Weighted ASE.

[gaborcsardi]

From #38.

[gaborcsardi]

In the non-weighted version this is put on the diagonal of the matrix by default: degree(graph)/(vcount(graph) - 1). Do you want to use graph.strength (the sum of weights of incident edges) instead of degree in the weighted version?

[gaborcsardi]

graph.strength it is.

[dpmcsuss]

Hi, I was trying to work with weighted graphs and ASE. My approach to getting the non-weighted version of ASE was to set weights=rep(1,ecount(g)).

I was working with the graph

g <- read.graph("http://openconnecto.me/data/public/MR/MIGRAINE_v1_0/KKI-42/small_graphs_graphml/KKI-21_KKI2009-01_small_graph.graphml",format="graphml")
X1 <- adjacency.spectral.embedding(g,2,weights=rep(1,ecount(g))$X
E(g)$weight=1
X1 <- adjacency.spectral.embedding(g,2)

I got vastly different results for X1 and X2 above.

Also, this ER example gives slightly different results.

set.seed(12345)
g <- erdos.renyi.game(15,.4)
X1 <- adjacency.spectral.embedding(g,2,options= list(maxiter = 5000))
X1a <- adjacency.spectral.embedding(g,2,options= list(maxiter = 5000))
E(g)$weight = -log(runif(ecount(g)))
Xw <- adjacency.spectral.embedding(g,2)
X2 <- adjacency.spectral.embedding(g,2,weights=rep(1,ecount(g)),options= list(maxiter = 5000))

X1$X
#             [,1]       [,2]
#  [1,] -0.1960136  0.4523541
#  [2,] -0.7022076 -0.5052613
#  [3,] -0.4802431 -0.6745986
#  [4,] -0.4411350 -0.2387668
#  [5,] -0.7248353 -0.2607279
#  [6,] -0.8338896  0.1462500
#  [7,] -0.8032891  0.7138957
#  [8,] -0.6263277  0.4690501
#  [9,] -0.6431580 -0.5757554
# [10,] -0.7885311 -0.1028077
# [11,] -0.8208309  0.1917610
# [12,] -0.8284541  0.2344697
# [13,] -0.4311922  0.5618437
# [14,] -0.5658762 -0.6231745
# [15,] -0.5692550  0.1849964
X1a$X
#             [,1]       [,2]
#  [1,] -0.1960136 -0.4523541
#  [2,] -0.7022076  0.5052613
#  [3,] -0.4802431  0.6745986
#  [4,] -0.4411350  0.2387668
#  [5,] -0.7248353  0.2607279
#  [6,] -0.8338896 -0.1462500
#  [7,] -0.8032891 -0.7138957
#  [8,] -0.6263277 -0.4690501
#  [9,] -0.6431580  0.5757554
# [10,] -0.7885311  0.1028077
# [11,] -0.8208309 -0.1917610
# [12,] -0.8284541 -0.2344697
# [13,] -0.4311922 -0.5618437
# [14,] -0.5658762  0.6231745
# [15,] -0.5692550 -0.1849964
X2$X
#             [,1]       [,2]
#  [1,] -0.1922274  0.4703508
#  [2,] -0.7417220 -0.5701688
#  [3,] -0.4547676 -0.6017120
#  [4,] -0.4201575 -0.1868288
#  [5,] -0.7403614 -0.2849648
#  [6,] -0.8917938  0.1685238
#  [7,] -0.7899966  0.7276508
#  [8,] -0.5938849  0.4272288
#  [9,] -0.6270755 -0.5111985
# [10,] -0.7881188 -0.1318171
# [11,] -0.8001522  0.1806378
# [12,] -0.8225983  0.2150546
# [13,] -0.4285555  0.5780003
# [14,] -0.5510811 -0.5994857
# [15,] -0.5516544  0.1856551

[gaborcsardi]

See #50.