Probabilistic Graph Layout for Uncertain Network Visualization

• Christoph Schulz (Univ. of Stuttgart)• Arlind Nocaj (Univ. of Konstanz)• Jochen Goertler (Univ. of Konstanz)• Oliver Deussen (Univ. of Konstanz)• Ulrik Brandes (Univ. of Konstanz)• Daniel Weiskopf (Univ. of Stuttgart)

Presented By:-Subhashis Hazarika

(Ohio State University)

Objective

• Goal: To visualize the distribution of possible realizations of a probabilistic graph that reflects the certainty and uncertainty equally well.

• Contribution: Threefold– Provide a model of probabilistic graphs– Present a visualization technique for prob. graphs that combines splatting,

edge bundling, clustering and graph coloring.– Demonstrate and validate using representative example datasets.

Graph Model

• Probabilistic Graph, GP = (V, E, F)– V : set of nodes– E : set of edges– F : ( fij ){i,j} ∊ E is a set of PDFs of edge weights.

• Assumption: all edge weight probabilities are mutually independent.

Overview of Probabilistic Graph Layout

Graph Layout

• Sample weighted graphs GW1, …. GW

k from GP by sampling the edge weights independently.

• For each sample GWi : compute its node positions Pi using a force

directed layout with alignment to references node positions PR.

• For each node: use its positions in P1,… Pk as approximation to its distribution in 2D space.

Graph Layout• Force-directed Layout:

– Stress minimization, where

– For weighted graphs we use the inverted weights in the shortest path computation.

• Alignment with Anchoring:– To obtain stable orientation of the sample graphs transform them w.r.t an

anchor graph– Generally, the expected graph GW

E is computed using the expected edge weights.

– The positions PE from the force-directed layout is used as reference positions PR for anchoring.

– New stress function to minimize,

Graph Visualization (Node Splatting)• Apply KDE to the samples of each node to approximate the

underlying continuous distribution.

Graph Visualization (Node Splatting)• Result of bandwidth on the smoothness.

Graph Visualization (Edge Splatting)• Hierarchical edge bundling to preserve the network structure and

visible mental association of nodes and edges at the same time.

Graph Visualization (Edge Splatting)• Bundling strategy: using rational quadratic Bezier Curves.

Node Coloring and Labeling• Distinctness• Distribution• Overlap• Solution:

– Reduce it to a country graph.

– Use Welsh-Powell graph coloring algorithm.

Clustering• Cluster each set of node positions (DBSCAN)• Compute a smooth concave hull per cluster• Compute a hull contour with visibility based on cluster to cluster

geometry. Using cel-shading.

Synthetic Data

Synthetic Data• Deciding optimal anchoring stability value:

Synthetic Data

STRING Data (protein- protein interaction)

STRING Data (protein- protein interaction)

Travel times by Car

Limitation• Layout Stability• Layout Ambiguity• Computational Scalability : O(n.(n+m) + n2.r)• Perceptual Scalability

Thank you