Hank Childs, University of Oregon November 22 nd, 2013 Force Directed Layouts

Upcoming Schedule 11/21: alternate lecture #1 (force directed layouts) – 5pm, Deschutes /22: uncertainty visualization (KP) 12/2: alternate lecture #2 (force directed layouts) – 2pm, HEDCO /4: medical visualization (Erik Anderson) 12/6: unstructured grids Faculty fireside (parallel visualization): – Week of 12/2 or week of 12/9 Final: Thurs 12/12, 3:15PM, Rm 220

Undirected graphs G = (V, E) – V: set of vertices – E: set of edges, (a,b), where a,b in V Possible: weights – Weights on edges – Weights on vertices

Inspiration: LinkedIn Maps

Is this a good graph? Why or why not? Positive aspects: 1)Related nodes are near each other 2)Aesthetically pleasing Positive aspects: 1)Related nodes are near each other 2)Aesthetically pleasing

Aesthetic Considerations Crossings – minimize towards planar Total edge length – minimize towards proper scale Area – minimize towards efficiency Maximum edge length – minimize longest edge Uniform edge length – minimize variance Total bends – minimize orthogonal towards straight-line Some details from this slide borrowed from John Stasko’s Graph lecture: Slide c/o: R. Maciejewski, ASU

What is the source data? LinkedIn: – I send you a LinkedIn request, or you send me a LinkedIn request. Data: – a list of people – a list of people they are connected to LinkedIn Maps: – only consider connections to my connections if I am connected to person X, and they are connected to Y, and I am not connected to Y, then just ignore Y

How is LinkedIn data converted to graphs? Let P be the list of my connections I have an edge to every one of my connections – (hank, q) for all people q in P Create edge (x,y) if x and y are in P and x is connected to y – Edge weights: number of shared connections between x and y Given data like this, how can we make a “good” graph? (“Good” = related nodes close to each other, aesthetically pleasing)

Force-directed layouts Common information visualization algorithm Not clear this is the algorithm LinkedIn Maps is using – Still graph G = (V, E), vertices V, edges E – Still edge weights on E Goal: edges are more or less of equal distance, as few crossing edges as possible

Force-directed layouts: idea Two competing forces: – Edges become springs pull vertices together Hooke’s law – Vertices become electric particles push vertices apart Coulomb’s law

Force-directed layouts: idea Place vertices in random initial position Iteratively change vertex positions based on forces This iterative process ultimately converges, in a way that minimizes energy (over both spring & electric repulsion) – If it doesn’t converge add dampening factor The final position of the vertices is the force- directed layout

Interactivity Use Cases Watching the graph converge Modifying a graph after convergence – Just modify layout – Associate two vertices together more closely – Set constraints (sticky layout)

Force-directed layouts: problem Updating vertex v_i requires considering forces from v_1, v_2, … v_n, as well as all edges incident to v_i. Result is O(n^2) work per iteration – Number of iterations estimated as O(n) Total work is O(n^3) This becomes very expensive when n > 1000

Algorithms for improved performance Overlaps with physics: n-body particle equations Multiple approaches Barnes-Hut – When considering one vertex, minimize # of other vertices considered – Drops to O(n*log(n)) per iteration, O(n^2*log(n)) overall – Depends on quadtree data structure

Octree Source: wikipedia

Quadtree Source: wikipedia

Barnes-Hut Divide graph into quadtree Iterate over each vertex. – Do NOT consider Coulomb effects for all other vertices – Instead: group vertices in distant quad tree cells together consider these vertices as a single vertex (with a higher mass) –  less vertices considered Intuition on why this works: the close ones are most important and they are still considered individually

Gephi Gephi: open-source network analysis and visualization software package – Maintained by French non-profit (Gephi Consortium) Written in Java on the NetBeans platform Example usages: – Twitter network traffic – Network analysis We will look at relationships in “Les Miserables” using data set compiled by Donald Knuth.

Les Miserables

Les Miserables Movie Jean Valjean Fantine Cosette Javert + many others, including revolutionaries, priests & nuns, prisoners, criminals, policemen Marius Thenardiers

Demonstration (Now Gephi demonstration with Samuel Li)