Kamada kawai

Project.toml

@@ -9,8 +9,10 @@ ColorTypes = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
 Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
 Compose = "a81c6b42-2e10-5240-aca2-a61377ecd94b"
 DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"
+Distances = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
 LightGraphs = "093fc24a-ae57-5d10-9952-331d41423f4d"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Optim = "429524aa-4258-5aef-a3af-852621145aeb"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 

REQUIRE

@@ -4,3 +4,5 @@ Colors
 ColorTypes
 Compose 0.7.0
 LightGraphs 1.1.0
+Optim
+Distances

src/KamadaKawai.jl

@@ -0,0 +1,103 @@
+import Optim
+using Distances
+@doc raw"""
+ Computes the layout corresponding to
+
+ ```math
+\min \sum_{i,j} (K_{ij} - \|x_i - x_j\|)^\frac{1}{2},
+ ```
+where $K_{ij}$ is the shortest path distance between vertices `i` abd `j`, and $x_i$ and $x_j$ are the positions of vertices `i` and `j` in the layout, respectively.
+
+Inputs:
+
+ - G: Graph to layout
+ - X: starting positions. If no starting positions are provided a shell_layout is constructed.
+
+Optional keyword arguments:
+
+ - maxiter: maximum number of iterations Optim.optimize will perform in an attempt to optimize the layout.
+ - distmx: Distance matrix for the Floyd-Warshall algorithm to discern shortest path distances on the graph. By default the edge weights of the graph.
+
+ Outputs:
+
+ - (`locs_x`, `locs_y`) positions in the x and y directions, respectively.
+
+"""
+function kamada_kawai_layout(G, X=nothing; maxiter=100, distmx=weights(G) )
+    if !is_connected(G)
+        @warn "This graph is disconnected. Results may not be reasonable."
+    end
+    if X===nothing
+        locs_x = zeros(nv(G))
+        locs_y = zeros(nv(G))
+    else
+        locs_x = X[1]
+        locs_y = X[2]
+    end
+
+    function Objective(M,K)
+        D = pairwise(Euclidean(),M, dims=2)
+        D-= K
+        R = sum(D.^2)/2
+        return R
+    end
+
+    function dObjective!(dR,M,K)
+        dR .= zeros(size(M))
+        Vs = size(M,2)
+        D = pairwise(Euclidean(),M, dims=2)
+        D += I # Prevent division by zero
+        D .= K./D # Use negative for simplicity, since diag K = 0 everything is fine.
+        D .-= 1.0 # (K-(D+I))./(D+I) = K./(D+I) .- 1.0
+        D += I # Remove the false diagonal
+        for v1 in 1:Vs
+            dR[:,v1] .= -M[:,v1]*sum(D[:,v1])
+        end
+        dR .+= M*D
+        dR .*=2
+        return dR
+    end
+
+    function scaler(z, a, b)
+        2.0*((z - a)/(b - a)) - 1.0
+    end
+    N = nv(G)
+    Vertices=collect(vertices(G))
+
+    if X !== nothing
+        _locs_x = locs_x
+        _locs_y = locs_y
+    else
+        Vmax=findmax([degree(G,x) for x in vertices(G)])[2]
+        filter!(!isequal(Vmax), Vertices)
+        Shells=[[Vmax]]
+        VComplement = copy(Shells[1])
+        while !isempty(Vertices)
+            Interim = filter(!∈(VComplement),vcat([collect(neighbors(G,s)) for s in Shells[end]]...))
+            unique!(Interim)
+            push!(Shells,Interim)
+            filter!(!∈(Shells[end]),Vertices)
+            append!(VComplement,Shells[end])
+        end
+        _locs_x, _locs_y = shell_layout(G,Shells)
+    end
+
+    # The optimal distance between vertices
+    # Currently only LightGraphs are supported using the Dijkstra shortest path algorithm
+
+    K = floyd_warshall_shortest_paths(G,distmx).dists
+
+    M0 =  vcat(_locs_x',_locs_y')
+    OptResult = Optim.optimize(x->Objective(x,K),(x,y) -> dObjective!(x,y,K), M0, method=Optim.LBFGS(), iterations = maxiter )
+    M0 = Optim.minimizer(OptResult)
+
+    (min_x, max_x), (min_y, max_y) = extrema(M0,dims=2)
+    locs_x .= M0[1,:]
+    locs_y .= M0[2,:]
+
+    # Scale to unit square
+    map!(z -> scaler(z, min_x, max_x), locs_x, locs_x)
+    map!(z -> scaler(z, min_y, max_y), locs_y, locs_y)
+
+    return locs_x,locs_y
+end

src/layout.jl

@@ -197,7 +197,7 @@ Vector of Vector, Vector of node Vector for each shell.
 julia> g = smallgraph(:karate)
 julia> nlist = Array{Vector{Int}}(2)
 julia> nlist[1] = [1:5]
-julia> nlist[2] = [6:num_vertiecs(g)]
+julia> nlist[2] = [6:num_vertices(g)]
 julia> locs_x, locs_y = shell_layout(g, nlist)
 ```
 """
@@ -284,3 +284,5 @@ function _spectral(A::SparseMatrixCSC)
     index = sortperm(real(eigenvalues))[2:3]
     return real(eigenvectors[:, index[1]]), real(eigenvectors[:, index[2]])
 end
+
+include("KamadaKawai.jl")