In neurodata/fselect: Linear Optimal Low-Rank Projection

## MDP-example 1

X0 <- matrix(rnorm(400, mean = 1),nrow = 10)
X1 <- matrix(rnorm(400, mean = -1),nrow = 10)  # X of another class

bar.X0 <- colMeans(X0)
bar.X1 <- colMeans(X1)
X0c <- X0 - outer(rep(1,10),colMeans(X0))
X1c <- X1 - outer(rep(1,10),colMeans(X1))
C <- cbind(t(X0c),t(X1c))
tX <- cbind(t(X0),t(X1))
X <- rbind(X0,X1)
Xc <- rbind(X0c,X1c)

Q <- diag(40) - C %*% ginv(C)
v.M <- Q %*% (bar.X0 - bar.X1)

mdp <- t(v.M) %*% tX

## CCA-equivalence
Y <- cbind(c(rep(1,10),rep(0,10)),c(rep(0,10),rep(1,10)))
Yc <- (Y - outer(rep(1,20),colMeans(Y)))
SY <- t(Yc) %*% Yc
SXY <- t(Xc) %*% Yc
SYX <- t(SXY)
SX <- t(Xc) %*% Xc
Xbar <- colMeans(X)
SR <- (bar.X0 - Xbar) %*% t(bar.X0 - Xbar)*0.5 + (bar.X1 - Xbar) %*% t(bar.X1 - Xbar)*0.5

flda <- svd(ginv(SX-SR) %*% SR)

eigenY <- svd(ginv(SY) %*% SYX %*% ginv(SX) %*% SXY)
cca <- svd(ginv(SX) %*% SXY %*% ginv(SY) %*% SYX)

print(mdp)
print(flda$u[,1])
print(cca$u[,1])

neurodata/fselect documentation built on March 6, 2021, 12:54 p.m.