# Cross Validation to Determine Error of Embedding Alg composed with Classifier

require(lolR)
require(ggplot2)
n = 400
d = 30
r = 3

Here, we look at how to see the generalizability of a given model in the form of the cross-validated error. We simulate data with n=200 and d=30:

testdat <- lol.sims.rtrunk(n, d)
X <- testdat$X Y <- testdat$Y

data <- data.frame(x1=X[,1], x2=X[,2], y=Y)
data$y <- factor(data$y)
ggplot(data, aes(x=x1, y=x2, color=y)) +
geom_point() +
xlab("x1") +
ylab("x2") +
ggtitle("Simulated Data")

We arbitrarily select LOL as our algorithm, and look at the leave-one-out (loo) cross-validated error with the LDA classifier. We project the resulting model to 3 dimensions and visualize the first 2:

result <- lol.xval.eval(X, Y, r, alg = lol.project.lol, alg.return="A",
classifier=MASS::lda, classifier.return="class", k='loo')

data <- data.frame(x1=result$model$Xr[,1], x2=result$model$Xr[,2], y=Y)
data$y <- factor(data$y)
ggplot(data, aes(x=x1, y=x2, color=y)) +
geom_point() +
xlab("x1") +
ylab("x2") +
ggtitle(sprintf("Projected Data using LOL, L=%.2f", result$lhat)) # Cross Validation to Determine Optimal Embedding Dimensions of Embedding Alg composed with Classifier result <- lol.xval.optimal_dimselect(X, Y, rs=c(5, 10, 15), alg = lol.project.lol, alg.return="A", classifier=MASS::lda, classifier.return="class", k='loo') data <- data.frame(x1=result$model$Xr[,1], x2=result$model$Xr[,2], y=Y) data$y <- factor(data$y) ggplot(data, aes(x=x1, y=x2, color=y)) + geom_point() + xlab("x1") + ylab("x2") + ggtitle(sprintf("Projected Data using LOL, L=%.2f", result$optimal.lhat))

ggplot(result$foldmeans.data, aes(x=r, y=lhat)) + geom_line() + xlab("Embedding Dimensions, r") + ylab("Misclassification Rate, L") + ggtitle("Impact on Misclassification Rate of Embedding Dimension") print(sprintf("optimal dimension: %d", result$optimal.r))
## [1] "optimal dimension: 5"
print(sprintf("Misclassification rate at rhat = %d: %.2f", result$optimal.r, result$optimal.lhat))
## [1] "Misclassification rate at rhat = 5: 0.07"
## [2] "Misclassification rate at rhat = 5: 0.07"