112 lines
3.4 KiB
R
112 lines
3.4 KiB
R
|
|
||
|
|
################################################################################
|
||
|
|
### LDA (sparse Linear Discrimina Analysis) ###
|
||
|
|
################################################################################
|
||
|
|
devtools::load_all('tensorPredictors/')
|
||
|
|
|
||
|
|
C <- function(rho, p) {
|
||
|
|
res <- matrix(rho, p, p)
|
||
|
|
diag(res) <- 1
|
||
|
|
res
|
||
|
|
}
|
||
|
|
R <- function(rho, p) {
|
||
|
|
rho^abs(outer(1:p, 1:p, `-`))
|
||
|
|
}
|
||
|
|
|
||
|
|
dataset <- function(nr) {
|
||
|
|
K <- 3 # Nr. Groups
|
||
|
|
n.i <- 30 # Sample group size for each of the K groups
|
||
|
|
n <- K * n.i # Sample size
|
||
|
|
p <- 200 # Nr. of predictors
|
||
|
|
|
||
|
|
# Generate test data
|
||
|
|
V <- cbind(matrix(c(
|
||
|
|
2, 1, 2, 1, 2,
|
||
|
|
1,-1, 1,-1, 1,
|
||
|
|
0, 1,-1, 1, 0
|
||
|
|
), 3, 5, byrow = TRUE),
|
||
|
|
matrix(0, 3, p - 5)
|
||
|
|
)
|
||
|
|
W <- cbind(matrix(c(
|
||
|
|
-1, 1, 1, 1, 1,
|
||
|
|
1,-1, 1,-1, 1,
|
||
|
|
1, 1,-1, 1, 0
|
||
|
|
), 3, 5, byrow = TRUE),
|
||
|
|
matrix(0, 3, p - 5)
|
||
|
|
)
|
||
|
|
|
||
|
|
if (nr == 1) { # Model 1
|
||
|
|
y <- factor(rep(1:K, each = n.i))
|
||
|
|
X <- rmvnorm(n, mu = rep(0, p)) + V[y, ]
|
||
|
|
B <- cbind(V[1, ] - V[2, ], V[2, ] - V[3, ])
|
||
|
|
} else if (nr == 2) { # Model 2
|
||
|
|
y <- factor(rep(1:K, each = n.i))
|
||
|
|
X <- rmvnorm(n, sigma = C(0.5, p)) + (V %*% C(0.5, p))[y, ]
|
||
|
|
B <- cbind(V[1, ] - V[2, ], V[2, ] - V[3, ])
|
||
|
|
} else if (nr == 3) { # Model 3
|
||
|
|
y <- factor(rep(1:K, each = n.i))
|
||
|
|
X <- rmvnorm(n, sigma = R(0.5, p)) + (V %*% R(0.5, p))[y, ]
|
||
|
|
B <- cbind(V[1, ] - V[2, ], V[2, ] - V[3, ])
|
||
|
|
} else if (nr == 4) { # Model 4
|
||
|
|
y <- factor(rep(1:K, each = n.i))
|
||
|
|
X <- rmvnorm(n, sigma = C(0.5, p)) + (W %*% C(0.5, p))[y, ]
|
||
|
|
B <- cbind(W[1, ] - W[2, ], W[2, ] - W[3, ])
|
||
|
|
} else if (nr == 5) { # Model 5
|
||
|
|
K <- 4
|
||
|
|
n <- K * n.i
|
||
|
|
|
||
|
|
W.tilde <- 2 * rbind(W, colMeans(W))
|
||
|
|
mu.tilde <- W.tilde %*% C(0.5, p)
|
||
|
|
|
||
|
|
y <- factor(rep(1:K, each = n.i))
|
||
|
|
X <- rmvnorm(n, sigma = C(0.5, p)) + mu.tilde[y, ]
|
||
|
|
|
||
|
|
B <- cbind(W[1, ] - W[2, ], W[2, ] - W[3, ])
|
||
|
|
} else {
|
||
|
|
stop("Unknown model nr.")
|
||
|
|
}
|
||
|
|
|
||
|
|
list(X = X, y = y, B = qr.Q(qr(B)))
|
||
|
|
}
|
||
|
|
|
||
|
|
# # Model 1
|
||
|
|
# fit <- with(dataset(1), {
|
||
|
|
# with(GEP(X, y, 'lda'), POI(lhs, rhs, ncol(B), method = 'POI-C'))
|
||
|
|
# })
|
||
|
|
# fit <- with(dataset(1), {
|
||
|
|
# with(GEP(X, y, 'lda'), POI(lhs, rhs, ncol(B), method = 'FastPOI-C'))
|
||
|
|
# })
|
||
|
|
# fit <- with(dataset(1), {
|
||
|
|
# with(GEP(X, y, 'lda'), POI(lhs, rhs, ncol(B), method = 'POI-C', use.C = TRUE))
|
||
|
|
# })
|
||
|
|
# fit <- with(dataset(1), {
|
||
|
|
# with(GEP(X, y, 'lda'), POI(lhs, rhs, ncol(B), method = 'FastPOI-C', use.C = TRUE))
|
||
|
|
# })
|
||
|
|
|
||
|
|
# head(fit$vectors, 10)
|
||
|
|
|
||
|
|
count <- 0
|
||
|
|
nr.reps <- 100
|
||
|
|
sim <- replicate(nr.reps, {
|
||
|
|
res <- double(0)
|
||
|
|
for (model.nr in 1:5) {
|
||
|
|
for (method in c('POI-C', 'FastPOI-C')) {
|
||
|
|
for (use.C in c(FALSE, TRUE)) {
|
||
|
|
dist <- with(dataset(model.nr), {
|
||
|
|
fit <- with(GEP(X, y, 'lda'), {
|
||
|
|
POI(lhs, rhs, ncol(B), method = 'POI-C', use.C = use.C)
|
||
|
|
})
|
||
|
|
# dist.subspace(B, fit$vectors, is.ortho = FALSE, normalize = TRUE)
|
||
|
|
dist.projection(B, fit$vectors)
|
||
|
|
})
|
||
|
|
names(dist) <- paste('M', model.nr, '-', method, '-', use.C)
|
||
|
|
res <- c(res, dist)
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
cat("Counter", (count <<- count + 1), "/", nr.reps, "\n")
|
||
|
|
res
|
||
|
|
})
|
||
|
|
|
||
|
|
(stats <- as.matrix(rowMeans(sim)))
|