context("Spectral embedding of the Laplacian")
std <- function(x) {
x <- zapsmall(x)
apply(x, 2, function(col) {
if (any(col < 0) && col[which(col != 0)[1]] < 0) { -col } else { col }
})
}
mag_order <- function(x) {
order(abs(x), sign(x), decreasing=TRUE)
}
mag_sort <- function(x) {
x[mag_order(x)]
}
test_that("Undirected, unweighted, D-A case works", {
library(igraph)
library(Matrix)
set.seed(42)
g <- random.graph.game(10, 20, type="gnm", directed=FALSE)
no <- 3
A <- as(Matrix(diag(degree(g)), doDiag=FALSE), "generalMatrix") - g[]
ss <- eigen(A)
D <- ss$values
U <- ss$vectors
X <- std(ss$vectors %*% sqrt(diag(ss$values)))
Y <- std(ss$vectors %*% sqrt(diag(ss$values)))
## LA
au_la <- embed_laplacian_matrix(g, no=no, which="la", type="D-A",
scaled=TRUE)
as_la <- embed_laplacian_matrix(g, no=no, which="la", type="D-A",
scaled=FALSE)
expect_that(au_la$D, equals(D[1:no]))
expect_that(std(au_la$X), equals(std(X[,1:no])))
expect_that(as_la$D, equals(D[1:no]))
expect_that(std(as_la$X), equals(std(U[,1:no])))
## LM
au_lm <- embed_laplacian_matrix(g, no=no, which="lm", type="D-A",
scaled=TRUE)
as_lm <- embed_laplacian_matrix(g, no=no, which="lm", type="D-A",
scaled=FALSE)
expect_that(au_lm$D, equals(mag_sort(D)[1:no]))
expect_that(std(au_lm$X), equals(std(X[,mag_order(D)][,1:no])))
expect_that(as_lm$D, equals(mag_sort(D)[1:no]))
expect_that(std(as_lm$X), equals(std(U[,mag_order(D)][,1:no])))
## SA
au_sa <- embed_laplacian_matrix(g, no=no, which="sa", type="D-A",
scaled=TRUE)
as_sa <- embed_laplacian_matrix(g, no=no, which="sa", type="D-A",
scaled=FALSE)
expect_that(au_sa$D, equals(D[vcount(g)-1:no+1]))
expect_that(std(au_sa$X), equals(std(X[,vcount(g)-1:no+1])))
expect_that(as_sa$D, equals(D[vcount(g)-1:no+1]))
expect_that(std(as_sa$X), equals(std(U[,vcount(g)-1:no+1])))
})
test_that("Undirected, unweighted, DAD case works", {
library(igraph)
set.seed(42)
g <- random.graph.game(10, 20, type="gnm", directed=FALSE)
no <- 3
D12 <- diag(1/sqrt(degree(g)))
A <- D12 %*% g[] %*% D12
ss <- eigen(A)
D <- ss$values
U <- ss$vectors
X <- std(ss$vectors %*% sqrt(diag(abs(ss$values))))
Y <- std(ss$vectors %*% sqrt(diag(abs(ss$values))))
## LA
au_la <- embed_laplacian_matrix(g, no=no, which="la", type="DAD",
scaled=TRUE)
as_la <- embed_laplacian_matrix(g, no=no, which="la", type="DAD",
scaled=FALSE)
expect_that(au_la$D, equals(abs(D[1:no])))
expect_that(std(au_la$X), equals(std(X[,1:no])))
expect_that(as_la$D, equals(D[1:no]))
expect_that(std(as_la$X), equals(std(U[,1:no])))
## LM
au_lm <- embed_laplacian_matrix(g, no=no, which="lm", type="DAD",
scaled=TRUE)
as_lm <- embed_laplacian_matrix(g, no=no, which="lm", type="DAD",
scaled=FALSE)
expect_that(au_lm$D, equals(mag_sort(D)[1:no]))
expect_that(std(au_lm$X), equals(std(X[,mag_order(D)][,1:no])))
expect_that(as_lm$D, equals(mag_sort(D)[1:no]))
expect_that(std(as_lm$X), equals(std(U[,mag_order(D)][,1:no])))
## SA
au_sa <- embed_laplacian_matrix(g, no=no, which="sa", type="DAD",
scaled=TRUE)
as_sa <- embed_laplacian_matrix(g, no=no, which="sa", type="DAD",
scaled=FALSE)
expect_that(au_sa$D, equals(D[vcount(g)-1:no+1]))
expect_that(std(au_sa$X), equals(std(X[,vcount(g)-1:no+1])))
expect_that(as_sa$D, equals(D[vcount(g)-1:no+1]))
expect_that(std(as_sa$X), equals(std(U[,vcount(g)-1:no+1])))
})
test_that("Undirected, unweighted, I-DAD case works", {
set.seed(42)
g <- random.graph.game(10, 20, type="gnm", directed=FALSE)
no <- 3
D12 <- diag(1/sqrt(degree(g)))
A <- diag(vcount(g)) - D12 %*% g[] %*% D12
ss <- eigen(A)
D <- ss$values
U <- ss$vectors
X <- std(ss$vectors %*% sqrt(diag(abs(ss$values))))
Y <- std(ss$vectors %*% sqrt(diag(abs(ss$values))))
## LA
au_la <- embed_laplacian_matrix(g, no=no, which="la", type="I-DAD",
scaled=TRUE)
as_la <- embed_laplacian_matrix(g, no=no, which="la", type="I-DAD",
scaled=FALSE)
expect_that(au_la$D, equals(abs(D[1:no])))
expect_that(std(au_la$X), equals(std(X[,1:no])))
expect_that(as_la$D, equals(D[1:no]))
expect_that(std(as_la$X), equals(std(U[,1:no])))
## LM
au_lm <- embed_laplacian_matrix(g, no=no, which="lm", type="I-DAD",
scaled=TRUE)
as_lm <- embed_laplacian_matrix(g, no=no, which="lm", type="I-DAD",
scaled=FALSE)
expect_that(au_lm$D, equals(mag_sort(D)[1:no]))
expect_that(std(au_lm$X), equals(std(X[,mag_order(D)][,1:no])))
expect_that(as_lm$D, equals(mag_sort(D)[1:no]))
expect_that(std(as_lm$X), equals(std(U[,mag_order(D)][,1:no])))
## SA
au_sa <- embed_laplacian_matrix(g, no=no, which="sa", type="I-DAD",
scaled=TRUE)
as_sa <- embed_laplacian_matrix(g, no=no, which="sa", type="I-DAD",
scaled=FALSE)
expect_that(au_sa$D, equals(D[vcount(g)-1:no+1]))
expect_that(std(au_sa$X), equals(std(X[,vcount(g)-1:no+1])))
expect_that(as_sa$D, equals(D[vcount(g)-1:no+1]))
expect_that(std(as_sa$X), equals(std(U[,vcount(g)-1:no+1])))
})
test_that("Undirected, weighted, D-A case works", {
library(igraph)
library(Matrix)
set.seed(42*42)
g <- random.graph.game(10, 20, type="gnm", directed=FALSE)
E(g)$weight <- sample(1:5, ecount(g), replace=TRUE)
no <- 3
A <- as(Matrix(diag(graph.strength(g)), doDiag=FALSE), "generalMatrix") - g[]
ss <- eigen(A)
D <- ss$values
U <- ss$vectors
X <- std(ss$vectors %*% sqrt(diag(abs(D))))
Y <- std(ss$vectors %*% sqrt(diag(abs(D))))
## LA
au_la <- embed_laplacian_matrix(g, no=no, which="la", type="D-A",
scaled=TRUE)
as_la <- embed_laplacian_matrix(g, no=no, which="la", type="D-A",
scaled=FALSE)
expect_that(au_la$D, equals(abs(D[1:no])))
expect_that(std(au_la$X), equals(std(X[,1:no])))
expect_that(as_la$D, equals(D[1:no]))
expect_that(std(as_la$X), equals(std(U[,1:no])))
## LM
au_lm <- embed_laplacian_matrix(g, no=no, which="lm", type="D-A",
scaled=TRUE)
as_lm <- embed_laplacian_matrix(g, no=no, which="lm", type="D-A",
scaled=FALSE)
expect_that(au_lm$D, equals(mag_sort(D)[1:no]))
expect_that(std(au_lm$X), equals(std(X[,mag_order(D)][,1:no])))
expect_that(as_lm$D, equals(mag_sort(D)[1:no]))
expect_that(std(as_lm$X), equals(std(U[,mag_order(D)][,1:no])))
## SA
au_sa <- embed_laplacian_matrix(g, no=no, which="sa", type="D-A",
scaled=TRUE)
as_sa <- embed_laplacian_matrix(g, no=no, which="sa", type="D-A",
scaled=FALSE)
expect_that(au_sa$D, equals(D[vcount(g)-1:no+1]))
expect_that(std(au_sa$X), equals(X[,vcount(g)-1:no+1],
tolerance=.Machine$double.eps ^ 0.25))
expect_that(as_sa$D, equals(D[vcount(g)-1:no+1]))
expect_that(std(as_sa$X), equals(std(U[,vcount(g)-1:no+1])))
})
test_that("Undirected, unweighted, DAD case works", {
library(igraph)
set.seed(42)
g <- random.graph.game(10, 20, type="gnm", directed=FALSE)
no <- 3
D12 <- diag(1/sqrt(degree(g)))
A <- D12 %*% g[] %*% D12
ss <- eigen(A)
D <- ss$values
U <- ss$vectors
X <- std(ss$vectors %*% sqrt(diag(abs(ss$values))))
Y <- std(ss$vectors %*% sqrt(diag(abs(ss$values))))
## LA
au_la <- embed_laplacian_matrix(g, no=no, which="la", type="DAD",
scaled=TRUE)
as_la <- embed_laplacian_matrix(g, no=no, which="la", type="DAD",
scaled=FALSE)
expect_that(au_la$D, equals(abs(D[1:no])))
expect_that(std(au_la$X), equals(std(X[,1:no])))
expect_that(as_la$D, equals(D[1:no]))
expect_that(std(as_la$X), equals(std(U[,1:no])))
## LM
au_lm <- embed_laplacian_matrix(g, no=no, which="lm", type="DAD",
scaled=TRUE)
as_lm <- embed_laplacian_matrix(g, no=no, which="lm", type="DAD",
scaled=FALSE)
expect_that(au_lm$D, equals(mag_sort(D)[1:no]))
expect_that(std(au_lm$X), equals(std(X[,mag_order(D)][,1:no])))
expect_that(as_lm$D, equals(mag_sort(D)[1:no]))
expect_that(std(as_lm$X), equals(std(U[,mag_order(D)][,1:no])))
## SA
au_sa <- embed_laplacian_matrix(g, no=no, which="sa", type="DAD",
scaled=TRUE)
as_sa <- embed_laplacian_matrix(g, no=no, which="sa", type="DAD",
scaled=FALSE)
expect_that(au_sa$D, equals(D[vcount(g)-1:no+1]))
expect_that(std(au_sa$X), equals(std(X[,vcount(g)-1:no+1])))
expect_that(as_sa$D, equals(D[vcount(g)-1:no+1]))
expect_that(std(as_sa$X), equals(std(U[,vcount(g)-1:no+1])))
})
test_that("Undirected, unweighted, I-DAD case works", {
library(igraph)
set.seed(42)
g <- random.graph.game(10, 20, type="gnm", directed=FALSE)
no <- 3
D12 <- diag(1/sqrt(degree(g)))
A <- diag(vcount(g)) - D12 %*% g[] %*% D12
ss <- eigen(A)
D <- ss$values
U <- ss$vectors
X <- std(ss$vectors %*% sqrt(diag(abs(ss$values))))
Y <- std(ss$vectors %*% sqrt(diag(abs(ss$values))))
## LA
au_la <- embed_laplacian_matrix(g, no=no, which="la", type="I-DAD",
scaled=TRUE)
as_la <- embed_laplacian_matrix(g, no=no, which="la", type="I-DAD",
scaled=FALSE)
expect_that(au_la$D, equals(abs(D[1:no])))
expect_that(std(au_la$X), equals(std(X[,1:no])))
expect_that(as_la$D, equals(D[1:no]))
expect_that(std(as_la$X), equals(std(U[,1:no])))
## LM
au_lm <- embed_laplacian_matrix(g, no=no, which="lm", type="I-DAD",
scaled=TRUE)
as_lm <- embed_laplacian_matrix(g, no=no, which="lm", type="I-DAD",
scaled=FALSE)
expect_that(au_lm$D, equals(mag_sort(D)[1:no]))
expect_that(std(au_lm$X), equals(std(X[,mag_order(D)][,1:no])))
expect_that(as_lm$D, equals(mag_sort(D)[1:no]))
expect_that(std(as_lm$X), equals(std(U[,mag_order(D)][,1:no])))
## SA
au_sa <- embed_laplacian_matrix(g, no=no, which="sa", type="I-DAD",
scaled=TRUE)
as_sa <- embed_laplacian_matrix(g, no=no, which="sa", type="I-DAD",
scaled=FALSE)
expect_that(au_sa$D, equals(D[vcount(g)-1:no+1]))
expect_that(std(au_sa$X), equals(std(X[,vcount(g)-1:no+1])))
expect_that(as_sa$D, equals(D[vcount(g)-1:no+1]))
expect_that(std(as_sa$X), equals(std(U[,vcount(g)-1:no+1])))
})
test_that("Directed, unweighted, OAP case works", {
library(igraph)
set.seed(42*42)
g <- random.graph.game(10, 30, type="gnm", directed=TRUE)
no <- 3
O12 <- diag(1/sqrt(degree(g, mode="out")))
P12 <- diag(1/sqrt(degree(g, mode="in")))
A <- O12 %*% g[] %*% P12
ss <- svd(A)
D <- ss$d
U <- ss$u
V <- ss$v
X <- std(ss$u %*% sqrt(diag(ss$d)))
Y <- std(ss$v %*% sqrt(diag(ss$d)))
au_la <- embed_laplacian_matrix(g, no=no, which="la", type="OAP",
scaled=TRUE)
as_la <- embed_laplacian_matrix(g, no=no, which="la", type="OAP",
scaled=FALSE)
expect_that(au_la$D, equals(D[1:no]))
expect_that(std(au_la$X), equals(std(X[,1:no])))
expect_that(std(au_la$Y), equals(std(Y[,1:no])))
expect_that(as_la$D, equals(D[1:no]))
expect_that(std(as_la$X), equals(std(U[,1:no])))
expect_that(std(as_la$Y), equals(std(V[,1:no])))
au_lm <- embed_laplacian_matrix(g, no=no, which="lm", type="OAP",
scaled=TRUE)
as_lm <- embed_laplacian_matrix(g, no=no, which="lm", type="OAP",
scaled=FALSE)
expect_that(au_lm$D, equals(D[1:no]))
expect_that(std(au_lm$X), equals(std(X[,1:no])))
expect_that(std(au_lm$Y), equals(std(Y[,1:no])))
expect_that(as_lm$D, equals(D[1:no]))
expect_that(std(as_lm$X), equals(std(U[,1:no])))
expect_that(std(as_lm$Y), equals(std(V[,1:no])))
au_sa <- embed_laplacian_matrix(g, no=no, which="sa", type="OAP",
scaled=TRUE)
as_sa <- embed_laplacian_matrix(g, no=no, which="sa", type="OAP",
scaled=FALSE)
expect_that(au_sa$D, equals(D[vcount(g)-1:no+1]))
expect_that(std(au_sa$X), equals(std(X[,vcount(g)-1:no+1])))
expect_that(std(au_sa$Y), equals(std(Y[,vcount(g)-1:no+1]),
tolerance=sqrt(sqrt(.Machine$double.eps))))
expect_that(as_sa$D, equals(D[vcount(g)-1:no+1]))
expect_that(std(as_sa$X), equals(std(U[,vcount(g)-1:no+1])))
expect_that(std(as_sa$Y), equals(std(V[,vcount(g)-1:no+1])))
})
test_that("Directed, weighted case works", {
library(igraph)
set.seed(42*42)
g <- random.graph.game(10, 30, type="gnm", directed=TRUE)
E(g)$weight <- sample(1:5, ecount(g), replace=TRUE)
no <- 3
O12 <- diag(1/sqrt(graph.strength(g, mode="out")))
P12 <- diag(1/sqrt(graph.strength(g, mode="in")))
A <- O12 %*% g[] %*% P12
ss <- svd(A)
D <- ss$d
U <- ss$u
V <- ss$v
X <- std(ss$u %*% sqrt(diag(ss$d)))
Y <- std(ss$v %*% sqrt(diag(ss$d)))
au_la <- embed_laplacian_matrix(g, no=no, which="la", type="OAP",
scaled=TRUE)
as_la <- embed_laplacian_matrix(g, no=no, which="la", type="OAP",
scaled=FALSE)
expect_that(au_la$D, equals(D[1:no]))
expect_that(std(au_la$X), equals(std(X[,1:no])))
expect_that(std(au_la$Y), equals(std(Y[,1:no])))
expect_that(as_la$D, equals(D[1:no]))
expect_that(std(as_la$X), equals(std(U[,1:no])))
expect_that(std(as_la$Y), equals(std(V[,1:no])))
au_lm <- embed_laplacian_matrix(g, no=no, which="lm", type="OAP",
scaled=TRUE)
as_lm <- embed_laplacian_matrix(g, no=no, which="lm", type="OAP",
scaled=FALSE)
expect_that(au_lm$D, equals(D[1:no]))
expect_that(std(au_lm$X), equals(std(X[,1:no])))
expect_that(std(au_lm$Y), equals(std(Y[,1:no])))
expect_that(as_lm$D, equals(D[1:no]))
expect_that(std(as_lm$X), equals(std(U[,1:no])))
expect_that(std(as_lm$Y), equals(std(V[,1:no])))
au_sa <- embed_laplacian_matrix(g, no=no, which="sa", type="OAP",
scaled=TRUE)
as_sa <- embed_laplacian_matrix(g, no=no, which="sa", type="OAP",
scaled=FALSE)
expect_that(au_sa$D, equals(D[vcount(g)-1:no+1]))
expect_that(std(au_sa$X), equals(std(X[,vcount(g)-1:no+1])))
expect_that(std(au_sa$Y), equals(std(Y[,vcount(g)-1:no+1]),
tolerance=sqrt(sqrt(.Machine$double.eps))))
expect_that(as_sa$D, equals(D[vcount(g)-1:no+1]))
expect_that(std(as_sa$X), equals(std(U[,vcount(g)-1:no+1])))
expect_that(std(as_sa$Y), equals(std(V[,vcount(g)-1:no+1])))
})
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