Chapter 10 Arrange Networks and Trees Vis/Visual Analytics, Chap 10 - - PowerPoint PPT Presentation

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Chapter 10 Arrange Networks and Trees Vis/Visual Analytics, Chap 10 Arrange Networks/Trees 1 CGGM Lab., CS Dept., NCTU Jung Hong Chuang The Big Picture Relational data A set of entities and a network of relationships among them

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Chapter 10 Arrange Networks and Trees

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 1

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The Big Picture

  • Relational data

– A set of entities and a network of relationships among them – Appear in a wide array of disciplines

  • Complex relational data

– Wikipedia has millions of articles that form a network through cross-references – FB connects more than a billion users in a complex structure of friends, group invitations, games, advertising.. – Continue to expand and evolve daily

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 2

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The Big Picture

  • Deal with complex network

– Using statistics to reason about the dynamics of such complex network is not generally effective

  • r practical

– Visual analytics – visualization + interactions

  • Complex network drawing
  • Time-varying network

– Each node addition/deletion can affect large-scale patterns, such as clusters

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 3

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The Big Picture

  • Node-link diagram visual encoding idioms

– Use the connection marks

  • Marks represent links rather than nodes

– For tree and network data

  • Matrix views

– Directly show adjacency relationships – For tree and network data

  • Enclosure

– Show with the containment marks

  • Enclosing link marks show hierarchical relationships

through nesting

– For tree data, network data too?

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 4

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The Big Picture

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 5

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Connection: Link Marks

  • Node-link diagram

– The most common visual encoding idiom for tree and network data

  • Nodes: point mark
  • Links: line marks
  • Tree examples

– Small trees

  • Triangular vertical node-link layout
  • Spline radial (circular) layout

– Depth of tree is encoded as distance away from the circle center – Links are smooth curve splines

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 6

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Connection: Link Marks

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 7

Node–link layouts of small trees. (a)Triangular vertical for tiny tree. (b) Spline radial layout for small tree.

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Connection: Link Marks

– Larger trees

  • Rectangular horizontal node-link layout

– Edges are colored with a purple to orange continuous colormap according to the Strahler centrality metric

  • Bubble tree node-link layout

– Radial rather then rectilinear » Subtrees are laid out in full circles rather than partial arcs – Spatial position does encode information about tree depth » As relative distance to the center of parent rather than as absolute distances in screen space

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Connection: Link Marks

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 9

Two layouts of a 5161-node tree. (a) Rectangular horizontal node–link layout. (b) BubbleTree node–link layout.

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Connection: Link Marks

  • Network

– Commonly represented as node-link diagrams – Distance between two nodes

  • The number of hops within a path

– Well suited for tasks that involve understanding network topology

  • The direct and indirect connections between nodes
  • Tasks

– Finding all possible paths from one node to another – Finding the shortest path between two nodes – Finding all the adjacent nodes one hop away from a node – Finding nodes that act as a bridge between two components that would otherwise be disconnected

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 10

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Connection: Link Marks Layout methods

  • Force-directed layout
  • Multiscale approach
  • Begin by laying out a small approximation of the graph,

and then progressively layout finer approximation until entire original graph is completed

  • Algebraic methods
  • Uses linear algebra to calculate the layout directly.
  • Faster than previous two. Tend to work well on regular

grid-like networks.

  • Clustering-based methods
  • Clustering the graph in a preprocessing and then using

the clustering to do the layout itself

  • Treemap, Space-filling curve

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 11

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Connection: Link Marks Force-Directed Layout

  • Force-directed placements
  • Start by placing nodes randomly with a spatial region
  • Iteratively refine node locations according to the

pushing and pulling of the simulated spring forces to gradually improve the layout

  • Typically do not directly use spatial position to encode

attribute values of either nodes or links

– A side effect of the layout computation

  • Analyzing the visual encoding of force-directed layout

is somewhat subtle

– Spatial proximity does indicate grouping through a strong perceptual cue; but sometimes arbitrary » Nodes near each other because they were repelled from elsewhere, not because they are closely connected

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 12

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Connection: Link Marks Force-Directed Layout

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 13

(a) Force-directed placement of small network of 75 nodes, with size coding for link attributes. (b) Larger network, with size coding for node attributes.

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Connection: Link Marks Force-Directed Layout

  • Another problem of force-directed placement

– Layouts are often nondeterministic because the use of randomness » The layouts will look different each time the layout is computed » Spatial memory cannot be exploited across different runs » Region-based identifications such as “the stuff in the upper left corner” are not useful » Lead to different proximity relationships each time

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 14

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Connection: Link Marks Force-Directed Layout

  • A major problem of force-directed placement: scalability

– Scalability both in terms of visual complexity of the layout and the time required – Yield readable layouts quickly for tiny graphs with dozens

  • f nodes

– Quickly degenerates into a hairball of visual clutter with even a few hundred nodes

  • Many force-directed placements

– Have many parameters to tune » One set is good for a dataset, but is bad for another – Can get stuck in local minimum energy configuration

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 15

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Connection: Link Marks Force-Directed Layout

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 16

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Connection: Link Marks Multilevel Layout

  • Multilevel network idioms – scalable

– Original network is augmented with a derived cluster hierarchy to form a compound network

  • The cluster hierarchy is computed by coarsening the
  • riginal network into successive simpler networks that

attempt to capture the most essential aspects of the

  • riginal one
  • Layout the simplest version first, and then improve the

layout with the more and more complex versions

– Both the speed and quality of layout can be improved – Do better at avoiding the local minimum problem – Still cannot avoid hairball problem

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 17

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Connection: Link Marks Multilevel Layout

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 18

Multilevel graph drawing with sfdp [Hu 05]. (a) Cluster structure is visible for a large network of 7220 nodes and 13,800 edges. (b) A huge graph of 26,028 nodes and 100,290 edges is a “hairball” without much visible structure.

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Connection: Link Marks Multilevel Layout

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 19

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Connection: Link Marks Comparison

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 20

(6107 nodes, 15160 edges)

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Connection: Link Marks Comparison

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 21

For rapid overview, only clustering –based layout methods provide rapid and insightful results, particularly with larger networks. SFC methods clearly use the screen space more efficiently and the clusters are more clearly distinct.

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Matrix Views

  • Adjacency matrix

– All the nodes are laid out along vertical and horizontal edges – Edges are indicated by coloring an area mark in the cell – Encoding matrix cell for another attribute

  • Color encoding
  • Size encoding

– Typically only a few levels

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 22

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Matrix Views

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 23

Comparing node–link matrix and matrix views of a network. (a) Node–link and matrix views of small network. (b) Matrix view of larger network. (c) Node–link view of larger network.

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Matrix Views

  • Can achieve very high information density

– Up to a limit of 1000 nodes and 1 M edges

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 24

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Costs and Benefits: Connection vs. Matrix

Node-link layout

  • Strength

– For small networks, extremely intuitive for supporting many of the abstract tasks

  • For tasks that rely on understanding the topological

structure

– Path tracing, searching local topological neighborhoods a small number of hops from a node

  • For tasks such as general overview or finding similar

substructures

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 25

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Costs and Benefits: Connection vs. Matrix

Node-link layout

  • Weakness

– Past a limit of network size and link density

  • Occlusion from edge crossing each other and crossing

underneath nodes

  • Link density: # of links/# of nodes

– Upper limit: 3 or 4

  • Even for networks with a link density below 4

– Network size increases  hairball problems

  • Multilevel idioms help, limits do and will remain
  • Interactive navigation and exploration idioms can

address the problems partially but not fully

  • Filtering, aggregation, and navigation can ameliorate

clutter problem, but impose cognitive load on users

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 26

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Costs and Benefits: Connection vs. Matrix

Matrix view

  • Strength

– Perceptual scalability for both large and dense networks

  • No occlusion problem. Effective even at very high

information densities

– Can handle dense graph up to the math limit #(edge)=#(node)^2

  • Predictability

– Be laid out within a predictable amount of space

  • Stability

– Adding a new item cause only a small visual change – For force-direct graph, may cause a major change

  • Support of reordering

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 27

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Costs and Benefits: Connection vs. Matrix

  • Weakness: Unfamiliarity, need training

– With sufficient training

  • Many aspects of matrix views can become salient

– Tasks of finding specific types of nodes or node groups that are supported by both matrix and node-link views » Clique in a graph is a square block of filled-in cells along the diagonal » Biclique structure of node subsets – edges connect each node in one subset with one in another is salient, but different, in both views » The degree of a node

  • Most crucial weakness

– Lack of supporting for investigating topological strudture

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 28

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Costs and Benefits: Connection vs. Matrix

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 29

Characteristic patterns in matrix views and node–link views: both can show cliques and clusters clearly.

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Costs and Benefits: Connection vs. Matrix

An empirical study compared node-link and matric views

– Node-link views are best for small networks and matrix views are best for large networks – Some tasks are more difficult for node-link views as size increased, but ok for matrix views

  • Estimate the number of nodes and edges
  • Finding the most connected node
  • Finding a node given its label
  • Finding a direct link between two nodes
  • Finding a common neighbor between two nodes

– Finding a path between two nodes is difficult in matrix view

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 30

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Containment: Hierarchy Marks Treemap

  • Containment marks

– Very effective at showing complete information about hierarchical structure – Connection mark

  • only show pairwise relation between two nodes
  • Treemaps

– An alternative to node-link tree

  • Hierarchical relationships are shown with containment

marks rather than connection mark

  • All children of a node are enclosed within the area of

that node, creating a nested layout

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 31

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Containment: Hierarchy Marks Treemap

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 32

Treemap layout showing hierarchical structure with containment rather than connection

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Containment: Hierarchy Marks Treemap

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 33

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Containment: Hierarchy Marks Comparison

Seven visual encoding idioms for tree data

(a) Rectilinear vertical node-link

  • Use connection to show relationship, with vertical

spatial position for depth and horizontal position for sibling order

(b) Icicle

  • With vertical spatial position and size showing depth
  • Horizontal position showing link relationship and

sibling order

(c) Radial node-link

  • Connection for link relation, radial depth spatial

position for tree depth, radial angular position for sibling order

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 34

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Containment: Hierarchy Marks Comparison

(d) Concentric circles

  • Radial spatial position and size showing depth, radial

angular position showing link relation and sibling order

(e) Nested circles

  • Radial containment, with nesting level and size

showing depth

(f) Treemap

  • Rectilinear containment, with nesting level and size

showing depth

(g) Indented outline

  • Horizontal spatial position showing depth and link

relation, vertical spatial position showing sibling order

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 35

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Containment: Hierarchy Marks Comparison

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 36

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Containment: Hierarchy Marks GrousFlocks

GrouseFlocks for compound networks

  • Network + derived cluster hierarchy

– Network nodes: leaves of the tree – Interior tree nodes encompass multiple nodes – Hierarchy is used only to accelerate force- directed layout

  • GrousFlocks

– Combined view using containment marks for the associated hierarchy and connection marks for the original network links

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 37

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Containment: Hierarchy Marks GrousFlocks

Vis/Visual Analytics, Chap 10 Arrange Networks/Trees CGGM Lab., CS Dept., NCTU Jung Hong Chuang 38

GrouseFlocks uses containment to show graph hierarchy structure. (a) Original graph. (b) Cluster hierarchy built atop the graph, shown with a node–link layout. (c) Network encoded using connection, with hierarchy encoded using containment.