeling Visual Analysis
Degree 40
Geographic size small island
Helper Functions
  • Visual Operators
  • Ex. Feed values into a histogram, layouts,
  • Creating/Deleting
  • Create/Delete a set of nodes/edges/attributes
  • Copy a graph

Phone Record Case Study
  • In an attempt to characterize the entire network,
    we loaded the entire data set into MobiVis, which
    links people (blue nodes) if they had a phone
    conversation. Unfortunately, the tight
    connectivity of the resulting network made it
    impossible to find interesting patterns.
    Following the lead that person 200 is likely to
    be FerdinandoCatalano, we filtered the data to
    visualize only its closest nodes. Figure 1 shows
    the social network of person 200. Figure 1.
    Overview of the social network of
    FerdinandoCatalano (id 200). This reflects the
    general social structure over, at least, the
    first seven days. We can further characterize
    this network by looking at the links between the
    immediate neighbors of person 200. Persons 5,
    200, 97 and 137 seem to form a clique, whereas
    persons 1,2 and 3 form another. Looking at the
    amount of communication between those, which is
    depicted as the thickness of the edges, we
    discovered that 200 and 5 talk a lot among
    themselves. The color coding of the edges helps
    visualize the symmetry of the calls. For example,
    a warm color (orange) in the middle indicates a
    symmetric connection (both parties call each
    other frequently), whereas a biased orange color
    indicates more calls in the direction of the
    bias. We then characterized the network as being
    the connection of the two families the
    Catalanos, represented in persons 200
    (FerdinandoCatalano), 5 (which we believe is
    EstabanCatalano, since its tight connection to
    200), 97 and 137. And the Vidros, represented in
    persons 1,2 and 3. We can further characterize
    the substructure of the Vidrosas hierarchical.
    Although it was not evident at first, person 1
    always calls persons 2 and 3, which led us to
    believe that he has a role of coordinator. We
    validated this with another capability of
    MobiVis, which allows us to display people in the
    social network according to some semantic
    filtering criteria. In Figure 2(a), we display
    the people called by 1 and people who called
    person 1 . Those people who called person 1 are
    connected to an orange node, while people who
    where called by person 1 are connected to a red
    node. We can see that person 1 had a
    bi-directional communication with
    FerdinandoCatalano, but only in one direction
    with 2,3 and 5. Figure 2(b) shows the same
    analysis for person 5. We noticed an inverse
    behavior 1, 2 and 3 always call 5, but not vice
    versa. Furthermore, it helped us characterized
    the social structure better. The high symmetry of
    communication between 200 and 5 validates our
    claim about their identities being of
    Ferdinandoand EstabanCatalano, respectively.
    Person 1, however, seems to coordinate the
    efforts of 2,3 and 5, which suggests that he can
    be associated to David

Phone Record Case Study
  • Original data set (10 days)
  • D G (V,E), X (Xv XphoneID, XE Xdate,
    Xduration, Xtower, XcallerID, XG )
  • View Entire Graph
  • Create 10 graphs (per day)
  • Predicate for day i calls
  • pday_i(V v1, v2, E e12 , XV , XE i, XG ,!E )
  • Labeling by day
  • µday_iD
  • Element Selection on day_igroup
  • ?element,day_iD D1, D2, D3, D4, D5, D6,
    D7,, D8,, D9,, D10
  • View Each Graph

Phone Record Case Study
  • Look at pattern change in node 200s neighborhood
  • Predicate for node 200 neighbor
  • p200Neighbor(V v1, v2, E e12 , XV
    Xv.1.callerID 200, XE , XG ,!E )
  • Labeling by day
  • µ200NeighborD1, D2, , D10
  • Selection on 200 neighbor group
  • ?element,200NeighborD1, D2, , D10 D1,
    D2, D3, D4, D5, D6, D7, D8, D9, D10
  • Aggregate days 1-7 and days 8-10 graphs
  • Set Aggregation
  • ?set, pdays1-7. pdays8-10(D1, D2, , D10)
    Dday1-7, Dday8-10
  • Element Aggregation on CallerID
  • ?element, pdays1-7. pdays8-10(Dday1-7,
    Dday8-10 )

Algebraic Visual Analysis The Catalano Phone
Call Data Set Case Study
  • Anna Shaverdian, Hao Zhou, George Michailidis,
    and H.V. Jagadish, VAKD 09
  • Simulate many existing analytical workflows with
    operators from visual analytic algebra
  • Ability to do analysis beyond existing workflows

Multiple Step Social Structure Analysis with
  • Hao Zhou, Anna Shaverdian, H.V. Jagadish, George
    Michailidis, VAST 09
  • VAST 09 Flitter Mini Challenge Award Good Tool
  • Demonstrates Cytoscapes utility in identifying
    the structure in a social network